Journal of Experimental Psychology: General
1999, Vol. 128, No. 2, 131-164
Copyright 1999 by the American Psychological Association, Inc.
0096-3445/99/S3.00
Predictors of Crossword Puzzle Proficiency and Moderators
of Age-Cognition Relations
David Z. Hambrick, Timothy A. Salthouse, and Elizabeth J. Meinz
Georgia Institute of Technology
Four studies, each with approximately 200 adults between the ages of 18 and 80, were
conducted to address two major goals. The first goal was to examine the relative contributions
of different factors to the successful solution of crossword puzzles. Correlations and structural
equation analyses revealed that general knowledge is the strongest predictor of crossword
puzzle proficiency. Surprisingly, abstract reasoning ability, as measured by several different
tests, had no direct relation to puzzle proficiency. The second goal of the project was to
examine moderators of the relations between age and measures of both fluid and crystallized
cognition. The results provide no evidence to suggest that amount of crossword puzzle
experience reduces age-related decreases in fluid cognition or enhances age-related increases
in crystallized cognition.
The studies described in this article were designed to
address two major goals. The first goal was to identify
individual-difference characteristics that contribute to the
successful solution of crossword puzzles. Intuition suggests
that crossword puzzle solving is similar to many real-world
endeavors in that knowledge may be a critical component of
successful performance. In addition, anecdotal reports by
crossword puzzlers suggest that reasoning abilities contribute to success in crossword puzzle solving because crossword puzzles sometimes include ambiguous and misleading
clues. Thus, success in crossword puzzle solving seems to be
influenced both by knowledge—a "crystallized" aspect of
cognition—and by reasoning abilities—a "fluid" aspect of
cognition (see Horn & Hofer, 1992, for a review of the
distinction between fluid cognition and crystallized cognition). Because many everyday activities are likely to require
both fluid and crystallized cognitive abilities, identifying
individual-difference characteristics related to success in
crossword puzzle solving may contribute to the theoretical
understanding of proficiency in complex cognitive domains.
In particular, to the extent that solving crossword puzzles
resembles certain kinds of work activities, research on the
factors associated with proficiency in puzzle solving may
help explain why there are surprisingly few age-related
differences in measures of work performance despite agerelated declines in relevant cognitive abilities (Salthouse &
Maurer, 1996).
The successful solution of crossword puzzles seems to
require a considerable amount of knowledge, both of words
and of general information. For example, whether a puzzle
solver can produce the answer to the clue "Ansazi dwellings" (caves) will obviously depend to a large extent on
whether he or she possesses knowledge relevant to that clue.
In addition, however, reasoning ability may be required to
understand the meanings of certain clues in crossword
puzzles, particularly those that are misleading and ambiguous. An example of such a clue is "iron clothes," because
making the assumption that iron is a verb leads the puzzle
solver away from the correct answer of "armor." In
addition, reasoning ability may be required to work within
the simultaneous multiple constraints imposed by the puzzle's interlocking grid (i.e., each answer in a crossword
puzzle must contain both a certain number of letters and the
correct letters of intersecting answers). Finally, strategies
related to memory access may also be involved in the
solution of crossword puzzles. Consistent with this view,
Nickerson (1977) pointed out that crossword puzzles can be
viewed as cued retrieval tasks.
Nickerson's (1977) discussion, and our introspective
analysis, suggests that at least three types of solution
processes occur while one is attempting to solve crossword
puzzles. First, some solutions seem to occur immediately,
from merely reading the clue, and often lead to identification
of the target without even considering constraints such as the
number of letters in the target word. A second type of
solution involves some deliberation and consideration of
constraints imposed by the clue, by the length of the word,
and by any letters that have already been identified. The third
type of solution process consists of extensive deliberation,
either in attempting to interpret the meaning of the clue,
trying to identify the relevance of the theme to the item, or in
searching one's storehouse of knowledge relevant to the
target. This last process, which does not always result in
success, often involves re-examination of earlier responses
and possibly a variety of conscious search and reasoning
processes.
David Z. Hambrick, Timothy A. Salthouse, and Elizabeth J.
Meinz, School of Psychology, Georgia Institute of Technology.
This research was supported by National Institute on Aging
Grant R37 AG06826. We gratefully acknowledge the assistance of
Kellie Hocking, Stefanie Sherwood, Michelle Wolbrette, and Carl
Valentino for assistance in scoring the data. We also thank Jack
Marr, Neil Charness, and John Nesselroade for valuable comments
on an earlier version of this article.
Correspondence concerning this article should be addressed to
David Z. Hambrick, School of Psychology, Georgia Institute of
Technology, Atlanta, Georgia 30332.
131
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HAMBRICK, SALTHOUSE, AND MEINZ
This speculative account of the steps involved in solving
crossword puzzles is also consistent with the reports of a
number of participants in the current project.1 That is, when
asked to describe the steps they follow when working on
crossword puzzles most said that they answer the easy items
first and then return to work on items with letters from
intersecting words. Some respondents reported that if the
puzzle has a theme, they consider whether it is helpful in
solving some of the clues, and 90% said that they use
reasoning, particularly to identify targets with letters from
intersecting words. Finally, 60% of the respondents said that
they consult a dictionary or other reference source (e.g.,
encyclopedia, another person) when they are unable to solve
a particular item in a puzzle.
The preceding analysis suggests that failures to solve
items in a crossword puzzle could originate because of lack
of knowledge necessary for target identification; inefficient
strategies for retrieving information from memory; ineffective manipulation or transformation of information; or weak
reasoning abilities needed to interpret clues, consider the
multiple simultaneous constraints imposed by the puzzle's
interlocking grid system, or both. In fact, Underwood,
Diehim, and Batt (1994) recently reported that scores on
vocabulary (assessing knowledge), anagram (assessing word
manipulation), and word generation (assessing memory
retrieval) tests were all correlated with crossword puzzle
success. A major goal of the current studies was to examine
the relative contributions of each of the factors listed above
to crossword puzzle proficiency.
The second goal motivating the studies in this project was
to examine moderators of the relations between age and
measures of both fluid and crystallized aspects of cognitive
functioning. Fluid cognition refers to aspects of cognition
that are at least somewhat independent of knowledge, and it
is typically measured with tests of abstract reasoning ability,
spatial visualization ability, and certain types of memory. In
contrast, crystallized cognition, which refers to one's accumulated knowledge, is often measured with tests of cultural
information and vocabulary. A consistent finding in research
on aging and cognition is that fluid and crystallized aspects
of cognition follow different developmental trajectories in
cross-sectional samples: Age-related decreases in fluid cognition begin in young adulthood, whereas crystallized cognition often remains stable or even increases into late adulthood (for reviews, see Horn & Hofer, 1992, and Salthouse,
1991).
According to one appealing view of cognitive aging,
age-related decreases in fluid cognition are attributable to
lack of recent use of cognitive abilities, or "disuse." This
view—captured by the popular saying "use it or lose
it"—was articulated in a recent Newsweek article in the
following manner: "An idle brain will deteriorate just as
surely as an unused leg.... And just as exercise can prevent
muscle atrophy, mental challenges seem to preserve both the
mind and the immune system" (Cowley, 1997, p. 67). The
disuse perspective has also been invoked in the scientific
literature as an explanation of age-related decline in fluid
cognition. For example, Sorenson (1933) claimed that "A
decrease in test ability among adults is probably caused by
the fact that adults, as they grow older, exercise their minds
less and less with the materials found in psychological tests"
(p. 736). More recently, in reporting a study of college
professors, Shimamura, Berry, Mangels, Rusting, and Jurica
(1995) suggested that "mental activity may protect cognitive functions from typical age-related changes" (p. 276).
The disuse perspective is also related to efforts designed to
remediate cognitive deficits through training. For example,
Schaie and Willis (1996) recently speculated, on the basis of
their research on cognitive training, that "much of the
cognitive decline observed in the elderly may be due to
disuse and is at least in part reversible" (p. 315).
It should be noted, however, that empirical evidence
relevant to the disuse view of aging and cognition is mixed
(for reviews, see Bosman & Charness, 1996, and Salthouse,
1991). For example, Shimamura et al. (1995) recently
reported that a sample of university professors had smaller
age-related decreases in performance on working memory
and prose recall tasks—indexes of fluid cognition—than
adults from the general population. To the extent that
university professors are more intellectually active than
adults from the general population, this finding suggests that
age-related decreases in cognitive functioning may be
partially attributable to disuse. Unfortunately, Shimamura et
al.'s results are inconsistent with those from several earlier
studies. As examples, Sward (1945) found pronounced
age-related decreases in several measures of fluid cognition
in comparisons of young and old college professors, and
Christensen and Henderson (1991) reported that academics
exhibited the same pattern of age-related cognitive differences as blue collar workers. In addition, Powell (1994)
found very similar patterns of age-related cognitive differences in a large sample of physicians and in a more typical
sample of nonphysician adults.
In the domain of music, Krampe and Ericsson (1996)
recently reported in one of two studies that expert pianists
showed smaller age-related differences in performance on a
music-related task that required bimanual reproduction of
short sequences of musical notes than did amateur pianists.
The pianists also played a relatively simple piece of music
and were rated by judges on several dimensions of musical
interpretation skill (e.g., selection of appropriate tempo,
evenness of touch, synchronization of hands, etc.). Unfortunately, Krampe and Ericsson were unable to reach a
conclusion about whether age-related differences in musical
interpretation were smaller among the experts than among
the amateurs because of lack of agreement among the
judge's ratings. They did report, however, that the Age X
Experience interaction was not statistically significant in
either of two studies on another measure of musical interpre1
Twenty participants from Study 4 were contacted by phone
approximately 6 months after their participation and asked questions about the steps involved in solving crossword puzzles,
whether reasoning was involved, and what they did when they were
unable to find the solution to the clue. The 20 respondents ranged in
age from 26 to 77 years (mean age = 48.6), and their estimates of
the number of puzzles attempted per week ranged from 1 to 15
(M = 6.2).
CROSSWORD PUZZLES
tation based on keystroke force variation. Furthermore, in a
recent test of recall of visually presented melodies, Meinz
and Salthouse (1998a) found similar patterns of age-related
differences for experienced musicians and for adults with
little or no musical experience. Finally, Salthouse, Babcock,
Skovronek, Mitchell, and Palmon (1990) found that agerelated decreases on measures of spatial visualization tasks
were no less severe for a sample of architects, who reported
using spatial visualization abilities on an everyday basis,
than for a sample of nonarchitects, who presumably had
much less experience using these abilities.
At least two studies have examined the effects of intellectually demanding activities such as playing bridge or solving
crossword puzzles on the relations between age and measures of cognitive performance. Clarkson-Smith and Hartley
(1990) reported that older bridge players had higher scores
on tests of reasoning and working memory than agematched adults who did not play bridge. However, these
researchers did not indicate whether the Age X Activity
interaction was statistically significant, and thus it is not
clear whether the activity of playing bridge moderated the
age-cognition relations. In a separate analysis, ClarksonSmith and Hartley did not find any significant differences
between crossword puzzlers and nonpuzzlers in the available measures of cognitive performance. Finally, a significant interaction of age and crossword puzzle experience on
anagram solution, in the direction of no age-related differences among those with the most crossword experience, was
found in one of two studies reported by Witte and Freund
(1995).
This brief review of the literature reveals that it is not yet
clear on the basis of the available evidence whether sustained intellectual activity throughout adulthood reduces the
magnitude of age-related decreases in measures of fluid
cognition. Moreover, similar analyses have apparently not
been conducted to determine whether amount of mental
activity moderates the relations between age and measures
of crystallized cognition.
In the current project we investigated the question of
whether continued intellectual activity, in the form of
attempting to solve crossword puzzles, reduces the magnitude of the negative relations between age and measures of
fluid cognition, or enhances the magnitude of the positive
relations between age and measures of crystallized cognition. If attempting to solve crossword puzzles is a form of
mental exercise, and if exercise prevents atrophy in cognitive abilities as it does in physical abilities, then one might
predict smaller age-related decreases in fluid cognition, and
greater age-related increases in crystallized cognition, for
people with extensive crossword experience.
There are at least two quite different perspectives on the
effects of experience on cognitive abilities. Research within
the expertise tradition has emphasized the specificity of
experiential effects because of findings indicating that
expertise is highly specific and that the advantages associated with expertise are limited to domains in which one has
direct experience. However, as alluded to earlier, the disuse
idea within the area of cognitive aging, and virtually all
research in the area of cognitive training, implies that mental
133
activity can have broad or general effects. In terms of the
analogy with physical exercise, experience with mentally
demanding activities might therefore have both specific
effects, perhaps corresponding to the development of particular muscle groups, and general or systemic effects, possibly
corresponding to improved cardiovascular or pulmonary
functioning. The exact effects of attempting to solve crossword puzzles on cognitive functioning are difficult to specify
a priori, but several possibilities can be imagined for how
this type of activity might influence both fluid and crystallized cognition. For example, working crossword puzzles
could enhance reasoning abilities because of frequent practice attempting to interpret ambiguous or misleading clues
and through searching for solutions that simultaneously
satisfy multiple constraints (such as the meaning of the clue,
the number of letters in the target word, and the identity of
intersecting letters). In addition, crossword puzzle experience may have indirect influences on reasoning abilities
because solving puzzles in everyday environments (e.g., on
a train, in a noisy office, or while listening to a radio or
television) may enhance one's ability to concentrate and to
inhibit distracting information. Crossword puzzle activity
could also have effects on knowledge and other aspects of
crystallized cognition by frequent practice at retrieving
different types of information from memory and by the
stimulation of new knowledge acquisition when the individual is confronted by items for which he or she does not
already know the answer. Another way that crossword
puzzle solving may facilitate knowledge acquisition is
through familiarity with external reference sources, including encyclopedias, dictionaries, or the Internet; that is, a
person who uses an external reference source when confronted with an unfamiliar crossword puzzle item may be
more likely to use that reference source to seek answers to
other types of questions. Finally, knowledge acquired through
crossword puzzle solving may make it easier to acquire new
knowledge. This idea is consistent with the speculation of
Charness and Bieman-Copland (1992) that there may be "a
'snowball' effect in knowledge acquisition, where the more
you know, the easier it is to add new knowledge" (p. 322). In
short, experience with activities such as crossword puzzle
solving may provide one explanation for why measures of
crystallized cognition remain stable or increase with age.
Crossword puzzle experience was assessed in these
studies with five questions designed to reflect different
aspects of experience. Four questions asked about current
experience in terms of number of puzzles or hours per week
spent on puzzles over the last 6 months. One question asked
about the number of crossword puzzles from sources other
than The New York Times that were attempted per week, and
a second question asked about the number of New York
Times puzzles attempted per week. Because puzzles in The
New York Times are often considered particularly challenging, the two questions may tap different types of experience.
The third question asked about the number of hours devoted
to attempting to solve crossword puzzles in a typical week,
and the fourth question asked about the number of hours per
week spent on other word puzzles or games, such as
acrostics, word jumbles, or Scrabble. Our assumption was
134
HAMBRICK, SALTHOUSE, AND MEINZ
that information about time investment would be slightly
different than information about the number of puzzles
attempted but that both are reflections of current experience.
The final question was designed to assess cumulative
experience and asked about the number of years for which
the individual had attempted to solve at least one crossword
puzzle per week.
