Ideal Answers to Chapter 3 Questions
QUESTION 3.1a. Based on a height of 62.88 inches Mauritania’s predicted weight is 134.8 lbs. The
correlation between height and weight is r = .769, p < .001. This means that for every standard deviation
a person is above or below the mean in height we predict their weight to deviate 0.769 weight standard
deviations from the weight mean in the same direction. This leads to: Mauritania’s height – mean height
= 62.88 – 67.27 = -4.39 inches. Because the SD for height is 4.39, Mauritania is 1.00 SDs below the mean
height. So Mauritania’s predicted weight is .769 x -1.00 or -0.769 standard deviations below the mean
weight, which is 153.43 + (-.769 x 27.55) = 153.43 – 21.19 = 132.24 lbs.
We can also determine this using the formula from the Appendix: Y' = bx + a
b = 4.83 (slope), x = 62.88 (Mauritania’s height), a = - 171.5 (intercept)
Mauritania’s predicted score is thus: (4.83 x 62.88) – 171.5 = 132.2.
QUESTION 3.1b. The difference between Mauritania’s actual weight and predicted weight is called the
residual, also known as error. In this case the residual is 146.8 – 132.2, which is +14.6 lbs. This means
that based on the magnitude of the correlation between height and weight and Mauritania’s known
height, we predicted a weight 14.6 lbs. lower than Mauritania’s actual weight. Mauritania is a bit heavier
than you’d expect for a short person.
QUESTION 3.2a. Now that we know Mauritania is a man we should correlated height and weight
separately for men only because men and women differ meaningfully in their mean heights and weights
(the correlation between the two could also differ a bit by sex). When we recalculate everything using
the correlation, means and standard deviations for men only, Mauritania’s predicted weight is 148.8 lbs.
Here are the details. Using the data from men only, Mauritania is much shorter than average. His height
minus the mean height for men is 62.88 - 70.2 = -7.32. In standard deviation units, this is -7.32/3.43,
which is -2.13. So he’s 2.13 SDs below the mean in height. Given the new r = .563 correlation between
height and weight, we thus predict that he’ll be -2.13 x .563 (= -1.199) standard deviations below the
mean in weight. The mean weight for men = 174.0 lbs., and the SD for weight for men is 21.02 lbs. So
Mauritania’s predicted weight is 174.0 + (-1.199 x 21.02), which is 174.0 - 25.2, which is 148.8 lbs.
QUESTION 3.2b. This new prediction is much closer to his actual weight of 146.8 lbs. The residual is now
only -2 lbs (he weighs 2 lbs. less than we predicted). It might seem strange that we predicted his weight
more accurately when the correlation got smaller (the original r was .769; for men only, it’s r =.563). All
else being equal, larger correlations allow for more accurate prediction. However, all else was not
equal. By focusing solely on men, we reduced the standard deviations for both height and weight – by
eliminating the variation in both variables associated with gender differences. In the extreme case, if
there were no variation in height among men, we could predict his height perfectly by just guessing the
mean. Incidentally, we also changed the means for both height and weight to be more appropriate for
his gender. Although Mauritania was now treated as further below the mean in height, we adjusted his
weight downward from a much higher starting point (174.0 lbs. instead of 153.4 lbs.).
QUESTION 3.3a. By far the two most interesting correlations in these data are those between height and
education (r = .42) and height and income (r = .51), both of which are significant at p < .05. The taller
people are, the more highly educated they are, and the more money they make. The most interesting
interpretation of these correlations is that there is some kind of potent social stereotype regarding
height. If we perceive taller people as better leaders by assuming that they are more intelligent, more
self-assured or simply more deserving, then this stereotype might serve as a self-fulfilling prophecy.
Teachers might pay more attention to taller students. Those interviewing taller candidates for jobs
might offer them higher starting salaries, promote them more quickly, etc.
These data suggest that if this is a stereotype, it is a very powerful one. Recall that when x and y are
significantly and positively correlated, as they are here, every 1 SD increase in x leads to a prediction of r
SDy units increase above the mean in y. In this case, the correlation between height and income is r =
.514. This means that if a person is 1 SD above the mean in height his or her predicted score for income
is the mean for income + .514 SDy. More specifically, increasing a person’s height by one standard
deviation (4.39 inches) seems to mean an average of .514 x $21,822 extra dollars ($11,217) of yearly
income. Even an inch of additional height predicts $2,555in additional yearly income ($11,217/4.39 =
$2,555).
