Ideal Answers to Chapter 6 Questions
QUESTION 6.1a. A one sample t-test showed that it does take more than the comparison standard of
$20 (twice the starting amount of $10) to make people feel twice as happy as if they had received $10, t
(19) = 4.06, p = .001. The sample mean was $43.75, and this value exceeded the normative (i.e., linear)
standard of $20 that would hold if people followed a linear rather than a curvilinear decision rule. The
comparison standard of $20 is highly appropriate in this case because the null hypothesis is based on
what would happen if people did follow a perfectly linear decision rule. It is, in a sense, the population
value that would exist for a hypothetical group of linear decision makers. The p value of .001 shows that
this finding would be significant even if we set alpha at the higher than usual level of p = .01. There is
only about 1 chance in a thousand (p = .001) of getting a result this extreme or more extreme by chance
if people are truly linear decision makers.
QUESTION 6.1b. My analysis confirmed that SPSS gave me the correct value for this t-test (and thus
must have correctly calculated the standard error of the mean). Based on the formula for the onesample t-test provided earlier, the t-test value should be:
t = (43.75 – 20.00) / (26.1873/√20)
= 23.75 / (26.1873 /4.472)
= 23.75 / 5.8558
= 4.056
QUESTION 6.2a. If you were to recode these data to reflect whether people exceeded the $20 standard,
a chi-square test to see if more than half of the participants exceeded this value would fail to yield a
significant result, apparently due to a large drop in power associated with using such a crude measure,
χ2 (1) = 3.2, p =.074, N = 20.
QUESTION 6.2b. This marginally significant result wouldn’t change much, t (19) = 1.90, p = .072, if you
conducted a t-test on the same recoded (dichotomized) data. The problem with recoding the data is that
they are now less sensitive to individual scores. Saying it would take $100 to be twice as happy as
getting $10 is much stronger support for the hypothesis than saying it would take $21, but the
dichotomous data do not reflect this important fact. Dichotomizing is a bad idea.
QUESTION 6.3.
Table 1. Mean Increase in IQ Scores as a Function of Manipulated Teacher Expectancies
Control Condition
12.00 (16.39)
Bloomer (Positive Expectancy)
27.36 (12.57)
Note. Standard deviations appear in parenthesis.
Children who were identified as bloomers (mean increase 27.4 points) in this field experiment showed
significantly greater increases in IQ over the course of the school year compared with those not labeled
bloomers (mean increase 12.0 points), t (28) = -2.68, p = .012. Presumably the increase shown by the
non-bloomers simply reflects normal maturation and learning. The extra 15 point increase shown by the
bloomers appears to reflect the effects of being labeled. Of course, it’s unlikely that teachers were
aware of any special treatment they were giving the bloomers, but they must have been treating the
bloomers better than they treated the typical child, perhaps by paying more attention to the bloomers
or giving them more encouragement. Of course, the fact that that the bloomers and non-bloomers
were chosen at random (unbeknown to the teachers) controls for all kinds of individual differences
between the kids about which we might otherwise worry. For example, it’s highly unlikely that the
bloomers were smarter to begin with or came from wealthier homes than the non-bloomers. These
results suggest that, even when such expectancies have no basis in fact, teacher expectancies may have
a dramatic impact on children’s intellectual development. Teachers should be taught about the subtle
forms of bias that must be responsible for these effects and, if at all possible, should be trained to avoid
such biases.
QUESTION 6.4. Recoding these data as dichotomous treats an IQ increase of 1 point exactly like an
increase of 40 points. This is not at all sensitive to the size of these IQ changes. Thus, it’s not surprising
that neither a chi square test of association (between treatment group and the dichotomous increase
score), χ2 (1) = 3.47, p =.062, nor an independent-samples t-test yielded a significant result, t (28) = 1.92, p = .066. See output file for details. These data should not be recoded, especially when the large
majority of children would be expected to show some small increases in IQ due to simple maturation
and learning. As was the case for the happiness study, there is no good reason to convert interval level
data to less sensitive nominal scales.