Four summary measures of experience also were analyzed
in each of the studies. One measure consisted of the total
number of crossword puzzles of any type attempted per
week, and another consisted of the total number of hours per
week spent on word puzzles or games. A third measure was a
composite index of current experience formed by averaging
the z scores for the total number of puzzles per week
measure and the total hours per week measure. Finally, the
fourth measure was an attempt to represent all aspects of
experience and consisted of the first principal component
from a principal-components analysis of the five original
experience measures.
A second question concerning moderators of age relations
on fluid and crystallized cognition examined in this project
was whether the level of self-reported interest in a particular
topic area moderates the relations between age and measures
of knowledge in that area. Given the commonsense view that
people's interests narrow as they become specialized within
an occupation, one might expect greater age-related increases in knowledge for topics within the individual's
self-designated areas of interest. The prediction that people
become more specialized in their knowledge as they grow
older is also consistent with Baltes's selective-optimizationwith-compensation framework (e.g., see Marsiske, Lang,
Baltes, & Baltes, 1995, for a description of these ideas). A
major tenet of this framework is that adult development is
characterized by gains in some aspects of functioning but
losses in other aspects of functioning. For example, normative age-related decreases in some aspects of cognition, such
as abstract reasoning ability, might be offset by increases in
knowledge within particular topic areas. We investigated the
possibility that self-rated interest and/or knowledge ratings
moderate age-cognition relations by evaluating the interactive effects of age and self-rated interest in a topic area (e.g.,
geography, world history) on objective knowledge within
that area.
The final question concerning moderators of agecognition relations investigated in this project was whether
the age relations in one type of cognition (e.g., fluid
cognition) were moderated by the level of functioning on the
other type of cognition (e.g., crystallized cognition). For
example, it is possible that older adults with high levels of
knowledge may be able to circumvent decreases in fluid
cognition because of reliance on superior strategic or
procedural knowledge. If so, the negative relations between
age and reasoning might be expected to be smaller in people
with high levels of knowledge. In addition, a greater
age-related increase in knowledge might be observed among
individuals with the highest levels of fluid cognition,
possibly because they are more efficient at learning (an
aspect of fluid cognition) than individuals with lower levels
of fluid cognition. We investigated the relations among age
and fluid and crystallized cognition by evaluating interactive
effects of age and fluid cognition on measures of crystallized
cognition and the interactive effects of age and crystallized
cognition on measures of fluid cognition.
Overview of Project
To summarize, the major goals of this project were (a) to
identify individual-difference characteristics that are associated with crossword puzzle proficiency and (b) to examine
moderators of the relations between age and fluid and
crystallized aspects of cognition. We conducted four studies
to examine these issues; each study included approximately
200 adults, ranging from 18 to over 80 years of age.
Participants in each study attempted to solve either two or
three crossword puzzles; answered questions about thenamount of experience with crossword puzzles; and performed tests of vocabulary, general knowledge, reasoning,
and other cognitive abilities. To investigate individualdifference characteristics that contribute to puzzle proficiency, we used multiple regression and structural equation
analyses, with measures of crossword puzzle proficiency as
the criterion variable and other variables as predictors. To
investigate moderators of age relations on fluid and crystallized aspects of cognition, we used regression analyses to
examine interactions of age and either crossword puzzle
experience, reasoning, knowledge, self-reported interest, or
self-reported knowledge, with measures of reasoning and
knowledge as criterion variables. Significant interactions in
these analyses would indicate that the age relations vary
according to the level of the moderator variable.
Study 1
Method
Participants
The participants in this study were 202 adults (see Table 1 for
descriptive characteristics) recruited from appeals to various groups,
advertisements in newspapers and other media outlets, and personal contacts. There was a higher volunteering rate among elderly
adults, and this resulted in an unequal distribution of ages, with
46% of the sample over the age of 60. There was also a higher
percentage of women than men, particularly in the oldest group. As
one might expect, amount of education was positively correlated
(i.e., r = .17-47) with the vocabulary and general knowledge
variables in each study. However, because amount of education
was significantly related to age only in Study 2 (i.e., r = —.25), and
to measures of puzzle proficiency only in Study 1 (i.e., r = .30.39), we ignored the education variable in subsequent analyses.
Procedure
On participants' arrival at the testing site, the study was briefly
described, and all participants read and signed an informed consent
form. The following tests and questionnaires were then administered in the same order to all participants in a single session of
approximately 2.5 hr: background questionnaire, Puzzle 1, word
copying test, Puzzle 2, word identification test, general information
test, synonym and antonym vocabulary tests, anagram test, word
switch test, Shipley abstraction test, Cattell matrix completion test,
135
CROSSWORD PUZZLES
Table 1
Descriptive Characteristics of Samples in the Four Studies
Age
18-39
60+
40-59
Correlation
with age
Study 1
N
% Female
Health rating
Education
Study 2
N
% Female
Health rating
Education
Study 3
50
59
93
58.0
2.0 (0.7)
3.4(1.1)
71.2
2.6 (0.8)
3.5 (1.0)
77.4
2.5 (0.9)
3.4 (1.3)
42
56.9
2.0 (0.8)
4.0(1.0)
48.6
2.1 (0.9)
3.7 (1.0)
47
86
62
61.7
1.6(0.8)
3.9 (0.9)
53.5
1.9 (0.9)
4.1 (1.0)
54.8
2.2 (0.9)
3.9(1.1)
N
47
76
77
% Female
Health rating
Education
48.9
1.7 (0.7)
3.7 (1.0)
61.8
1.8 (0.9)
3.8(1.0)
48.1
2.3 (0.9)
3.7 (1.2)
N
% Female
Health rating
Education
Study 4
.18*
-.02
74
102
78.6
1.8(0.7)
4.2 (0.7)
.16
-.18*
.13
-.25*
-.03
.24*
-.02
-.00
.26*
-.01
Note. Values in parentheses are standard deviations. The health ratings were made on a 5-point
scale ranging from 1 (excellent) to 5 (poor). Education was classified as 1 for less than 12 years, 2 for
high school graduate, 3 for 13-15 years of education, 4 for college graduate, and 5 for 17 or more
years of formal education.
*p < .01.
word fluency test, make-words test, letter comparison test, and
pattern comparison test. The background questionnaire contained
items about amount of education, self-assessed health, and amount
and type of crossword puzzle experience. Specifically, the questions used to assess amount and type of crossword puzzle
experience asked about: (a) the number of crossword puzzles from
sources other than The New York Times attempted in a typical week,
(b) the number of New York Times puzzles attempted in a typical
week, (c) the number of hours per week spent working on
crossword puzzles, (d) the number of hours per week devoted to
other types of word puzzles or games (e.g., including acrostics,
word jumbles, and Scrabble), and (e) the number of years in which
at least one crossword puzzle was attempted per week. The
performance tests are described below according to the theoretical
construct they were intended to represent.
Puzzle proficiency. The crossword puzzle tests were relatively
simple, athematic puzzles (i.e., 11X11 cells with 54 words and
13 X 13 cells with 66 words) obtained from sources on the World
Wide Web (i.e., Crossword Puzzle #3 from Crossword Mania and
Sample Crossword #1 from Lyriq). Participants were allowed 5
rnin for the solution of each puzzle; they were informed of this time
limit prior to working on the puzzle, and the score was the number
of target words answered correctly. The number of correctly
answered words was correlated .99 with the number of individual
letters answered correctly, and thus only the former measure was
used in the analyses.
The word identification test was also used to assess crossword
puzzle proficiency. This test consisted of a clue and a single target
word of a specified length with three completed letters. Because the
items are considered in isolation, this is a different format than that
of a typical crossword puzzle, but the identification of targets with a
specified number of letters from a clue is a major component in
crossword puzzle solution. Moreover, as Underwood et al. (1994)
noted, an advantage of this format is that the solution of one item is
independent of the solution of other items. The words used in the
test were obtained from items contained in the Appendix in
Goldblum and Frost's (1988) article from the condition with
nonadjacent letter clues in which the completed letters were not in
the initial position of the word.
General knowledge. The general information test was designed to provide a measure of general knowledge. It consisted of a
40-item (4-alternative multiple-choice) test of general information
with 5 items each on American history, American literature, art and
architecture, geography, music, mythology, world history, and
world literature. The items were selected from a book containing
questions about cultural literacy (Zahler & Zahler, 1988), and the
participants were allowed 10 min to answer as many of the
questions as possible. The other measures of general knowledge
were obtained from multiple-choice synonym and antonym tests
(ten 5-alternative items each) derived from tests described in
Salthouse (1993b). Participants were allowed 5 min to complete
both the synonym and antonym vocabulary tests.
Word retrieval and transformation efficiency. Four tests were
used to measure word retrieval and word transformation efficiency.
One was a fluency test in which the participant was to write as
many words as possible beginning with the letter F and with the
letter 5, for 1 min each. The make-words test consisted of
presenting a list of letters and asking the participant to write as
many words as possible from those letters in a period of 1 min (cf.
Salthouse, 1993b). One set of letters consisted of BFHILNORW,
and the other set consisted of ACDGKMPTU. Ten min were
allowed for an anagram test containing twenty-five 5-letter items
believed to have only a single solution. The word switch test (cf.
Salthouse, 1993b) consisted of 15 pairs of 4-letter words, with the
136
HAMBRICK, SALTHOUSE, AND MEINZ
task for the participant to switch the first word into the second word
by changing one letter at a time such that each intermediate set of
letters also made a word. Five min were allowed for this test.
Abstract reasoning. Two tests were used to assess abstract
reasoning. The Shipley abstraction test (Zachary, 1986) is a series
completion test involving numbers, letters, and words. Participants
were allowed 5 min to solve the 20 items. A slightly modified
version of the Cattell's Matrices (Scale 3, Form A, Test 3; Institute
for Personality and Ability Testing, 1973) nonverbal reasoning test
was used as the second test of reasoning. Items in this test consist of
either a 2 x 2 o r a 3 X 3 matrix containing geometric patterns with
one missing cell, and the task was to select the best completion of
the missing cell from a set of six alternatives. We administered the
three practice items followed by the first 11 test items and allowed
3 min for the actual test.
Perceptual speed. Two of the perceptual speed tests were
paper-and-pencil perceptual comparison tests involving pairs of
letters (letter comparison) or pairs of line patterns (pattern comparison). In each case the test form consisted of pairs of three, six, or
nine letters or line segments, and the task for the respondent was to
write the letter 5 between the pair if the two members were the
same, and to write the letter D if the two members were different.
Each test was administered twice, with 30 s allowed for each
administration. The remaining test of perceptual speed was obtained from the word copy test. This test was a crossword puzzle in
which the "clues" were the target words, and the respondent
simply had to copy the words in the designated positions as quickly
as possible. One min was allowed for this test, and the score was
the number of complete words copied in the allotted time.
Results and Discussion
Means and standard deviations for the various experience
measures are presented in Table 2. Also included in the table
are the correlations of the experience measures with age and
with a composite measure of puzzle proficiency created by
averaging the z scores for the two puzzle measures. Two
points are important to note about these data. The first is that
the means were generally smaller than the standard deviations, indicating that the distributions were skewed, with a
relatively large number of values of zero. The second point
is that the pattern of correlations with age and with the
measure of crossword puzzle proficiency was fairly similar
for each of the experience measures. This finding, along with
the results that the patterns were also similar with aggregate
measures of experience, such as the first principal component in a principal-components analysis on the five original
experience measures, suggests that the questions were
assessing similar dimensions of crossword puzzle experience. Subsequent analyses therefore focused on the measures reflecting total number of puzzles attempted per week
and total number of hours per week devoted to word puzzles.
The top left panel of Figure 1 contains the distribution of
ages and total number of puzzles attempted per week in this
sample. It can be seen that although a sizable proportion of
the sample reported working no puzzles per week, there was
nonetheless a substantial range of both the age and experience variables.
Table 3 displays correlations among the variables and the
means and standard deviations of each variable. We computed the reliability estimates for the letter comparison,
pattern comparison, word fluency, and make-words tests by
Table 2
Means, Standard Deviations, and Correlations
With Age and With Puzzle Performance
for Different Measures of Experience
Correlation
Experience variable
M
Puzzle prof.
SD
Age
4.40
1.95
1.25
3.08
15.18
5.23
3.74
0.93
1.00
.25*
.20*
.31*
.19*
.46*
.29*
.32*
.33*
.40*
.55*
.26*
.52*
.31*
.56*
.56*
.53*
.58*
.63*
7.49
2.85
4.10
2.94
14.05
8.22
5.54
0.81
1.00
.19*
.18*
.28*
.08
.54*
.24*
.25*
.30*
.45*
.18*
.29*
.04
-.06
.27*
.27*
-.00
.16
.25*
No. CW puzzles/week
No. NY Times/week
Hr CW puzzles/week
Hr other puzzles/week
Years 1 + puzzle/week
Total no. puzzles/week
Total hr puzzles/week
Composite no. & hr
First principal component
Study 1
2.66
0.53
0.66
2.12
11.59
3.19
2.78
0
0
Study 2
6.47
1.80
5.42
1.95
20.79
8.27
7.37
0
0
No. CW puzzles/week
No. NY Times/week.
Hr CW puzzles/week
Hr other puzzles/week
Years 1 + puzzle/week
Total no. puzzles/week
Total hr puzzles/week
Composite no. & hr
First principal component
Study 3
5.19
1.96
5.22
2.08
19.29
7.15
7.30
0
0
5.72
3.83
4.59
4.31
14.15
5.56
7.71
0.87
1.00
.20*
.17
.31*
.18
.54*
.32*
.29*
.35*
.41*
.16
.12
.09
.09
.44*
.25*
.11
.21*
.25*
No. CW puzzles/week
No. NY Times/week
Hr CW puzzles/week
Hr other puzzles/week
Years 1 + puzzle/week
Total no. puzzles/week
Total hr puzzles/week
Composite no. & hr
First principal component
Study 4
5.32
2.45
4.67
1.79
19.90
7.77
6.45
0
0
6.18
4.92
3.50
4.18
14.98
5.75
6.05
0.83
1.00
.01
.11
.14
.04
.48*
.11
.11
.13
.21*
.05
.25*
.19*
.04
.48*
.27*
.14
.24*
.30*
No. CW puzzles/week
No. NY Times/week
Hr CW puzzles/week
Hr other puzzles/week
Years 1 + puzzle/week
Total no. puzzles/week
Total hr puzzles/week
Composite no. & hr
First principal component
Note. prof. = proficiency; CW = crossword; NY Times = New
York Times crossword puzzles.
boosting correlations between scores on the two versions of
each test with the Spearman-Brown prophecy formula. All
other reliability estimates are coefficient alphas. It can be
seen that all of the measures had reasonable reliability; the
reliability coefficients ranged from .78 to .94. Because
Puzzles 1 and 2 had 54 and 66 words, respectively, the
means for these puzzles correspond to 44.8% of the words in
Puzzle 1 and 42.1% of the words in Puzzle 2.
CROSSWORD PUZZLES
137
Study 1
Study 2
«
m
(28)
£•20
•» »
^ 20
I
I
15
15
10
•5 10
|
•*. • •.•:"?••
5
Z
5
0
20
30
40 50 60 70 80
Chronological Age
2 0 3 0 4 0 5 0 6 0 70 8090
Chronological Age
90
Study 3
•
(40)
(38) (25PO
i
20
£
£
Study 4
«•
06)00)
20
15
15
•5 10
z 5
•
z
•
••• m» •
•
mm*
»m •
••
•
•
•
0
i
i
i
i
20 30 40 50 60 70 80 90
Chronological Age
2 0 3 0 4 0 5 0 6 0 70 8 0 9 0
Chronological Age
Figure 1. Distributions of age and number of puzzles attempted per week in the four samples.
