70 ❯ STEP 4. Review the Knowledge You Need to Score High
same range, but a different standard deviation, that are plotted on the same axes show a
difference in variability by their shapes. The taller and narrower frequency polygon shows
less variability and has a lower standard deviation than the short and wider one.
If you are not required to bring a calculator to the exam, you won’t be required to
figure out variance or standard deviation.Correlation
Scores can be reported in different ways. One example is the standard score or z score.
Standard scores enable psychologists to compare scores that are initially on different scales.
For example, a z score of 1 for an IQ test might equal 115, while a z score of 1 for the
SAT in mathematics might equal 600.The mean score of a distribution has a standard score
of zero. A score that is one standard deviation above the mean has a z score of 1. A standard
score is computed by subtracting the mean raw score of the distribution from the raw score
of interest and then dividing the difference by the standard deviation of the distribution of
raw scores. Another type of score, the percentile score, indicates the percentage of scores at
or below a particular score. Thus, if you score at the 90th percentile, 90 percent of the scores
are the same or below yours. Percentile scores vary from 1 to 99.
A statistical measure of the degree of relatedness or association between two sets of
data, X and Y, is called the correlation coefficient. The correlation coefficient (r) varies
from −1 to +1. One indicates a perfect relationship between the two sets of data. If the
correlation coefficient is −1, that perfect relationship is indirect or inverse; as one variable
increases, the other variable decreases. If the correlation coefficient (r) is +1, that perfect rela-
tionship is direct; as one variable increases, the other variable increases, and as one variable
decreases, the other variable decreases. A correlation coefficient (r) of 0 indicates no relation-
ship at all between the two variables. As the correlation coefficient approaches +1 or −1, the
relationship between variables gets stronger. Correlation coefficients are useful because they
enable psychologists to make predictions about Y when they know the value of X and the cor-
relation coefficient. For example, if r = .9 for scores of students in an AP Biology class and for
the same students in an AP Psychology class, a student who earns an A in biology probably
earns an A in psychology, whereas a student who earns a D in biology probably earns a D in
psychology. If r = .1 for scores of students in an English class and scores of the same students
in an AP Calculus class, knowing the English grade doesn’t help predict the AP Calculus grade.
Correlation does not imply causation. Correlation indicates only that there is a relation-
ship between variables, not how the relationship came about.
The strength and direction of correlations can be illustrated graphically in scattergrams
or scatterplots in which paired X and Y scores for each subject are plotted as single points
on a graph. The slope of a line that best fits the pattern of points suggests the degree and
direction of the relationship between the two variables. The slope of the line for a perfect
positive correlation is r = +1, as shown in Figure 6.2a. The slope of the line for a perfect
negative correlation is r = −1, as shown in Figure 6.2b. Where dots are scattered all over the
plot and no appropriate line can be drawn, r = 0 as shown in Figure 6.2c, which indicates
no relationship between the two sets of data.Inferential Statistics
Inferential statistics are used to interpret data and draw conclusions. They tell psycholo-
gists whether or not they can generalize from the chosen sample to the whole population,
if the sample actually represents the population. Inferential statistics use rules to evaluate
the probability that a correlation or a difference between groups reflects a real relationship
and not just the operation of chance factors on the particular sample that was chosen for
study. Statistical significance (p) is a measure of the likelihood that the difference betweenTIPKEY IDEA