QUESTION 6.5a. We created a simple independent variable based on whether these men did or did not
live in a state resembling their first names (e.g., Cal living in California and Tex living in Texas would both
would be coded affirmatively). We created a dependent variable by subtracting how much each man
liked the letter that did not begin his name from the letter that did begin his name. So for men named
Cal, for example, this score was liking for the letter C minus liking for the letter T (see the attached
syntax commands). An independent samples t-test yielded a nearly significant effect in the expected
direction, t (38) = 1.94, p = .060. The men living in states that resembled their names had a mean name
letter preference of +1.2, and those who lived in states that did not resemble their names had a mean
name letter preference of only +0.1. We must be very cautious about this result, however, because this
difference was not quite significant. Note to Instructors: Depending on how students coded these data,
the t value of 1.94 could be either positive or negative.
QUESTIONS 6.5b & 6.5c. Of course, if we had conducted a 1-tailed (directional) test, these findings
would be significant and would support the theory that name letter preferences may lie at the root of
men’s tendency to gravitate toward states that resemble their names. Even if we were generous
enough to conduct a one-tailed test, however, we would still need to be concerned about whether these
men who disproportionately resided in states resembling their names actually moved to these states or
whether they were disproportionately born there. If this alternate account of the results proved true,
then the exaggerated liking that men had for their initials when they lived in a state resembling their
names might simply reflect the positive social feedback they should be likely to get from the many loyal
residents of their home states. Anyone who has ever visited Texas and seen the “Let’s brag about
Texas” billboards might appreciate this concern. This alternate account is still interesting but it does not
support the idea of implicit egotism.
QUESTION 6.6. This archival study of heat and violence certainly seems to suggest that heat facilitates
violence. In 2006, the average murder rate in the 10 hottest U.S. cities was 10.96 murders per 100,000
residents. In contrast the average murder rate for the 10 coldest cities was 0.51 murders per 100,000
residents. If we treat cities as the unit of analysis (a very conservative analysis), an independent samples
t-test showed that this difference was significant, t (18) = 3.57, p = .002. However, we cannot safely
conclude from these data alone that heat facilitates violence. As it turns out, the 10 hot cities appear to
be much larger cities, on average, than the 10 cold cities. It is well documented that murder rates
increase dramatically with population density. That is, big cities have much higher murder rates than
small cities. Note to Instructors: Depending on how students coded these data, the t value could be
either positive or negative 3.57.
Without addressing this serious confound, the researcher cannot make any strong claims about the
connection between heat and violence. Another less obvious confound is that almost all of the hot
cities are located in Florida and Texas. Loosely speaking, these are both Southern states and it is possible
that murder rates are higher in these mostly Southern cities because of some aspect of Southern culture
(e.g., poverty, the culture of honor) rather than because of temperature per se.
QUESTION 6.7a. The average accuracy score for this group of participants was .41, meaning that on
average, they labeled 41% of the cola samples correctly. This value is only slightly higher than the
chance value of .33, which is the value that reflects random guessing. A one-sample t-test showed that
this observed value of .41 was not significantly greater than the chance value of 0.33, t (29) = 1.12, p =
.274. People seem to have little or no ability to discriminate between the three colas in a blind taste
test. Of course, to say this more convincingly we should use a much larger sample size. If the true
population accuracy value is .41, we would just need a very large sample to document this small
advantage over the chance value. Note: If students use the slightly more precise value of .333 as the
chance standard, the result should be t (29) = 1.075, p = .291.
QUESTION 6.7b. In contrast to this poor performance, the average person reported that he or she
would be able to label the three colas at well above chance levels. The average confidence rating was
0.56 (56% predicted accuracy). A one-sample t-test revealed that this value of .56 was higher than the
chance score of .33, t(29) = 5.68, p < .001. Note: t (29) = 5.60, p < .001, for those who use .333.
A second one-sample t-test showed that this confidence value of 0.56 was also significantly higher than
the actual accuracy score of 0.41, t (29) = 3.73, p = .001. Apparently, people are more confident than
correct. This finding is consistent with a large literature on overconfidence showing that people often
overestimate the accuracy of their judgments, especially when judgment tasks prove to be difficult (as
this one certainly did). Note: t (29) = 3.70, p < .001, for those who use .411.
QUESTION 6.7c. Women were slightly, but not significantly, more accurate than men. Respective
accuracy rates for women and men were 0.44 and 0.38, t (28) = -0.45, p = .655. Despite the fact that
women were slightly more accurate than men, men reported being significantly more confident than did
women; respective confidence levels for women and men were 0.48 and 0.65, t (28) = 2.15, p = .041.
Thus, despite performing slightly more poorly than women, men seem to be more confident than
women. Putting these two findings together it seems appropriate to say that men were more
overconfident than women.