138
HAMBRICK, SALTHOUSE, AND MEINZ
Table 3
Correlation Matrix, Study 1
Variable
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
Age
NumCWPuz
HrWPuz
CopyW
LetCom
PatCom
AntVoc
SynVoc
Genlnfo
Cattell
Shipley
MkWds
Fluency
WdSwitch
Anagram
Puzzl
Puzz2
WordID
10
1
—
.29
.32 .74
-.33 .12 .15 —
-.48 .04 .04 .58 (.84)
.46 .68 (.84)
-.61 -.08 -.10
.26 .39 .36 .37 .30
.09
.39 .40 .38 .36 .24
.00
.20 .29 .31 .44 .34
.12
.54
-.48 .10 .08 .51 .60
.52
-.35 .23 .20 .58 .65
.03 .38 .39 .40 .40
.21
-.24
.19 .25 .49 .54
.42
-.03
.24 .27 .38 .42
.20
.04 .42 .44 .43 .42
.28
.21 .50 .49 .43 .36
.13
.30 .60 .56 .36 .29
.07
.15 .38 .35 .42 .30
.07
54.6 3.2 2.8 29.4 9.4 16.2
18.3 5.2 3.7 12.2 3.6
4.8
(.88)
.86
.76
.29
.47
.57
.45
.49
.62
.75
.73
.65
5.7
3.3
11
(.89)
.77 (.89)
.25
.38 (.78)
.44
.51 .73 (.92)
.58
.56 .41
.55
.38
.44 .46
.56
.49
.54 .53
.57
.63
.56 .47
.58
.76
.57
.72 .38
.75
.67 .32
.50
.65
.69 .39
.55
6.5 18.7 3.9 12.1
3.3
8.2 2.3
4.5
12
13
14
15
16
17
18
(.82)
.68 (.82)
.59
.49
.71
.61
.69
.55
.67
.48
.60
.46
6.0 13.5
3.2
4.0
(.81)
.53 (.94)
.62
.73 —
.57
.71
.94 —
.56
.60
.74 .74 (.86)
M
1.6 17.1 24.2 27.8 5.1
SD
2.0
7.5 17.5 22.9 4.0
Note. N = 202. Correlations with an absolute magnitude greater than .17 were significant at p < .01. Values in parentheses along
the diagonal are reliability estimates. NumCWPuz = number of crossword puzzles attempted per week; HrWPuz = hours solving word
puzzles per week; CopyW = word copying; LetCom = letter comparison; PatCom = pattern comparison; AntVoc = antonym vocabulary;
SynVoc = synonym vocabulary; Genlnfo = general information; Cattell = Cattell matrix completion; Shipley = Shipley abstraction test;
MkWds = make words; Fluency = word fluency; WdSwitch = word switch; Anagram = anagram solution; Puzzl = Puzzle 1; Puzz2 =
Puzzle 2; WordID = word identification.
Inspection of the correlation matrix reveals two noteworthy patterns of correlations. First, there were strong correlations between performance on the three general knowledge
measures (synonym vocabulary, antonym vocabulary, and
general information) and performance on the puzzle proficiency measures (Puzzle 1, Puzzle 2, and word identification). In addition, the correlations of the puzzle proficiency
measures with performance on the word retrieval and
transformation measures were moderate in magnitude. These
correlations suggest that knowledge and word retrievaltransformation efficiency are two correlates of success in
solving crossword puzzles. Second, age was negatively
correlated with performance on the speed and reasoning
measures but positively correlated with performance on the
knowledge measures. This pattern of correlations is consistent with prior reports of different age relations for measures
of fluid and crystallized cognition.
We also conducted several additional analyses on the data
summarized in Table 3. For example, we conducted regression analyses on each of the performance variables to
determine whether there were any significant effects of
gender or of the interaction of age and gender. Small but
significant (p < .01) advantages for women were apparent
on the pattern comparison (squared semipartial correlation = .027) and Cattell reasoning (squared semipartial
correlation = .034) variables, but there were no significant
gender differences on any other variables, and none of the
Age X Gender interactions were significant.
We also examined interactions of age and experience on
the composite puzzle proficiency measure for all of the
experience measures summarized in Table 2. The interactions were significant for the total number of puzzles
attempted per week (increment in R2 - .034) and for the
years of attempting at least one puzzle per week (increment
in ^?2 = .061) variables. However, in both cases the direction was opposite to what one might expect, because the
age-puzzle relations were more positive among individuals
with the least amount of experience.
Confirmatory Factor Analyses
and Structural Analyses
Loadings of variables on the theoretical constructs, and
the fit statistics2 for confirmatory factor analyses in this and
subsequent studies, are contained in Table 4. For each study,
the first variable under each construct label was used to scale
the latent construct. The fit of the confirmatory factor
analysis for the current study was not particularly impres-
2
Several indices are available to evaluate the fit of confirmatory
factor analyses and structural equation models. Those reported here
are chi-square, reflecting whether there was a significant difference
between the reproduced and observed covariance matrices; the
non-normed fit index (NNFI) and the comparative fit index (CFI),
both reflecting the degree to which the reproduced covariance
matrix resembled the observed covariance matrix; and the standardized root mean square residual (Std. RMR) between the two
matrices.
CROSSWORD PUZZLES
Table 4
Loadings of Variables on Constructs in the Four Studies
Study
Construct and variable
Puzzle proficiency
Puzzle 1
Puzzle 2
1
2
3
.88
.91
.77
.82
.85
.78
.78
.63
Word identification
Puzzle experience
No. CW puzzles
.87
.90
.35
Hours of word puzzles
.85
General knowledge
.84
.75
General Information 1
General Information 2
Synonym vocab.
.93
.75
Antonym vocab.
.92
.74
Synonym vocab. adv.
Antonym vocab. adv.
Retrieval
.84
Anagrams
.66
Make words
.84
.82
Fluency
.74
.71
Word switch
.70
Reasoning
.62
Cattell
.79
Shipley
.92
.81
Analytical Reasoning 1
Analytical Reasoning 2
Cube assembly
Perceptual speed
Letter comparison
.88
.80
Pattern comparison
.75
.80
Word copy
.67
Correlations among factors
Puzzle proficiency
Puzzle experience
.64
.30
General knowledge
.85
.60
Retrieval
.57
.85
Reasoning
.35
.58
Perceptual speed
.36
.28
Puzzle experience
.47
General knowledge
.09
Retrieval
.50
.07
Reasoning
.24
-.14
Perceptual speed
.03
-.17
General knowledge
Retrieval
.75
.48
Reasoning
.52
.34
Perceptual speed
.33
.11
Retrieval
Reasoning
.76
.62
Perceptual speed
.48
.61
Reasoning
Perceptual speed
.83
.72
Fit statistics
.65
.97
.96
Puzzle 3 (NY Times)
Puzzle 4 (NY Times)
X2
N
df
CFl
NNFI
Std. RMR
4
.90
.91
.87
.58
.61
.66
.86
.89
.59
.64
.76
.99
.87
.76
.70
.70
.70
.63
.49
.79
.82
.83
.69
.28
.41
.37
.76
.04
.17
-.19
-.30
-.32
.05
-.05
.01
-.13
-.25
.22
.03
.30
.18
.69
.72
266.11
248.92
248.91
151.08
202
104
.94
.93
.08
218
89
.89
.85
.07
195
67
200
55
.91
.87
.08
.85
.80
.09
Note, vocab. = vocabulary; adv. = advanced; CFI = comparative fit index; NNFI = non-normed fit index; Std. RMR =
standardized root mean square residual.
139
sive, but we examined all standardized residuals, and no
pattern indicative of a misspecification of constructs and
variables was apparent. The lack of a better fit may be
attributable to high correlations between several of the
constructs (and their corresponding indicators), because the
correlations were .85 between general knowledge and
puzzle proficiency, .85 between retrieval and puzzle proficiency, .83 between speed and reasoning, .76 between
reasoning and retrieval, and .75 between general knowledge
and retrieval. These constructs are obviously highly related
but were kept separate because they are theoretically, and
operationally, distinct.
The structural model illustrated in Figure 2 provided the
best fit of those examined, x2(124, N = 202) = 305.17,
NNFI = .93, CFI = .94, Std. RMR = .08.3 The alternatives
that were investigated and found to be less satisfactory than
the model represented in Figure 2 were models with paths
from age, speed, and reasoning to puzzle proficiency; from
age and speed to word retrieval; from age to reasoning; and
from crossword puzzle experience to general knowledge.
Because none of these paths were significantly different
from zero, it can be concluded that the model summarized in
Figure 2 provides a better characterization of the data than
models containing any of these additional relations. Inspection of Figure 2 reveals that the model accounted for 85% of
the variance in the latent construct representing crossword
puzzle proficiency and 70% or more of the variance in the
constructs representing general knowledge, reasoning, and
word retrieval.
Several interesting relations are apparent in Figure 2. For
example, the relation between age and general knowledge
was very strong, indicating that vocabulary and general
information tended to be greater with increased age in this
sample. The relation between age and crossword puzzle
experience also was strong, indicating that older adults in
this sample reported more current experience with crossword puzzles than younger adults. In addition, there was a
moderately large linkage between speed and reasoning, but
there was no direct relation from age to reasoning. This latter
pattern is consistent with earlier findings that large proportions of the relations between age and measures of fluid
reasoning appear to be mediated through speed (e.g.,
Babcock, 1994; Bors & Form, 1995; Salthouse, 1993a;
Salthouse, Fristoe, & Rhee, 1996).
Reasoning was related to general knowledge, possibly
because the measures of reasoning reflect fluid cognition,
and higher levels of fluid cognition may contribute to easier
acquisition of knowledge. In addition, higher levels of fluid
cognition might increase the likelihood of engaging in
mentally challenging activities such as crossword puzzles,
3
Note that although age is represented as an antecedent variable
in this diagram, it should not be conceptualized as a causal factor
but rather as an index of the changes that occur across time. In other
words, in structural models such as these, whenever an arrow is
drawn between two variables it indicates that the relation between
the variables cannot be explained or accounted for by other
variables in the analysis.
140
HAMBRICK, SALTHOUSE, AND MEINZ
.29
.69
Figure 2. Structural equation model predicting puzzle proficiency for Study 1. The numbers
adjacent to the arrows are standardized path coefficients, and those at the end of the small circles
pointing to the larger circles indicate the proportion of unexplained variance in the construct.
thereby accounting for the relation between reasoning and
crossword puzzle experience. It is nevertheless interesting
that there was no direct relation between reasoning and
puzzle proficiency. Any influences of reasoning on puzzle
proficiency therefore appear to be mediated through general
knowledge, word retrieval, or crossword puzzle experience.
The three major predictors of puzzle proficiency were
general knowledge, word retrieval, and crossword puzzle
experience, and together these factors accounted for 85% of
the variance in the puzzle proficiency construct. The first
two factors are intuitively reasonable, because one would
expect greater success if the individual has extensive
knowledge of words and of general information and if he or
she is efficient at retrieving and transforming words. This
pattern also replicates and extends the earlier findings of
Underwood et al. (1994). The influence of crossword puzzle
experience on puzzle proficiency raises the possibility that
solving crossword puzzles may be associated with the
acquisition of crossword-specific knowledge that was not
captured by the general knowledge and word retrieval
measures used in this study. This possibility was investigated in Study 2.
The absence of a direct relation of processing speed on
puzzle proficiency suggests that speed is not directly involved in the effectiveness of solving crossword puzzles,
despite the use of relatively simple timed tests of crossword
puzzle proficiency. Moreover, the absence of a relation
between crossword puzzle experience and knowledge suggests that working on crossword puzzles does not lead to
increases in the amount of general knowledge. Such a
relation might be apparent if more comprehensive or sensitive measures of knowledge were available, but there is no
evidence of this type of influence with the measures in the
current study.
CROSSWORD PUZZLES
To summarize, the results of this study reveal a complex
but plausible pattern of influences on crossword puzzle
proficiency. Strong direct influences are apparent with
measures of knowledge and efficiency of word retrieval and
transformation, but any influences of abstract reasoning and
processing speed were indirect and mediated through either
knowledge, word retrieval, or crossword puzzle experience.
There were large negative relations between age and speed
and between age and reasoning but large positive relations
between age and general knowledge and between age and
crossword puzzle experience.
Moderator Analyses
We conducted a series of regression analyses to examine
moderators of age relations on measures of fluid and
crystallized cognition; that is, to determine whether the
relations between age and measures of fluid and crystallized
cognition varied according to the level of the suspected
moderator variables. In each of these analyses an index of
either fluid or crystallized cognition was predicted from the
cross-product interaction of age and a suspected moderator
variable after controlling for the main effects of these
variables. We created the index of fluid cognition by
averaging the z scores for the Cattell matrix completion and
Shipley abstraction measures, and we created the index of
crystallized cognition by averaging the z scores for the
synonym and antonym vocabulary and general information
measures.
We examined each of the measures of crossword puzzle
experience summarized in Table 2 as a possible moderator of
age-cognition relations in two sets of analyses. First, to
determine whether experience solving crossword puzzles
moderated the relations between age and fluid cognition, we
predicted the composite reasoning measure from the crossproduct interaction of age and amount of crossword puzzle
experience after controlling for the main effects of age and
crossword puzzle experience. Second, to determine whether
crossword puzzle experience moderated the relations between age and crystallized cognition, we predicted the
composite knowledge measure from the cross-product interaction of age and crossword puzzle experience after controlling for the main effects of age and crossword puzzle
experience.
Results of both sets of analyses are summarized in Table
5. Notice that none of the Age X Experience interactions
were statistically significant with any of the experience
measures. Because McClelland and Judd (1993) demonstrated that the power to detect interactions can be low with
samples composed of continuous distributions of the predictor variables, we repeated the analyses for two of the
summary experience measures after deleting individuals
from the middle 50% of the distribution on both the age and
experience variables. Inspection of the table reveals that
although some of the estimates of the magnitudes of the
experience effect were increased in this extreme-groups
141
Table 5
R2 for Main Effects of Experience and Interactions of Age
and Experience (Exper.) on Composite Measures of
Reasoning and Knowledge for Different
Measures of Experience
Exper. variable
Reasoning
AgeX
Exper. Exper.
Knowledge
AgeX
Exper. Exper.
No. CW puzzles/week
No. NY Times/week
Hr CW puzzles/week
Hr other puzzles/week
Years 1 + puzzle/week
Total no. puzzles/week
Total hr puzzles/week
Composite no. & hr
Extreme groups (n = 63)
First principal component
Extreme groups (n = 50)
Study 1
.028*
.008
.017
.019
.001
.030*
.023
.030*
.025
.025*
.004
.000
.002
.000
.000
.010
.002
.000
.004
.002
.002
.001
.115*
.053*
.150*
.019
.172*
.138*
.134*
.156*
.252*
.186*
.331*
.004
.014
.002
.000
.026
.013
.000
.006
.001
.009
.004
No. CW puzzles/week
No. NY Twiey/week
Hr CW puzzles/week
Hr other puzzles/week
Years 1 + puzzle/week
Total no. puzzles/week
Total hr puzzles/week
Composite no. & hr
Extreme groups (n = 57)
First principal component
Extreme groups (n = 60)
Study 2
.004
.005
.049*
.000
.049*
.007
.030*
.025
.072*
.050*
.251*
.000
.000
.004
.000
.006
.001
.002
.000
.000
.003
.002
.000
.046*
.010
.017
.030*
.006
.021
.002
.003
.003
.009
.006
.006
.010
.004
.023
.012
.008
.013
.010
.024
.019
.005
.000
.003
.021
.002
.004
.002
.000
.016
.000
.003
.033*
.010
.014
.002
.011
.014
.009
.015
.002
.010
.000
.000
.010
.000
.001
.033
.001
.000
.001
.001
.001
.000
Study 3
No. CW puzzles/week
.018
No. NY Times/week
.008
Hr CW puzzles/week
.057*
Hr other puzzles/week
.001
.041*
Years 1 + puzzle/week
Total no. puzzles/week
.040*
Total hr puzzles/week
.025*
.042*
Composite no. & hr
Extreme groups (n = 57)
.138*
.044*
First principal component
Extreme groups (n = 55)
.189*
Study 4
No. CW puzzles/week
.006
No. NY Times/week
.015
Hr CW puzzles/week
.010
.007
Hr other puzzles/week
.040*
Years 1 + puzzle/week
Total no. puzzles/week
.000
.013
Total hr puzzles/week
.006
Composite no. & hr
.022
Extreme groups (n = 52)
.036*
First principal component
.073
Extreme groups (n = 55)
Note. CW = crossword; NY Times =
puzzles.