QUESTION 3.3b. There are many criticisms of these findings. A weak criticism is that correlation does
not prove causation (it’s weak because it’s an obvious, knee jerk reaction that does not reveal any
careful analysis). A somewhat stronger criticism is that people from wealthier families may grow taller
due to superior nutrition and medical care, and it may be parental income that is the real reason why
taller people get more education & make more money. The reason this isn’t a great criticism is that it
seems unlikely in a very wealthy country such as the U.S. that people from rich families really do grow
appreciably taller. Probably the best criticism is that height is highly confounded with gender, and we
already know that women make only about 70% of what men make. Thus it is possible that the
correlation between height and income is really just a reflection of the well-known gender gap in pay.
This problem could apply to education as well as income if a substantial proportion of these people are
older Americans. In the past, many fewer women than men received a higher education.
QUESTION 3.4a. The main correlations for the stereotyping study did yield support for Blair’s
perspective. The more Afrocentric the White target faces were, the more people judged them to
possess all four of the stereotypically Black traits, all ps < .05. The correlations were as follows:
Trait Judgment
athletic
musical
aggressive
lazy
Correlation
with Afrocentrism
.46
.40
.60
.74
QUESTION 3.4b. The tendency to judge the targets more stereotypically on the positive traits went hand
in hand with the tendency to judge them more stereotypically on the negative traits. Thus, for example,
the lazier people thought a target face was, the more athletic and the more musical they tended to think
he was, respective rs = .56 and .58, both ps < .01. This is interesting because in the absence of a
stereotype, a general halo bias should tend to promote a negative correlation between desirable and
undesirable traits. Apparently, these four different traits tend to cluster together because they are all
part of the stereotype of African Americans. They may do so even when Afrocentric features that
people are not consciously thinking about activate the stereotype among White targets.
QUESTION 3.5. Some limitations to the validity of the new study are based on the fact that it is a
correlational study. Because the researcher did not systematically manipulate separate Afrocentric
features, we do not know exactly which features (e.g., lip size, skin tone, hair) were responsible for the
observed effects. We also cannot be absolutely sure that participants were completely unaware of the
fact that some of the faces had Afrocentric features. Though it seems unlikely, it is possible, in principle,
that some participants guessed what the researcher was studying. Another limitation is that the study
involved only male targets. It would be useful to know, which, if any of these traits would be applied to
female targets. Some ethnic stereotypes are gender contingent. For example, the assumption that
Blacks are athletic probably applied about equally well to male and female targets, but the assumption
that Blacks are aggressive may apply more strongly to male than to female targets.
QUESTION 3.6. Although the correlation between perceived corruption and press freedom is negative,
as suggested by Brandeis’s idea that transparency reduces corruption, this correlation does not
approach statistical significance, r (18) = -.21, p = .371. So we cannot say that there is any good evidence
for the idea that freedom of the press goes hand in hand with a lack of corruption.
QUESTION 3.7. The test for a curvilinear association between press freedom and perceived corruption in
European countries reveals a significant quadratic effect, F (2, 17) = 9.69, p = .002, quadratic R squared =
.533. In countries in which there is very little press freedom, perceived corruption is very low (perhaps
because censorship does what it is intended to do). As press freedom increases, perceptions of
corruption increase up to a certain point. However, as press freedom increases beyond moderate levels
greater press freedom is associated with lower levels of perceived corruption. This may reflect the fact
that countries with extremely free presses enjoy low levels of corruption.
These findings provide qualified support for Brandeis’s thesis by suggesting that at very low levels of
press freedom, the public may not have enough information to realize how much corruption there is in
their country. Increasing levels of press freedom from very low to moderate levels may bring to light
corruption that would remain hidden in countries where there is little or no freedom of the press.
However, as press freedom increases from moderate to high levels, people may realize, correctly, that
corruption levels in their country are low.