.001
.000
.007
.002
.011
.002
.006
.002
.009
.003
.019
New York
.005
.003
.014
.001
.028
.000
.005
.002
.000
.096*
.014
.002
.026
.002
.020
.000
.006
.088
.009
.015
.034
.033
Times crossword
HAMBRICK, SALTHOUSE, AND MEINZ
142
2
2
1.5
More than 5
(N=53, Age=64)
1.5
1
1
Med. Know!
Age=54)
----,(N=101,Age
O>
O)
•I
M
O
* * «•
% °
<D
CC -0.5
CC -0.5
(N=121.Age=50)
-1
Low Know.
(N-50.Age=49)
-1
-1.5
-1.5
-2
* *»
"**••
o
2 to 5
(N=28.Aae=60)
O
'.
HiQh Know.
(N=51,Age=61)
20
30
40
50
60
-2
70
20
30
40
50
60
70
2
1.5
1.5
2 to 5
„
(N=28.Age
1
More than 5
(N=53. Age=64)
1
High Reas.
(N=51.Age=44)
O
•g 0.5
O
0.5
o
-0.5
-0-5
Less than 2
(N=121,Age=50)
-1
'' Med. Reas.
(N=100, Age=55)
-1
-1.5
Low Reas.
(N=50. Age=64)
-1.5
20
30
40
50
60
-2
70
Chronological Age
20
30
40
50
60
70
Chronological Age
Figure 3. Relations of age to composite measures of fluid (top) and crystallized (bottom) cognition
as a function of amount of crossword experience (left) and level of the other type of cognition (right),
Study 1. The lines represent the regression equations relating the performance measures to age in
each of the groups.
sample, the interactions of age and experience still did not
differ significantly from zero.4
The top left and bottom left panels of Figure 3 portray
data relevant to the analyses just described, with experience
represented in terms of three ranges of total number of
puzzles attempted per week. As would be expected from the
nonsignificant Age X Experience interactions, the functions
relating age to both fluid and crystallized intelligence were
nearly parallel across different amounts of experience. Taken
together, the results of these analyses provide no support for
the view that the relations between age and measures of
either fluid cognition or crystallized cognition are moderated
by amount of cognitive activity in the form of experience
working on crossword puzzles.
We performed similar types of regression analyses to
evaluate whether the effects associated with age on one type
of cognition were moderated by level of functioning on the
other type of cognition. That is, were the age-related effects
on fluid cognition moderated by the level of crystallized
4
We conducted similar analyses of the Age X Experience
interactions on the composite reasoning and knowledge measures
using the combined data (n = 420) from Studies 1 and 2 and the
composite number- and hours-per-week experience measure. A
small (increment in R2 = .032) interaction was apparent on the
composite knowledge measure, but it was in the direction of
slightly greater age-related increases in knowledge among individuals with the least amount of experience. A similar analysis on the
102 individuals in the top and bottom 25% of both the age and
experience variables failed to exhibit significant interactions for
either the composite reasoning variable or the composite knowledge variable.
143
CROSSWORD PUZZLES
cognition, and vice versa? We conducted two analyses to
answer this question. First, we predicted the index of fluid
cognition from the cross-product interaction of age and the
index of crystallized cognition after controlling for the main
effects of age and crystallized cognition. Data relevant to
this comparison are displayed in the top right panel of Figure
3 in terms of the age relations for the top 25%, middle 50%,
and bottom 25% of the distribution on the composite
knowledge variable. It can be seen that the age relations
were very similar across different levels of knowledge, and
the Age X Knowledge interaction was not statistically
significant, F(l, 198) = 0.79.
Second, to evaluate whether the effects of age on knowledge were moderated by level of reasoning, we predicted the
index of crystallized cognition from the cross-product
interaction of age and the index of fluid cognition after
controlling for the main effects of age and fluid cognition.
The bottom right panel of Figure 3 displays the relevant data
in terms of the top 25%, middle 50%, and bottom 25% of the
distribution on the composite reasoning variable. The nonparallel age functions suggest that there was a tendency toward
an Age X Reasoning interaction, but it did not approach
conventional significance, F(l, 198) = 1.97, p = .16.
In summary, these analyses of moderators of agecognition relations provide no evidence to suggest that
experience solving crossword puzzles reduces the magnitude of age-related decreases in fluid cognition or enhances
the magnitude of age-related increases in crystallized cognition. There is also no evidence that the negative relations
between age and reasoning are moderated by level of
knowledge or that the positive relations between age and
knowledge are moderated by level of reasoning.
derives from an intimate knowledge of the materials of
puzzles, namely, letters and the structure of words. Second,
crossword puzzlers may acquire a vocabulary of words and
facts encountered relatively infrequently outside of crossword puzzles. For example, although words such as sley (a
weaver's reed) and alee (antonym ofaweather) are probably
unfamiliar to most literate adults, such esoteric words are
common in challenging crossword puzzles. Finally, keeping
abreast of popular culture may facilitate successful crossword puzzle solving, because many crossword puzzles are
replete with references to films, television shows, actors
and actresses, authors, and so on. To illustrate, it seems
unlikely that many educated nonpuzzlers would possess a
repertoire of knowledge that would enable them to answer
"Tod" to the clue "Route 66 character" or "Omar" to
the clue "Barbra's 'Funny Girl' costar." We therefore
obtained measures of letter sequence knowledge, of esoteric
word meanings, and of popular culture to determine
the degree to which they were associated with crossword
puzzle proficiency.
The final question addressed in Study 2 concerned the role
of the same moderator variables examined in Study 1 but in
a sample with greater amounts of experience solving crossword puzzles; that is, in a sample of individuals with
moderate to extensive experience solving crossword puzzles,
does crossword puzzle experience moderate the relations
between age and either fluid or crystallized cognition, and
are the age relations in one type of cognition moderated by
the level of functioning in the other type of cognition?
Study 2
The participants in this study were 218 adults (see Table 1 for
descriptive characteristics) recruited through a newspaper advertisement that specified that the individuals had to complete at least one
crossword puzzle per week to participate. As in Study 1, there was a
higher percentage of women than men. However, adults over the
age of 60 years accounted for only 34% of the sample, whereas
adults between the ages of 40 and 59 years, and under the age of 40,
accounted for 47% and 19% of the sample, respectively.
Means and correlations for the experience measures are presented in Table 2, and the distributions of age and number of
puzzles attempted per week are portrayed in the top right panel of
Figure 1. As planned, the participants in this study had considerably
more crossword puzzle experience than the participants in Study 1.
For example, whereas participants in this study attempted an
average of 8.3 crossword puzzles per week, participants in Study 1
attempted an average of only 3.2 crossword puzzles per week.
Furthermore, participants in this study reported working on crossword puzzles an average of 4.6 more hours per week than the
participants in Study 1. Despite the greater amounts of puzzle
experience in this sample, the different experience measures again
had similar correlations with age and with puzzle proficiency.
General knowledge, word retrieval and transformation
efficiency, and crossword puzzle experience all had independent and direct effects on crossword puzzle proficiency in
Study 1, and together they accounted for 85% of the
variance in puzzle proficiency. Nevertheless, only 109 of the
202 participants in Study 1 reported completing at least one
crossword puzzle per week, and only 105 of the participants
reported spending at least 1 hr per week solving crossword
puzzles. Furthermore, the criterion crossword puzzles were
relatively easy and contained few, if any, deceptive clues.
The first question addressed in Study 2 therefore concerned
the generalizability of the results of Study 1 to a sample of
participants with greater amounts of crossword puzzle
experience and to a more challenging crossword puzzle.
The second question of interest in Study 2 concerned the
contributions to puzzle proficiency of forms of knowledge
that may be somewhat specific to crossword puzzle solving.
Three types of knowledge might be postulated to be related
to the successful solution of crossword puzzles. First,
because an obvious requirement of solving crosswords is
generating the missing letters of incomplete words, crossword puzzlers may become more sensitive to the likelihood
of different letter combinations in the English language. In
fact, Schulman (1996) suggested that puzzle expertise
Method
Participants
Procedure
Participants who arrived for testing at least 15 min early
completed a pretest questionnaire. The following tests and questionnaires were then administered in a fixed order in a single session of
approximately 2.5 hr: background questionnaire, Puzzle 3, Puzzle
144
HAMBRICK, SALTHOUSE, AND MEDSTZ
1, Puzzle 2, word identification test, general information test,
Esoteric Knowledge Test A, Sequential Dependencies Test A,
popular culture test, Shipley abstraction test, anagram test, word
fluency test, pattern comparison test, letter comparison test,
make-words test, Cattell matrix completion test, Sequential Dependencies Test B, Esoteric Knowledge Test B, synonym and antonym
vocabulary tests. The tests and questionnaires not administered in
Study 1 are described below.
The pretest questionnaire included two open-ended questions
about puzzle solving: (a) what are the most important factors in
crossword puzzle solving skill? and (b) what makes a crossword
puzzle difficult? We included these questions to examine the
correspondence between puzzlers' intuitions about puzzle solving
and empirical findings regarding predictors of puzzle proficiency,
but we made no specific hypotheses with respect to the nature of the
responses.
We chose the New York Times puzzle (Puzzle 3) from The New
York Times Daily Crossword Puzzles: Volume 35 (1993). The
puzzles in this collection appeared between Monday and Friday in
The New York Times between March 1, 1985, and May 21, 1985,
thus minimizing the possibility that participants would remember,
or have recently solved, the puzzle selected for the study. The
selected puzzle (Puzzle #48) did not have a specialized theme and
was 78 words in length (39 across clues and 39 down clues) within
a 15 X 15 grid. Participants were allowed 15 min to work on the
puzzle.
Five tests were designed to assess potential forms of specialized
crossword puzzle knowledge: (a) two versions of a sequential
dependencies test, (b) two versions of an esoteric knowledge test,
and (c) a popular culture test. The two versions of the sequential
dependencies test were designed to assess knowledge of the
likelihood of different combinations of letters. Part A was a 5-min,
40-item test in which each item consisted of a pair of 2-letter
combinations (i.e., bigrams) separated by a space. The task for
participants was to circle the bigram (e.g., AF or LH) that occurred
more frequently in the English language. Data on the frequency of
bigrams (Solso, Barbuto, & Juel, 1979) were log transformed, and
then we created two levels of item difficulty (low and medium) by
specifying the distance in log units between the pairs of bigrams.
Low-difficulty items were separated by an average of 5.5 log units,
and medium-difficulty items were separated by an average of 3.5
log units. Thirty items appeared in each difficulty level, and no
bigram was used more than once.
Part B of the sequential dependencies test was a 5-min, 60-item
test in which each item consisted of two letters, a blank space, a
colon, and four letters (e.g., EM
: B P E S). The task for
participants was to circle the letter to the right of the colon that
formed the 3-letter combination (i.e., the trigram) that occurred
most frequently in the English language. The items were constructed such that the most frequent trigram occurred in at least
1,000 words per million more than the less frequent alternatives. To
illustrate with reference to the example provided above, the trigram
EME appears 3,066 times per 1 million words, whereas the
trigrams EMB, EMP, and EMS occur 1,367,1,292, and 1,112 times
per 1 million words, respectively.
The two versions of the esoteric knowledge test were designed to
measure knowledge of "crosswordese," or esoteric terms encountered in crossword puzzles. Part A was a 5-minute, 34-item
fill-in-the-blank test. The test was two pages in length, with 17
items per page, and for each item the task for participants was to
complete a definition by filling in the blanks with the appropriate
term. Items for Part A were obtained from a section in the New York
Public Library Desk Reference (1993) entitled "Common Crossword Puzzle Words." Part B was a 5-min, 30-item matching test.
The test was three pages in length, and for each page the task for
participants was to match 10 terms with 10 definitions, using each
definition only once. Items for Part B were obtained from 20
crossword puzzles published in the Masters' Crossword Puzzle
Collection (1996). Among the terms and definitions used in the two
parts of the esoteric knowledge test were aril (seed covering), bane
(judge's bench), and etui (needle case).
The popular culture test was a 5-min, 30-item fill-in-the-blank
test designed to assess knowledge of actors and actresses, movie
titles, song titles and musicians, and literature. Blank spaces
indicated the number of letters in each term. Items on the popular
culture test also were obtained from 20 crossword puzzles published in the Masters' Crossword Puzzle Collection (1996). Examples of items from the popular culture test included Jabberwacky creator (Carroll), Actor Tayback (Vic), and Woody Allen's
"
Days" (Radio). The test was three pages in length, with 10
items on each page.
Results and Discussion
Table 6 displays correlations among the variables, and
means, standard deviations, and reliability estimates for each
variable. It can be seen that the reliability estimates ranged
from .17 to .94, indicating that, with the exception of
Sequential Dependencies B, the measures had reasonable
reliability. We excluded Sequential Dependencies B from
the structural analyses reported below because of poor
reliability. Because at least two measures of a construct are
required to generate a latent variable for use in structural
equation analyses, we also excluded Sequential Dependencies A from the structural analyses, as it was the only
remaining measure of letter sequence knowledge. Performance levels on the puzzles expressed in percentage of
items answered correctly were 79.8% for Puzzle 1, 76.7%
for Puzzle 2, and 57.1% for Puzzle 3. The values for the first
two puzzles are considerably higher than the values in Study
1, which is reasonable in light of the greater experience of
the current sample (cf. Table 2).
Inspection of Table 6 reveals that there were weak
relations (r = .15-.32) between the measures of letter sequence knowledge and the measures of puzzle proficiency.
To determine whether these effects were independent of the
effects of general knowledge, we conducted a hierarchical
regression analyses in which the composite measure of
puzzle proficiency (i.e., average of z scores for the three
puzzles) was predicted from a composite measure of letter
sequence knowledge (i.e., average of z scores for Sequence
A and Sequence B) after control of a composite measure of
general knowledge (i.e., average of z scores for antonym
vocabulary, synonym vocabulary, and general information).
The increment in A 2 associated with letter sequence knowledge was .05 (p < .01), indicating that there was a small
unique effect of knowledge of letter sequences on puzzle
proficiency after controlling for the influence of general
knowledge. There were also moderate correlations (r = .39.48) between the popular culture measure and the measures
of puzzle proficiency. When the popular culture measure
was entered as a predictor of the composite measure of
puzzle proficiency after statistical control of the composite
general knowledge measure it was associated with an R2
increment of .09 (p < .01). These two sets of results
indicate that, in addition to having higher levels of general
145
CROSSWORD PUZZLES
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HAMBRICK, SALTHOUSE, AND MEINZ
knowledge than less successful solvers, people who are
successful in solving crossword puzzles are more sensitive
to the frequency of letter sequences and know more about
popular culture.
Table 6 also reveals that the correlations between the
measures of general knowledge and puzzle proficiency were
statistically significant but somewhat weaker than in Study
1. However, the correlations between the measures of
esoteric knowledge and puzzle proficiency were very large
(r = .61-.87). In fact, the correlation (r = .87) between
Esoteric Knowledge A and the New York Times puzzle
(Puzzle 3) was higher than the correlations between that
puzzle measure and the Puzzle 1 and Puzzle 2 measures and
was nearly identical to the estimated reliability of the
Esoteric Knowledge A measure. These findings suggest that
a challenging crossword puzzle may largely be a test of
esoteric knowledge.
Finally, it can be seen in Table 6 that age was negatively
correlated with the speed and reasoning measures and
positively correlated with the general knowledge measures.
Although the correlations between age and the general
knowledge measures were somewhat weaker than in Study
1, this pattern of correlations is again consistent with the
finding that fluid cognition decreases with increasing age,
whereas crystallized cognition often remains stable or even
increases.
As in Study 1, we conducted regression analyses on all
performance variables to test for main effects of gender and
interactions of age and gender. Men performed at higher
levels than women on two variables: Esoteric Knowledge
Test A (squared semipartial correlation = .056) and Puzzle 1
(squared semipartial correlation = .028), and men exhibited
larger age-related declines on the Shipley abstraction test
(men, r = -.64; women, r - -.39) and Sequential Dependencies Test B (men, r = —.31; women, r = .08) variables.
The interactions of age and experience on the composite
puzzle proficiency measure were significant for two experience measures. The corresponding increments in R2 were
.032 for the hours per week devoted to working crossword
puzzles and .046 for the first principal-component measure.
In both cases the interactions reflected more positive agepuzzle relations among individuals with the least amount of
experience.
Summary of Pretest Questionnaire Results
A total of 143 participants completed the pretest questionnaire. We identified the five most common responses to the
first question in the pretest questionnaire (i.e., what are the
most important factors in crossword puzzle-solving skill?)
to determine whether participants' intuitions about crossword puzzle solving were consistent with empirical findings
from Study 1. The most frequently mentioned responses
were: good vocabulary (83 responses), general knowledge
(43 responses), spelling ability (29 responses), experience/
practice with puzzles (32 responses), and flexibility of clue
interpretation (25 responses). With the exception of spelling
ability, the responses of the pretest questionnaire appear
consistent with findings from Study 1; that is, participants
indicated that vocabulary and general knowledge, flexibility
of clue interpretation (which might be interpreted as word
retrieval and transformation efficiency), and experience/
practice contribute to the successful solution of crossword
puzzles. The most frequent responses to the question of what
makes a crossword puzzle difficult were: obscure references
(42 responses), foreign language terms (31 responses),
uncommon words (29 responses), and ambiguous or tricky
clues (25 responses).
Confirmatory Factor Analyses and Structural
Analyses
The results of the confirmatory factor analysis for Study 2
are displayed in Table 4. The fit of the measurement model
was again not particularly impressive, but no obvious
misspecification of the factors was apparent. Moreover, it
can be seen that the pattern of loadings of the variables on
the constructs was similar in Studies 1 and 2.
We examined a specialized knowledge construct, composed of two measures of esoteric knowledge and one
measure of popular culture knowledge, in additional confirmatory factor analyses. The rationale for referring to these
measures as reflections of specialized knowledge was that
the items on the tests were taken from crossword puzzles or
from a source of words commonly found in crossword
puzzles. Furthermore, the tests were similar to crossword
puzzles in that they required participants to produce an
answer given a definition, synonym, or other clue. The
specialized knowledge construct correlated .99 with the
puzzle proficiency construct in the measurement model.
This finding suggests that there is nearly complete overlap of
individual differences on the measures of performance in our
puzzle tasks and on the specialized knowledge measures.
Because the puzzle proficiency and specialized knowledge
variables were too highly correlated to examine as distinct
constructs in a single structural equation model, these latent
variables were predicted in separate analyses.
The structural model with puzzle proficiency as the
criterion variable is illustrated in Figure 4. The fit of the
model was acceptable, x2(107, N = 218) = 305.07, NNFI =
.85, CFI = .88, Std. RMR = .08, and all paths not
represented in Figure 4 were tested but found not to be
statistically significant. As in Study 1, general knowledge,
word retrieval, and crossword puzzle experience had direct
effects on puzzle proficiency. However, age and speed also
had statistically significant direct effects on puzzle proficiency in this study. The structural model with the specialized knowledge construct as the criterion variable, X2(95,
N = 218) = 245.81, NNFI = .86, CFI = .89, Std. RMR =
.09, yielded a similar pattern of relations, as would be
expected given the very strong correlation between the
specific knowledge and puzzle proficiency constructs. However, there were no significant direct effects of speed or age
on specialized knowledge, and general knowledge had a
larger direct effect on the specialized knowledge criterion
variable (.88) than on the puzzle proficiency criterion
variable (.39).
CROSSWORD PUZZLES
147
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Puzzle . - „
Proficiency l*""^ •'Rf
Figure 4.
Structural equation model predicting puzzle proficiency for Study 2.
Item Analyses for Puzzle 3
To more closely examine relations between the predictors
and performance on the more difficult New York Times
puzzle, we carried out additional analyses at the level of
individual items; that is, we computed point-biserial correlations between the accuracy of each individual item (coded 0
for incorrect and 1 for correct) and the various predictor
variables. If the relation between the predictor varied
according to the difficulty of the item, operationalized in
terms of solution probability (i.e., the proportion of the 218
participants who answered the clue correctly), then the
correlations should either systematically increase or decrease as a function of solution probability.
Figure 5 portrays the point-biserial correlations between
accuracy of each of the 78 items in Puzzle 3 and a composite
reasoning variable (i.e., average of z scores for the Cattell's
matrix completion and Shipley's abstraction tests) and a
composite knowledge variable (i.e., average of z scores for
the general information, synonym vocabulary, and antonym
vocabulary tests). The items are ordered along the abscissa
in terms of their solution probability, with the most difficult
items corresponding to those with the lowest solution
probabilities (on the left) and the easiest items corresponding to those with the highest solution probabilities (on the
right). The average point-biserial correlation for the composite reasoning variable was .04, and the average for the
composite knowledge variable was .35. (By way of comparison, the correlations of these predictors with the total
number of items answered correctly in the puzzle were .06
for the composite reasoning variable and .59 for the
148
HAMBRICK, SALTHOUSE, AND MEINZ
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Figure 5. Point-biserial correlations between composite reasoning and knowledge measures and accuracy for individual items in
Puzzle 3, Study 2.
composite knowledge variable.) It is apparent in Figure 5
that the correlations for both variables were relatively stable
across the range of item solution probabilities. In fact, the
average correlations were nearly the same for item solution
probabilities above the median (i.e., .02 for reasoning and
.34 for knowledge) as for item solution probabilities below
the median (i.e., .05 for reasoning and .36 for knowledge).
The point-biserial correlations were also similar across the
range of item solution probabilities for the composite speed
(average = -.01), number of puzzles per week (average = .17), and age (average = .25) variables.
We performed additional analyses to examine the relation
between item solution probability and the ordinal position of
the clue for the item in the list of horizontal (across) and in
the list of vertical (down) clues. If one of the factors
contributing to performance on the puzzle is that the last
items could not be completed because of lack of time, then
the lowest levels of accuracy might be expected on the last
items in the list. Although there was a tendency for negative
correlations between ordinal position and solution probability, the correlations did not differ significantly from zero for
across (r = -.21) or down (r = -.17) clues.
Relations Between Studies 1 and 2
The results of the structural analyses in this study confirm
and extend the results of Study 1 by demonstrating that
general knowledge, word retrieval, and crossword puzzle
experience, but not reasoning, had direct effects on puzzle
proficiency in a sample of participants with greater amounts
of crossword puzzle experience. In addition, the discovery
that there was nearly complete overlap between individual
differences in crossword puzzle proficiency and individual
differences in specialized knowledge suggests that solving
crossword puzzles is to a great extent determined by aspects
of crystallized cognition.
Nevertheless, at least two differences in the results of
Studies 1 and 2 should be mentioned. First, general knowledge, word retrieval, and crossword puzzle experience
accounted for 85% of the variance in puzzle proficiency in
Study 1 but for only 61% of the variance in puzzle
proficiency in Study 2. A likely explanation for this finding
is that there was a greater range of scores on most of the
predictor and criterion tasks in Study 1 than in Study 2 (cf.
standard deviations in Tables 3 and 6). Second, there were
direct effects of age and speed on puzzle proficiency in
Study 2. One possible reason for the different age patterns
across the two studies was the inclusion of a more difficult
crossword puzzle in Study 2. In fact, inspection of Table 6
reveals that the correlations with age were close to zero for
the easy puzzles (Puzzles 1 and 2) but moderately large for
the difficult puzzle (Puzzle 3). Furthermore, when the
structural equation analysis was repeated without the difficult puzzle there was no longer a significant relation
between age and puzzle proficiency. This combination of
results suggests that the positive relation between age and
puzzle proficiency in this study is largely attributable to the
difficult New York Times puzzle.
The direct relation between speed and puzzle proficiency
in this study but not in Study 1 may be attributable to the
higher knowledge levels of the participants in the second
study; that is, because the participants in this study had
higher levels of vocabulary and general information than
their counterparts in Study 1, their performance on at least
the two easier puzzles may have been more limited by
factors related to speed than was the case for the participants
in Study 1.
Predictors of Puzzle Proficiency Across Levels of
Puzzle Difficulty
We performed additional regression analyses to determine
whether each predictor had a significant effect on puzzle
proficiency at the challenging level of puzzle difficulty after
taking into account that predictor's effect on puzzle proficiency at the easy level of puzzle difficulty. The specific aim
of these analyses was to evaluate the prediction that
reasoning might have a stronger effect on puzzle proficiency
at the challenging level of puzzle difficulty than at the easy
level of puzzle difficulty. We carried out a separate analysis
for each predictor variable with performance on the New
York Times crossword puzzle (Puzzle 3) as the criterion
variable and performance on the easy crossword puzzles
(Puzzles 1 and 2) entered before the predictor variable. Only^
two variables—Cattell's matrices and general informationhad significant (p < .01) effects on puzzle proficiency at the
CROSSWORD PUZZLES
challenging level of puzzle difficulty after their effects on
puzzle proficiency at the easy level of puzzle difficulty were
taken into account. Inspection of the regression coefficients
for the predictor variables revealed that these differential
effects were attributable to a stronger effect of Cattell's
matrices on puzzle proficiency at the easy level of puzzle
difficulty and to a stronger effect of general information on
puzzle proficiency at the challenging level of puzzle difficulty. The latter result is consistent with the view that more
difficult puzzles place greater demands on knowledge, but
we have no explanation for the counterintuitive discovery
that abstract reasoning appears to have larger effects on the
easier puzzles.
Moderator Analyses
We repeated in Study 2 the analyses performed in Study 1
to examine moderators of the relations between age and fluid
149
and crystallized cognition. To review, with a composite
index of either fluid or crystallized cognition as the criterion
variable, we evaluated the interactions of age and the
suspected moderator variables after controlling for the main
effects of these variables. We created the composite index of
reasoning by averaging z scores for the Shipley abstraction
test and Cattell's matrix completion test, and we created the
composite index of knowledge by averaging the z scores for
the general information test and the synonym and antonym
vocabulary tests.
The results of the moderator analyses for Study 2 are
summarized in Table 5. Note that, as in Study 1, none of the
interactions of age and crossword puzzle experience with
any of the experience measures were significant. Data
relevant to the analysis on the composite reasoning measure
are displayed in the top left panel of Figure 6, where it can be
seen that the age functions for three crossword puzzle
2
Less than 2
<N=14.Afle=47)
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(N 133,AQe=56)
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(N=104.Age=51)
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20
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50
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(N=111,Age=52)
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(N=14.Age=47) .,
.
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20
30
40
50
60
Chronological Age
Figure 6. Relations of age to composite measures of fluid (top) and crystallized (bottom) cognition
as a function of amount of crossword experience (left) and level of the other type of cognition (right),
Study 2.
70
HAMBRICK, SALTHOUSE, AND MEINZ
150
experience groups were nearly parallel. There is thus no
indication that amount of crossword puzzle experience alters
the magnitude of age-related decreases in measures of
abstract reasoning. Data relevant to the analysis on the
composite knowledge measure are displayed in the bottom
left panel of Figure 6, where it appears that there is a
tendency for a somewhat greater age-related increase in
knowledge for participants with the least amount of crossword experience. This finding is counterintuitive and should
be treated cautiously, because none of the interactions were
significant and there were very few individuals with low
amounts of crossword puzzle experience in this study.
The interaction of age and knowledge predicting the
composite index of reasoning was not significant, F(l, 214) =
2.12, p> .10. The top right panel of Figure 6 contains results
relevant to this analysis, and one can see that there was a
tendency for greater age-related reasoning decreases in
participants with the lowest levels of knowledge. The
interaction of age and reasoning predicting knowledge also
was not significant, F(l, 214) = 2.69, p > .10. The age
functions displayed in the bottom right panel of Figure 6
suggest that there were somewhat smaller age-related increases in knowledge for participants with the lowest levels
of reasoning.
Study 3
The results of Studies 1 and 2 suggest that abstract
reasoning ability plays little role in determining puzzle
proficiency. However, the tests of reasoning administered in
those studies may not have reflected the primary type of
reasoning involved in crossword puzzle solving. Specifically, crossword puzzle solving requires working within
both semantic constraints and physical constraints imposed
by the puzzle's interlocking grid system, because the answer
to a clue must not only have the correct semantic content but
must also contain specific letters in positions compatible
with intersecting answers. We attempted to capture this
aspect of problem solving in Study 3 by including a test of
analytical reasoning in which successful solutions require
simultaneous consideration of multiple constraints. Reasoning should emerge as a significant predictor of puzzle
proficiency if solving crossword puzzles involves this type
of reasoning. Primarily for purposes of contrast, we also
administered another test of reasoning: the cube assembly
test. Cube assembly is a spatial visualization task that has no
apparent relation to crossword puzzle solution, and thus we
predicted weak or nonexistent relations to puzzle proficiency
for this measure.
The second objective of Study 3 was to evaluate whether
either the level of self-rated interest or the level of self-rated
knowledge for a particular topic area interacted with age in
the prediction of an individual's level of objective knowledge in that area. That is, self-evaluations of interest may
function as moderators of the age relations if people tend to
narrow their interests and concentrate in a smaller number of
domains as they grow older. Similarly, self-evaluations of
knowledge may function as moderators of the relations
between age and measures of objective knowledge if with
increasing age people tend to concentrate in domains for
which they feel most knowledgeable. In short, one might
expect greater age-related knowledge increases in topic
areas with high ratings of interest, high self-ratings of
knowledge, or both. We investigated these predictions by
obtaining ratings of interest and knowledge levels for 10
topic areas (e.g., American history, geography, mythology,
etc.) before administration of the general information test
and of a new test of general information. We then evaluated
the interactive effects of age and self-ratings of interest and
knowledge on objective knowledge in multiple regression
analyses. In addition, we examined the standard deviations
of self-rated interest and self-rated knowledge to determine
whether there is a narrower range of self-rated interest or
self-rated knowledge with increasing age.
Method
Participants
The participants in this study were 195 adults (see Table 1 for
descriptive characteristics) recruited through the same newspaper
advertisement used to solicit participants for Study 2. There was a
higher percentage of women than men and, as in Study 2, the
participants had more crossword puzzle experience than the
participants in Study 1 (cf. Table 2). As in previous studies, the
relations to age and to a composite measure of puzzle proficiency
were generally similar across the different measures of experience.
The bottom left panel of Figure 1 portrays the distributions of age
and number of puzzles attempted per week in this sample.
Procedure
The following tests and questionnaires were administered in the
same order to all participants in a single session of approximately
2.5 hr: background questionnaire, New York Times puzzle (Puzzle
3), Puzzle 1, Puzzle 2, word identification test, cube assembly test,
General Information Test A, analytical reasoning test, General
Information Test B, pattern comparison test, letter comparison test,
and synonym-antonym vocabulary tests. The tests and questionnaires not administered in Studies 1 and 2 are described below.
In the cube assembly test, participants were shown a pattern of
six squares, representing an unfolded cube. One of the squares was
shaded and corresponded to the bottom of the cube, and two of the
squares contained arrows. The task for participants was to mentally
fold the squares into a cube, and then to decide whether the tips of
the arrows were pointing at one another. The participants were
instructed to check yes if the tips were pointing at one another and
no if they were not. The cube assembly test included two practice
items and 24 test items. Participants were allowed 10 min to work
on the test items.
Two 5-question sections were added to the general information
test to assess knowledge of sports and science and technology. The
revised general information test (now designated General Information Test A) therefore consisted of five questions to measure
knowledge in each of 10 topic areas: American history, American
literature, art and architecture, geography, music, mythology,
science and technology, sports, world history, and world literature.
The new general information test, designated General Information
CROSSWORD PUZZLES
Test B, was a 50-item fill-in-the-blank test designed to assess
knowledge of the same 10 topic areas included in General
Information Test A. Five questions were devoted to each topic area,
and most of the questions were taken from Nelson and Narens's
(1980) article. Participants were allowed 10 min to complete each
of these tests.
The 20 questions in the analytical reasoning test were obtained
from the analytical sections of the Graduate Record Examination
(ORE; as found in GRE: Practicing to Take the General Test,
1994). The test consisted of five groups of statements specifying
the relations among fictitious people, places, things, or events.
Each group of statements appeared on a separate page and was
prefaced by two to three sentences describing the fictitious
scenario. For example, one scenario described rules for designing
two maps, one of subway routes and the other of bus routes. Each
route was assigned a different color, and the following constraints
were specified: (a) blue cannot be used on the same map as purple,
and (b) orange cannot be used on the same map as red, or on the
same map as yellow. The task for participants was to answer four
5-alternative multiple-choice questions designed to assess reasoning based on the relations specified in the statements. An example
of a question from the scenario described above was: "If yellow
and purple are used on the subway map, the third color used on the
map must be: (blue, orange, purple, tan, or yellow)." Participants
were allowed 20 min to work on this test.
151
between the general knowledge measures and the puzzle
proficiency measures. It can also be seen that there was a
strong negative correlation between age and the analytical
reasoning measure but a strong positive correlation between
age and the difficult puzzle measure (Puzzle 3). These latter
correlations are intriguing, because although both the analytical reasoning test and the New York Times puzzle are
intellectually challenging the age relations for these measures were opposite in direction. Inspection of the correlations of other variables with the analytical reasoning and
Puzzle 3 measures suggests that knowledge, and particularly
knowledge of word meanings, may be responsible for this
different pattern of age relations. To illustrate, the correlations of the two vocabulary measures were .08 and —.06
with the analytical reasoning measure but .42 and .48 with
the Puzzle 3 measure.
Although the analytical reasoning test was postulated to
be more closely related to crossword puzzle solving than
was the cube assembly test, inspection of Table 7 reveals that
both measures had near-zero correlations with the crossword
puzzle measures. These two measures were moderately
correlated with one another (i.e., r = .48), but neither was
related to success at solving crossword puzzles.
Regression analyses that tested for main effects of gender
and interactions of age and gender revealed two variables
with significant gender differences and two variables with
significant Age X Gender interactions. Men performed at
higher levels than women on General Information Test B
(squared semipartial correlation = .044) and on the cube
assembly test (squared semipartial correlation = .040), and
men exhibited larger age-related declines on Puzzle 1 (men,
r = —.33; women, r = .21) and Puzzle 2 (men, r = —.16;
women, r = .33).
The interactions of age and experience on the composite
Results and Discussion
Table 7 displays correlations among the variables and
means and standard deviations of each variable. Reliability
estimates for the predictor tests ranged from .70 to .89,
indicating that all of the measures had adequate reliability.
Mean performance on the puzzles expressed in percentage
of items answered correctly were 78.1 % for Puzzle 1,74.1%
for Puzzle 2, and 54.4% for Puzzle 3.
As in Studies 1 and 2, there were significant correlations
Table 7
Correlation Matrix, Study 3
Variable
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1. Age
—
.32 —
2. NumCWPuz
3. HrWPuz
.29
.51 —
-.52 -.18 -.23
(.84)
4. LetCom
.65
5. PatCom
-.58 -.22 -.22
(.83)
6. AntVoc
.10 -.08 -.07 -.02
.00 (.75)
7. SynVoc
.34
.03 -.05 -.17
-.16
.60
(.70)
8. GenlnfoA
-.08 -.20 -.16
.13
.13
.51
.46
(.88)
.53
.49
(.87)
9. GenlnfoB
.11 -.14 -.02 -.01
-.03
.79
.52
.08 -.06
.32
.14
(.89)
10. AnalReas
-.67 -.25 -.22
.58
.18
.01
.24
.14
.48
-.38 -.10 -.05
.31
.01
(.83)
11. CubeAssm
—
.02
.29
.28
.21
.15
-.01
.11
.19
.22
.23
.10
12. Puzzl
.27
.12
.22
.08
.23
.14
.30
.13
.20
.03
.01
.75 —
13. Puzz2
.42
.48
.46 -.14
.60
.63 (.98)
.46
.33
.19 -.05
-.17
.34
-.06
14. Puzz3
.11 -.00
.37
.33
.36
.09
.00
.49
.53
.57 (.78)
15. WordID
.11
.14
.03
.29
8.0
8.4
9.0
15.5
9.2
42.2 48.9 42.3
51.5
7.2
17.8
30.5
14.3
M
7.3 11.6
5.4
5.4
3.9
15.7
3.2
1.5
8.4
7.3
10.5 14.9 20.5
5.6
7.7
4.7
2.0
SD
Note. N = 195. Correlations with an absolute magnitude greater than .17 were significant at p < .01. Values in parentheses along the
diagonal are reliability estimates. NumCWPuz = number of crossword puzzles attempted per week; HrWPuz = hours solving word puzzles
per week; LetCom = letter comparison; PatCom = pattern comparison; AntVoc = antonym vocabulary; SynVoc = synonym vocabulary;
GenlnfoA = General Information A; GenlnfoB = General Information B; AnalReas = analytical reasoning; CubeAssm = cube assembly;
Puzzl = Puzzle 1; Puzz2 = Puzzle 2; Puzz3 = (New York Times) Puzzle 3; WordID = word identification.
152
HAMBRICK, SALTHOUSE, AND MEINZ
puzzle proficiency measure were significant for four experience measures. The corresponding increments in R2 were
.077 for the total number of puzzles attempted per week,
.090 for the years of attempting at least one puzzle per week,
.083 for the first principal-component measure, and .070 for
the composite of number of puzzles attempted and number
of hours devoted to puzzles per week. In all cases the
interactions reflected greater age-related increases in puzzle
performance among individuals with the least amount of
crossword puzzle experience.
Confirmatory Factor Analyses
and Structural Analyses
The results of the confirmatory factor analysis are displayed in Table 4, where it can be seen that the pattern of
factor loadings was consistent with Studies 1 and 2. The
structural model for this study is displayed in Figure 7,
X2(81, N = 195) = 304.05, NNFI = .80, CFI = .85, Std.
RMR = .10. Although the fit of the model was only
marginal, all relations not represented in Figure 7 were
tested but found to be not significantly different from zero.
As in Studies 1 and 2, general knowledge and crossword
puzzle experience had direct effects on puzzle proficiency
(recall that word retrieval measures were not administered in
the current study), and there was no direct effect of
reasoning. In addition, as in Study 2, both age and speed had
direct effects on puzzle proficiency. Inspection of the
correlations in Table 7 reveals that the age relations were
again largely attributable to the more difficult puzzle (i.e.,
Puzzle 3) and that the speed relations were restricted to the
easier puzzles (i.e., Puzzles 1 and 2).
Figure 7. Structural equation model predicting puzzle proficiency for Study 3.
CROSSWORD PUZZLES
Item Analyses for Puzzle 3
Figure 8 displays the point-biserial correlations between
accuracy of each item in Puzzle 3 and a composite reasoning
variable (i.e., average of z scores for the cube assembly and
analytical reasoning tests) and a composite knowledge
variable (i.e., average of z scores for General Information
Test A, General Information Test B, and the synonym
vocabulary and antonym vocabulary tests). The average
point-biserial correlations were - .07 for reasoning and .30
for knowledge. (The correlations with total number of items
answered correctly were -.11 for the composite reasoning
variable and .30 for the composite knowledge variable.) As
in Study 2, the relations were fairly stable across item
solution probabilities as the average correlations above and
below the median solution probability were -.05 and —.09,
respectively, for reasoning, and .34 and .27, respectively, for
knowledge. The influences were also uniform across solution probabilities for the composite speed (average = - .07),
number of puzzles per week (average = .20), and age
(average = .27) variables. Finally, the correlations between
the ordinal position of the clue in the list and the solution
probability were again not significantly different from zero
(rs = - .21 for down clues and - .26 for across clues).
Moderator Analyses
The composite measure of knowledge in this study
consisted of the average of the z scores for the synonym and
Knowledge
o
Reasoning
0.5
0 0
o
0.4
o
o o
u
ou
o o o
"
o
o
o °o
o
"? 0.2
03
0
A
0
0
o
0.1
A
A
A
-0.1 A
8
AA
AA
A A
A
* AA
-0.2 -
A
A
I
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
l_
0.8
0.9
1
Proportion Correct
Figure 8. Point-biserial correlations between composite reasoning and knowledge measures and accuracy for individual items in
Puzzle 3, Study 3.
153
antonym vocabulary tests and the two general information
tests. The composite measure of reasoning was based on the
average of the z scores from the cube assembly and
analytical reasoning tests.
We repeated the analyses performed in Studies 1 and 2 to
examine moderators of the relations between age and fluid
and crystallized cognition, and the results are summarized in
Table 5. As in earlier studies, none of the interactions of age
and crossword puzzle experience were statistically significant, and once again the data suggest that amount of
cognitive activity, in the form of crossword puzzle solving,
does not alter the magnitude of age-related decreases in
measures of abstract reasoning or of age-related increases in
measures of knowledge. Data relevant to these analyses are
displayed in the left panels of Figure 9.
Neither the interaction of age and knowledge predicting
reasoning, F(l, 191) = 1.05, nor the interaction of age and
reasoning predicting knowledge, F(l, 191) = 0.45, was
statistically significant. Results relevant to these analyses are
displayed in the top right and bottom right panels of Figure
9, respectively. As in the prior studies, therefore, there is
little evidence that the relations between age and measures
of fluid or crystallized cognition are moderated by amount of
crossword puzzle experience or by the level of the other type
of cognition.
Self-Rated Interest and Self-Rated Knowledge
We performed the next series of analyses to examine the
relations among age, self-rated interest, self-rated knowledge, and objective knowledge. Inspection of the correlations among these variables revealed that age was significantly correlated with the self-ratings of interest for three
topic areas—mythology (r = .20), science and technology
(r = .20), and sports (r = .19)—and with self-ratings of
knowledge for four topic areas—music (r = .21), mythology (r = .20), science and technology (r = .20), and sports
(r = .23). Because self-ratings ranged from 1 for high to 5
for low, these correlations indicate lower interest or perceived knowledge with increased age. Age was significantly
correlated with amount of objective knowledge (indexed by
number of questions answered correctly) in only two
domains: mythology (r = —.20) and geography (r = .26).
We next examined the effects associated with age and
either self-rated interest or self-rated knowledge on objective knowledge in a series of hierarchical regression analyses. In these analyses, objective knowledge was predicted
from the cross-product interaction of age and either self-rated
interest or self-rated knowledge after controlling for the
main effects of these variables. The results of the analyses
are summarized in Table 8, where it can be seen that
although there were moderately strong relations between the
self-ratings of interest and the self-ratings of knowledge and
the objective knowledge measures, only 1 of the 21 possible
interactions was statistically significant. These findings are
inconsistent with the view that interest level and perceived
knowledge level moderate the relations between age and
objective measures of knowledge. Finally, neither the corre-
HAMBRICK, SALTHOUSE, AND MEINZ
154
O)
2
2
1.5
1.5
1
1
O)
2to5
^.^ (N=61.Age=45)
O
•ji 0.5
o
More than 5
(N=118,Afle=56)
OC -0.5
DC -0.5
Less than 2
(N=16.Age=45)
-1
Med. Know.
(N=100,Age=51)
(N=47,Age=50)
-1
-1.5
-1.5
-2
20
30
40
50
60
70
-2
20
30
40
50
60
70
2
2
1.5
High Know.
(N=48, Age=53)
1.5
.
Less than 2
(N=16.Age=45)
1
1
High I
(N=51,Age=39)
O) 0.5
0) 0.5
O)
2to5
(N=61.Age=45)
.....
o
—•
....
More than 5
(N=118.Age=56)
0
-0.5 -
7^-"'
-0.5
-1 •
-1
-1.5 -
-1.5
.9
1
20
1
30
1
40
1
50
1
60
1
70
-2
Chronological Age
Med. Reas.
(N=99, Age=52)
20
30
40
Low Reas.
(N=44.Age=64)
50
60
70
Chronological Age
Figure 9. Relations of age to composite measures of fluid (top) and crystallized (bottom) cognition
as a function of amount of crossword experience (left) and level of the other type of cognition (right),
Study 3.
lation between age and the standard deviation of an individual's self-interest ratings across the 10 topic areas (r = - .03),
nor the correlation between age and the standard deviation
of the knowledge ratings (r = —.04), was statistically significant. However, there was a significant negative correlation
(r = -.21) between age and the number of topics for which
the individual rated his or her interest as high or very high.
These findings are therefore mixed with respect to the idea
that interests or perceptions of knowledge narrow with
increasing age, because although there are fewer topics of
high interest with increased age, there was little relation of
age to the range of interest ratings or the rank of knowledge
ratings across the different topics.
Study 4
Despite the use of a test of analytical reasoning requiring
simultaneous consideration of multiple constraints, there
Table 8
Proportions of Variance Associated With Age, Either
Self-Rated Knowledge (SRKnow) or Self-Rated Interest
(SRInt), and Their Interaction, Study 3
Age X
Age X
Age SRKnow SRKnow SRInt SRInt
Art
.003
.139*
.002
.138* .001
American history
.022
.090*
.007
.078* .017
American literature .005
.161*
.002
.060* .017
Geography
.067* .109*
.002
.049* .000
Music
.000
.108*
.000
.123* .000
Mythology
.041*
.323*
.302* .004
.001
Science/Technology .011
.166*
.007
.187* .003
Sports
.007
.296*
.022
.266* .014
World history
.026
.107*
.008
.116* .001
World literature
.023
.232*
.026*
.262* .007
Overall
.000
.217*
.000
.163* .006
*p<.01.
Domain
CROSSWORD PUZZLES
was again no direct effect of reasoning on puzzle proficiency
in Study 3. One explanation for this finding is that most clues
in crossword puzzles are straightforward factual references
that require only knowledge to solve. However, it also is
possible that even the daily New York Times puzzle administered in Studies 2 and 3 (i.e., Puzzle 3) was quite easy for
avid puzzlers to solve and that more challenging crossword
puzzles include clues that require reasoning to solve. To
examine this possibility, we administered a weekend New
York Times puzzle (designated Puzzle 4) in Study 4, because
anecdotal reports suggest that weekend puzzles are considerably more difficult than daily puzzles.
Two new sets of tests were included in this study to
provide mixed or hybrid tests of reasoning and knowledge.
These tests, consisting of verbal analogies and sentence
completions, were postulated to require both verbal knowledge and reasoning. For example, in the verbal analogies test
the successful respondent must not only know the meanings
of all relevant words, but he or she must also determine how
the relation between the first two words might apply to a
second pair of words. The sentence completion test consisted of sentences with one or two blanks that were to be
filled with words from among a set of alternatives. As in the
verbal analogies test, the successful respondent must have
sufficient knowledge to comprehend the meaning of the
sentence in addition to the ability to deduce the best
completions of the missing words. If the reasoning involved
in crossword puzzle solving resembles the type of contextually embedded reasoning that seems to be required by these
tests, then there should be a significant relation of the scores
on these tests to the measures of crossword puzzle proficiency after measures of verbal knowledge have been
statistically controlled.
Another consistent finding of the previous studies was
that knowledge, as measured by tests of general information
and vocabulary, is an important predictor of puzzle proficiency. Furthermore, knowledge of esoteric words was a
particularly important predictor of puzzle proficiency in
Study 2. To illustrate, the scores on the difficult puzzle
correlated .87 with the Esoteric Knowledge A measure, but
only .56 with the general information measure, and .38 and
.49 with the antonym and synonym vocabulary measures,
respectively. Although the strong relation between puzzle
proficiency and esoteric knowledge is not particularly surprising given that the items on the esoteric knowledge tests were
selected from crossword puzzles, this pattern of correlations
could be interpreted as suggesting that experience solving
crossword puzzles is associated with the acquisition of
specialized knowledge in the form of common crossword
puzzle words. However, another possibility is that the
esoteric knowledge tests are simply more difficult assessments of knowledge than are the general information and
synonym-antonym vocabulary tests. If this latter interpretation is correct, puzzle proficiency would also be expected to
have stronger relations with more advanced knowledge
measures consisting of items not specifically selected from
crossword puzzles than with the synonym-antonym and
general information measures. We therefore administered
two more difficult vocabulary tests in the current study.
155
The final objective of Study 4 was to replicate and extend
earlier analyses examining moderators of age-cognition
relations in a new sample.
Method
Participants
The participants in this study were 200 adults (see Table 1 for
descriptive characteristics) recruited through another newspaper
advertisement specifying that the individuals had to complete at
least one crossword puzzle per week to participate. The means,
standard deviations, and correlations with age and puzzle proficiency are summarized in Table 2, where it can be seen that
although there was some variation in the correlations across
experience measures, the patterns of relations were generally
similar across measures. The distributions of age and number of
puzzles attempted per week in this sample are portrayed in the
bottom right panel of Figure 1.
Procedure
Participants who arrived early were allowed 5 min for the
solution of Puzzle 2. The following tests and questionnaires were
then administered in the same order to all participants in a single
session of approximately 2.5 hr: background questionnaire, New
York limes Puzzle 3, New York Times Puzzle 4, General Information Test A, Analytical Reasoning A, Sentence Completion A,
Verbal Analogies A, synonym and antonym vocabulary, letter
comparison, pattern comparison, Sentence Completion B, Analytical Reasoning B, advanced synonym and antonym vocabulary, and
Verbal Analogies B. The tests not administered in previous studies
are described below.
The new puzzle (designated Puzzle 4) was obtained from The
New York Times Toughest Crossword Puzzles: Volume 4 (1993).
The puzzles in this collection appeared in the Saturday edition of
The New York Times between January 5, 1985, and December 27,
1986. The selected puzzle (Puzzle #82) did not have a specialized
theme and was 76 words in length (39 across clues and 37 down
clues) within a 15 X 15 grid. Participants were allowed 15 min to
solve the puzzle.
The two versions of the analytical reasoning test were identical
in format to the analytical reasoning test administered in Study 3,
except that new items were added and it was divided into two
12-question versions, A and B. Ten min were allowed for each
version.
The items on the sentence completion test were obtained from
verbal sections of the ORE (as found in ORE: Practicing to Take
the General Test, 1994). Each of the two versions consisted of 10
sentences in which one or two words had been omitted. To
illustrate, one of the items was "Aalto, like other modernists,
believed that form follows function; consequently, his furniture
designs asserted the
of human needs, and the furniture's form
was
human use." Five words or pairs of words appeared
below each sentence, and the participants' task was to choose from
among these alternatives the word or pair of words that best fit the
meaning of the sentence. Participants were allowed 5 min for each
version.
The items on the verbal analogies test were also obtained from
verbal sections of the ORE. The two versions of this test each
consisted of 10 related pairs of words (e.g., despotic:tyranny),
each followed by 5 pairs of words. Participants' task was to
complete the analogy by choosing from among the 5 alternatives
the pair of words that expressed a relationship similar to that
156
HAMBRICK, SALTHOUSE, AND MEINZ
expressed in the original pair. Participants were allowed 5 min to
work on each version of the test.
The items on the more difficult synonym and antonym vocabulary test (designated advanced synonym and antonym vocabulary)
were obtained from verbal sections of the ORE. The tests consisted
of 10 5-alternative synonym items and ten 5-alternative antonym
items. Among the items were treacle, paternoster, and calumnious.
Participants were allowed 5 min to work on the test.
Results and Discussion
Table 9 displays correlations among the variables and the
means, standard deviations, and estimated reliabilities for
each variable. Reliability estimates for most of the predictor
variables were respectable, with a range from .49 to .91.
Performance on the three puzzles expressed in terms of
percentage of words answered correctly were 63.8% for
Puzzle 2, 52.2% for Puzzle 3, and 24.2% for Puzzle 4.
Inspection of Table 9 reveals that several results from prior
studies were replicated in this study. For example, as in
Studies 2 and 3, the age correlations were stronger for the
New York Times puzzles (3 and 4) than for the less difficult
puzzle (2). And as in Study 3, age was negatively correlated
with the analytical reasoning measures but positively correlated with the difficult puzzle measures. This differential
pattern again seemed to be attributable to the role of word
knowledge, as the correlations with the vocabulary measures
ranged from .43 to .54 for the scores on the difficult puzzles
but only —.01 to .19 for the analytical reasoning measures. A
new result in this study is the discovery that the advanced
vocabulary measures had higher correlations with the difficult puzzle measures (i.e., .43 to .54) than with the easier
puzzle measure (i.e., .13 and .16). This pattern is consistent
with the assumption that success with die New York Tunes
puzzles is more dependent on knowledge of rare or unusual
words than is success with less difficult puzzles.
It also is apparent in Table 9 that both the sentence
completion and verbal analogies measures had moderate
correlations with the puzzle measures. We therefore performed regression analyses to evaluate whether the sentence
completion and verbal analogies measures contributed to the
prediction of puzzle proficiency after controlling for a
measure of verbal knowledge. In these analyses, a composite
measure of puzzle proficiency (the average of z scores for
Puzzles 3 and 4) was predicted from the verbal analogies and
sentence completion measures after control of a composite
measure of vocabulary based on the average of the z scores
for the original and advanced synonym and antonym vocabulary measures. These analyses revealed that neither the
increment in R2 for sentence completion (i.e., .001) nor that
for verbal analogies (i.e., .005) was statistically significant.
It therefore does not appear that the reasoning involved in
these tests is an important predictor of crossword puzzle
performance.
We conducted another regression analysis to determine if
there was unique variance in the measures of crossword
puzzle proficiency associated with the advanced vocabulary
measures after statistical control of the easy vocabulary
measures. The increment in R2 associated with the advanced
vocabulary measures was significantly greater than zero
(i.e., .062, p < .01), suggesting that the two sets of vocabulary tests were assessing somewhat different information.
Confirmatory Factor Analyses and Structural
Analyses
The results of the confirmatory factor analysis are displayed in Table 4, where it can be seen that the pattern of
factor loadings was generally consistent with those of the
previous studies. The structural model for Study 4, which
provided an adequate fit to the data, x2(69, N = 200) =
192.23, NNFI = .87, CFI = .90, Std. RMR = .08, is
portrayed in Figure 10. Notice that general knowledge and
crossword puzzle experience again had direct effects on
puzzle proficiency. Unlike the previous two studies, however, there were no direct effects of age or speed on puzzle
proficiency, and there was a significant negative relation
between reasoning and puzzle proficiency. This latter result
is the first indication of a direct relation between reasoning
and puzzle proficiency, but the fact that it is negative
indicates that people who did better on the analytical
reasoning test answered fewer of the items in the puzzles.
Because the correlations between the analytical reasoning
and puzzle measures were close to zero (see Table 9), some
type of suppressor relationship may have been operating
among the reasoning, puzzle proficiency, and either knowledge or puzzle experience measures.
Item Analyses for Puzzles 3 and 4
We carried out analyses at the level of individual items for
both Puzzles 3 and 4. Figure 11 displays the point-biserial
correlations between item accuracy in Puzzle 3 and a
composite reasoning variable (i.e., the average of z scores
for the Analytical Reasoning A and B tests) and a composite
knowledge variable (i.e., the average of z scores for the
general information, synonym vocabulary, and antonym
vocabulary tests). The average point-biserial correlations
were .02 for reasoning and .36 for knowledge. (The correlations with the total number of items answered correctly were
.03 for the composite reasoning variable and .62 for the
composite knowledge variable.) Inspection of Figure 11
reveals that the relations were fairly stable across item
solution probabilities, and the averages above and below the
median solution probability were .05 and .00, respectively,
for reasoning, and .36 and .36, respectively, for knowledge.
Stable patterns were also evident for the composite speed
(average = -.04), number of puzzles per week (average = .19), and age (average = .23) variables. Correlations
between the ordinal position of the clues and the solution
probabilities were again not significant for the across clues
(r = -.20) or for the down clues (r = -.27).
The point-biserial correlations between item accuracy and
the composite reasoning and knowledge variables for Puzzle
4 are displayed in Figure 12. The average point-biserial
correlations were .03 for reasoning and .25 for knowledge,
and the correlations with the total number of items answered
157
CROSSWORD PUZZLES
Stu
O\ •
ariabl
i;
i
OS |
U &
3 ?
^ o >cooi
HAMBRICK, SALTHOUSE, AND MEINZ
158
.60
Figure 10. Structural equation model predicting puzzle proficiency for Study 4.
correctly were —.06 for reasoning and .66 for knowledge.
Again, die pattern was very similar across the range of item
solution probability, as the average correlations above and
below the median solution probability were .02 and .05,
respectively, for reasoning, and .31 and .19, respectively, for
knowledge. The correlations were also stable with the
composite speed (average = .01), number of puzzles per
week (average = .09), and age (average = .12) variables.
Finally, there was a small but significant positive correlation
between solution probability and the ordinal position of the
clue in the list of down clues (r = .33) but no significant
correlation between solution probability and ordinal position
in the list of across clues (i.e., r = .02).
Moderator Analyses
Analyses examining moderators of age-cognition relations are summarized in Table 5. As in the previous studies,
the Age X Experience interactions were not significant in
the prediction of either an index of fluid cognition (i.e., the
average of scores on the two versions of the analytical
reasoning test) or an index of crystallized cognition (i.e.,
average of z scores for the four vocabulary measures and the
general information measure). Data relevant to these analyses are illustrated in the left panels of Figure 13.
There was a significant Age X Knowledge interaction in
the prediction of the composite index of reasoning, F(l,
196) = 13.65, p < .01. The results displayed in the top right
panel of Figure 13 indicate that this interaction was attributable to greater age-related decreases in reasoning for adults
with greater amounts of knowledge. This finding is obviously counterintuitive, and we have no satisfactory explanation for it. Finally, the Age X Reasoning interaction in the
prediction of knowledge was not statistically significant,
F(l, 196) = 0.30. Data relevant to this comparison are
portrayed in the bottom right panel of Figure 13.
CROSSWORD PUZZLES
Knowledge
o
Reasoning
0.5
0.4
0
O
o
o
cP
o
O
o
cP
0.2
•£•
-0.1
-0.2 -
-0.3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Proportion Correct
Figure 11. Point-biserial correlations between composite reasoning and knowledge measures and accuracy for individual items in
Puzzle 3, Study 4.
General Discussion
Before discussing the major results of this project it is
important to briefly review the nature of the criterion
measures and the levels of experience of the samples in these
studies. Four different puzzles were used to assess crossword puzzle proficiency, and they can be assumed to
represent a wide range of difficulty because, although some
were solved by many participants within 5 min, one puzzle,
from a weekend New York Times, was not completely solved
by any of the participants within the allocated 15 min. The
average time per solved clue can serve as a rough index of
difficulty, and the ranges for this measure were 5.9-12.4 s
per item for Puzzles 1 and 2, 20.0-22.1 s per item for Puzzle
3, and 48.9 s per item for Puzzle 4. The range of difficulty
with this index is therefore about a factor of 8 between the
easiest and most difficult puzzles. Figures 5, 8, 11, and 12
indicate that there was also an extensive range of difficulty,
as indexed by the probability of solution, across individual
items in the New York Times puzzles administered in Studies
2, 3, and 4.
The puzzles were administered under timed conditions,
but we have four reasons for believing that this 4id not
compromise the meaningfulness of the results. First, as just
noted, the solution times per item ranged from 5.9 to 48.9 s
per word, whereas the time required merely to copy the
words in Study 1 was only 2.0 s per word, suggesting that
additional processes besides copying the items were in-
159
volved in solving the puzzles. Second, the correlations
between the perceptual speed measures and the puzzle
proficiency measures were generally low, particularly for the
challenging New York Times puzzles. This implies that
individual differences in speed were not a major factor in the
individual differences in the puzzle proficiency measures.
Third, only one of the correlations between ordinal position
of the clue and probability of solution of the item was
statistically significant, and it was positive rather than
negative; thus it does not appear that the participants were
simply not able to attempt all of the items in the puzzles.
Fourth, allowing only a limited time to work on the puzzles
is not necessarily unrealistic, because many people probably
devote a fixed period, such as during breakfast, or while
commuting, to work on a given puzzle. Finally, it should
also be noted that we are not claiming that our assessments
have measured the maximum levels of performance of
which the participants were capable. Instead, we are suggesting that performance under the timed conditions of these
studies appears to provide a sensitive and valid assessment
of an individual's proficiency in solving certain types of
crossword puzzles.
The participants in the studies also had a wide range of
experience working crossword puzzles. For example, inspection of Table 2 reveals that the average number of puzzles
attempted per week was 3.2 in Study 1 and between 7.2 and
8.3 in Studies 2—4. Furthermore, the mean number of hours
per week spent working on word puzzles ranged from 2.8 to
Knowledge
o
Reasoning
0.5
0.4
oo° o
=•0.3
0.1
A
f
A
-Ai--
-0.1
-0.2
0
0.1
0.2
0.3
0.4
1
1
1
0.5
0.6
0.7
I
0.8
I
0.9
1
Proportion Correct
Figure 12. Point-biserial correlations between composite reasoning and knowledge measures and accuracy for individual items in
Puzzle 4, Study 4.
HAMBRICK, SALTHOUSE, AND MEINZ
160
2
2
1.5
1.5
2 to 5
(N=40, Age=44)
1
O)
O)
f
0.5
.§0.5
O
o
o
Med. Know. N «>
(N=100. Age=52) *
1
-0.5
-0.5
More than 5
(N=123, Age=55)
-1
Low Know.
(N=50, Age=48)
-1
Less than 2
(N=16,Age=50)
-1.5
-2
High Know.
(N=50, Age=58)
1
-1.5
20
30
40
50
60
-2
70
20
30
40
50
60
70
£
1.5 •
1.5
More than 5
(N=123, Age=55)
1
2 to 5
(N=40,Age=44)
8, W
_o>
O
o
1 .
0)
T? 05
O
£
o
-0.5
-1
-1.5
-1.5 •
20
30
40
50
60
70
Chronological Age
-^Tff*~
—~~
---•""""
—
_2 -0.5
Less than 2
(N=16,Age=50)
-1
o
High Reas.
(N=49. Age=41)
v
—
*
-'tied. Reas.
(N=100, Age=53)..
....-•'
_.••*"
.. '
Low Reas.
(N=51,Age=62)
•""
.9
20
•
30
,
40
i
50
i
60
70
Chronological Age
Figure 13. Relations of age to composite measures of fluid (top) and crystallized (bottom)
cognition as a function of amount of crossword experience (left) and level of the other type of
cognition (right), Study 4.
7.4, meaning that, on average, the participants in these
studies devoted from 24 to 63 min per day attempting to
solve crossword puzzles. By virtually any standard, this is a
fairly substantial investment of time, particularly when
extended over a period of years, as was the case for many
participants. In fact, the entries in Table 2 reveal that only in
Study 1 was the average amount of cumulative experience
working puzzles less than 19 years, and even in that sample
it was over 11 years. The results of this project can therefore
be assumed to apply to a fairly wide range of crossword
puzzles and to samples of individuals ranging from novices
to serious crossword aficionados.
Predictors of Puzzle Proficiency
Inspection of Tables 3, 6, 7, and 9 reveals that many
variables had statistically significant correlations with the
measures of puzzle proficiency. For example, measures of
vocabulary, general information, anagram solution, and
knowledge of the frequency of letter sequences were all
significantly related to one or more measures of crossword
puzzle proficiency. However, the variables do not all reflect
distinct constructs, and their relations to puzzle proficiency
are not all independent of one another. It is for these reasons
that it is desirable that the analyses be conducted at the level
of broader constructs and that the influences be examined
simultaneously rather than separately. The confirmatory
factor analyses and structural equation models were designed to accomplish these goals.
The results of the confirmatory factor analyses are summarized in Table 4. The generally similar pattern of factor
loadings for the variables common to each study implies that
comparable constructs were assessed in each study. The
structural equation models portrayed in Figures 2, 4, 7, and
CROSSWORD PUZZLES
10 were also similar in several respects. For example, in all
four models there were significant direct positive relations
between the knowledge and experience constructs and the
puzzle proficiency construct. The knowledge relations are
not surprising, because in many respects crossword puzzles
can be considered tests of knowledge. In fact, the correlation
of .99 in Study 2 between the construct representing puzzle
proficiency and the construct representing the type of
knowledge commonly queried in crossword puzzles suggests that the individual differences in certain types of
knowledge overlap completely with the individual differences associated with successful crossword puzzle solution.
There also were direct relations of crossword puzzle
experience on puzzle proficiency in every study. Although
one might suspect that greater amounts of experience
contribute to more effective crossword puzzle performance
because of increased quantities of knowledge, these relations were found to be independent of those from the
knowledge construct. It is possible that the experiential
influences are attributable to the acquisition of certain types
of crossword-specific knowledge, perhaps in the form of
particular types of solution strategies or information rarely
encountered outside of the context of crossword puzzles.
There was some evidence of a relation between crossword
puzzle experience and the measures of esoteric knowledge
in Study 2, but little or no relation was evident between
puzzle experience and other crossword-specific knowledge
measures (e.g., knowledge of the frequencies of letter
sequences). An alternative interpretation of the direct relations between experience and puzzle proficiency is that a
third factor is responsible for both crossword puzzle experience and crossword puzzle proficiency. For example, it is
possible that some type of personality characteristic is
related to interest in solving particular kinds of puzzles and
that it is responsible for the observed relation between
crossword experience and puzzle proficiency.
The word retrieval and transformation efficiency construct had a direct relation to puzzle proficiency in both
studies (1 and 2) in which it was examined. This relation
indicates that people who are better at solving crossword
puzzles are also better at solving anagrams, creating words
from sets of letters, and so on. Because this relation is
independent of those from knowledge and experience, it can
be inferred that facility at manipulating words is another
factor contributing to success at crossword puzzle solution.
There were also some differences across studies, particularly with respect to the direct relations of age and speed on
puzzle proficiency. Both of these relations were significant
in Studies 2 and 3, but not in Studies 1 and 4. These
discrepancies may be attributable to a combination of the
experience level of the samples and the difficulty of the
puzzles; that is, the difficult puzzles (Puzzles 3 and 4) had
stronger positive relations to age and weaker relations to the
perceptual speed measures than the easy puzzles (Puzzles 1
and 2). The correlations between age and the puzzle
measures were positive in Study 1, but most of the participants in that sample were considerably less experienced than
those in the other studies. It is therefore possible that
the absence of significant direct relations of age and speed
161
on puzzle proficiency in Study 1 was attributable to the
speed and experience factors canceling one another. The
lack of a significant direct relation from age to puzzle
proficiency in Study 4 may be attributable to knowledge
mediating most of the positive age relations on the measures
of puzzle performance.
The positive relations between age and success on the
more difficult New York Times puzzles (Puzzles 3 and 4) in
Studies 2, 3, and 4 are intriguing. One possible explanation
is that items in these puzzles are more likely than those in
easier puzzles to refer to cohort-specific knowledge possessed to a greater extent by older individuals than younger
ones. For example, one of the items with the strongest
positive age relations was "Soprano Gluck" (Alma), and
because Alma Gluck was popular in the early years of this
century this information may have been more accessible to
the older participants.
Perhaps the most surprising result from the predictor
analyses was the lack of any direct influences of the
reasoning measures on puzzle proficiency. We certainly
expected a positive relation, as did many of the participants
when they were asked whether reasoning is involved in
solving crossword puzzles. However, we not only found no
direct influences with the Cattell matrices measure involving
geometric pattern stimuli and the Shipley series completion
measure involving verbal and numeric material, but also
none with the analytical reasoning measure, which we had
specifically selected because it required simultaneous consideration of multiple constraints. Even the measures of
performance in the verbal analogies and sentence completion tests in Study 4 did not have significant relations to the
puzzle measures after controlling for the influence of
vocabulary knowledge. The only significant direct relation
between the reasoning measures and the puzzle proficiency
construct was in Study 4, and that was actually negative,
indicating that individuals with higher scores on the analytical reasoning tests were less successful on the crossword
puzzles than individuals with lower scores.
We also considered the possibility that reasoning might be
important as a predictor of puzzle proficiency only at certain
levels of knowledge. For example, there might be greater
requirements for reasoning at low levels of knowledge in
order to decipher clues that are easily recognized by people
with greater knowledge. Alternatively, some clues may
require a certain amount of knowledge before sufficient
information is available for reasoning to occur. We investigated both of these possibilities by examining the interaction
of the composite reasoning and knowledge variables in the
prediction of puzzle proficiency. However, in none of the
studies was the interaction significant, and in all cases it was
quite small (i.e., increment in R2 < .011).
The item analyses for Puzzles 3 and 4 in Studies 2, 3, and
4 are also relevant to the role of reasoning, because the item
solution probabilities ranged from less than. 1 to greater than
.9. This represents a very large range in item difficulty, but
there is little indication in Figures 5, 8, 11, and 12 that the
relations of reasoning were greater for the more difficult
items than for the easier items.
HAMBRICK, SALTHOUSE, AND MEINZ
162
The consistency of the results across the four studies
indicates that there is little evidence that crossword puzzle
solving involves processes of reasoning. Of course, our
conclusions may not generalize beyond the conditions of
these studies, but it is important to note that we examined a
wide range of puzzle difficulty and several different types of
reasoning. It is possible that other types of reasoning might
have stronger relations, or that the relations might be more
pronounced with alternative kinds of puzzles, such as
puzzles with a subtle theme or cryptic puzzles in which most
of the clues are deliberately ambiguous. Nevertheless, there
is no indication from the current studies that either inductive
or analytical reasoning processes contribute to success in
crossword puzzle solving.
Moderators of Age-Cognition Relations
The second major goal of this project was to investigate
possible moderators of the negative relations between age
and measures of fluid cognition (e.g., reasoning) and of the
positive relations between age and measures of crystallized
cognition (e.g., knowledge). Of primary interest was whether
people who had extensive amounts of experience with a
mentally demanding activity would exhibit smaller agerelated decreases in measures of fluid cognition, or greater
age-related increases in measures of crystallized cognition,
than people with less experience in that type of activity.
Solution of crossword puzzles was selected as the relevant
activity because of the ease of obtaining large samples of
participants and the widespread assumption that solving
crossword puzzles is an intellectually demanding activity.
The second, third, and fourth columns of Table 10 summarize
the results of the four studies in terms of the proportions of
variance associated with age, with the composite measure of
crossword puzzle experience, and with the interaction of age
and experience. It is apparent that there were large agerelated effects in each study and significant effects associTable 10
Proportions of Variance Associated With Age
and Potential Moderators in the Four Studies
Moderators and predictors
Experience
Study
Age
1
2
3
4
.201*
.336*
.368*
.294*
1
2
3
4
.080*
.021
.021
.052*
*p < .01.
AgeX
Mod.
Criterion = reasoning
.030*
.002
.025
.000
.042*
.000
.006
.002
Criterion = knowledge
.138*
.013
.002
.013
.015
.001
.000
.020
Mod.
Knowledge/
reasoning
Mod.
AgeX
Mod.
.217*
.056*
.025*
.056*
.002
.007
.003
.037*
.217*
.056*
.025*
.056*
.005
.012
.002
.001
ated with crossword puzzle experience in Study 1. However,
the critical interaction of age and experience, testing whether
the age relations were moderated by the amount of experience, were very small and not statistically significant in any
of the studies. These data therefore provide no evidence that
the relations between age and either fluid or crystallized
measures of cognition vary according to the number of
crossword puzzles attempted in an average week.
The fifth and sixth columns in Table 10 summarize the
analyses of possible moderating effects of one type of
cognition on the relations of age to the other type of
cognition. The top four rows contain the results with the
reasoning measures as the criterion and the knowledge
measures as the potential moderators. Although in each case
there was a significant main effect of knowledge, corresponding to the different positions of the lines representing level of
knowledge in the top right panels of Figures 3, 6, 9, and 13,
only in Study 4 was the interaction of age and knowledge
statistically significant. Moreover, inspection of the results
depicted in Figure 13 reveals that this interaction was
opposite to what one might expect, because the smallest
age-related decreases in reasoning were evident among the
individuals with the lowest levels of knowledge.
Results with the knowledge measures as the criterion and
the reasoning measures as the potential moderators are
contained in the bottom four rows of Table 10. As one might
expect, people with high levels of reasoning also tended to
have high scores on the knowledge measures. However, the
lack of a significant interaction between age and reasoning
indicates that the relations between age and knowledge did
not vary according to the level of reasoning.
The role of self-assessed knowledge and self-assessed
interest as potential moderators of the relations between age
and knowledge was investigated in Study 3. Although there
were significant main effects of both self-rated interest and
self-rated knowledge on the measures of knowledge in each
of the 10 topic areas (see Table 8), none of the interactions
between age and self-rated interest was statistically significant, and only one interaction between age and self-rated
knowledge was significant. These results indicate that people
tend to be more knowledgeable in areas in which they
express interest and in which they believe that they are
knowledgeable but that neither self-rated interest nor selfrated knowledge moderate the relations between age and
scores on the knowledge tests. At least on the basis of these
results, therefore, it does not appear that there are larger
age-related increases in domains in which the individuals
report that they are most interested or knowledgeable. It is
possible that stronger moderating effects of the self-ratings
would be found in a sample in which there were larger
age-related increases in knowledge, but it should be noted
that the current samples were likely positively biased
relative to the general population, because the average level
of education was high, and most of die participants were
recruited because of their involvement in intellectually
engaging activities.
The findings of diese studies are consistent with several
other reports suggesting that it is relatively difficult to find
evidence of moderators of die relations between age and
CROSSWORD PUZZLES
measures of cognitive functioning. For example, Salthouse
(1991) reviewed results indicating that neither health status
nor educational level appear to be important moderators of
age-cognition relations. Fozard and Nuttall (1971) and
Avolio and Waldman (1994) both found that the relations
between age and different cognitive variables were very
similar across different occupational or socioeconomic levels, and Avolio and Waldman also reported that neither race
nor gender interacted with age in a sample of more than
24,000 adults. Finally, Meinz and Salthouse (1998b) found
little evidence of Age X Gender interactions in a variety of
cognitive variables in a meta-analysis involving more than
20 separate studies. Amount and type of experience with
crossword puzzles may therefore be similar to other kinds of
individual-difference variables that have been found to
affect the level of certain cognitive variables but not the
relations of age to those variables.
Summary
The results of the current studies seem convincing with
respect to the two major issues under investigation. First,
success in solving crossword puzzles largely appears to be a
function of the amount of knowledge possessed by the
individual, with little or no contribution of reasoning ability.
Second, there is no evidence of a moderating effect of
crossword puzzle experience on the negative relations
between age and reasoning, or on the positive relations
between age and knowledge. Furthermore, there is little
evidence mat the relations between age and one type of
cognition are moderated by the level of the other type of
cognition.
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Received September 12,1997
Revision received January 9,1998
Accepted April 8, 1998
Members of Under-represented Groups:
Reviewers for Journal Manuscripts Wanted
If you are interested in reviewing manuscripts for APA journals, the APA Publications
and Communications Board would like to invite your participation. Manuscript reviewers
are vital to the publications process. As a reviewer, you would gain valuable experience
in publishing. The P&C Board is particularly interested in encouraging members of
underrepresented groups to participate more in this process.
If you are interested in reviewing manuscripts, please write to Demarie Jackson at the
address below. Please note the following important points:
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To be selected as a reviewer, you must have published articles in peer-reviewed
journals. The experience of publishing provides a reviewer with the basis for
preparing a thorough, objective review.
To select the appropriate reviewers for each manuscript, the editor needs detailed
information. Please include with your letter your vita. In your letter, please identify
which APA journal you are interested in, and describe your area of expertise. Be as
specific as possible. For example, "social psychology" is not sufficient—you
would need to specify "social cognition" or "attitude change" as well.
Reviewing a manuscript takes time. If you are selected to review a manuscript, be
prepared to invest the necessary time to evaluate the manuscript thoroughly.
Write to Demarie Jackson, Journals Office, American Psychological Association, 750
First Street, NE, Washington, DC 20002-4242.