axes show a difference in variability by their shapes. The taller and narrower frequency poly-
gon shows less variability and has a lower standard deviation than the short and wider one.
Since you don’t bring a calculator to the exam, you won’t be required to figure out vari-
ance or standard deviation.Correlation
Scores can be reported in different ways. One example is the standard scoreorzscore,
Standard scores enable psychologists to compare scores that are initially on different scales. For
example, a zscore of 1 for an IQ test might equal 115, while a zscore of 1 for the
SAT I 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 zscore of 1. A standard score is
computed by subtracting the mean raw score of the distribution from the raw score of inter-
est, 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% of the scores are the same or
below yours.
A statistical measure of the degree of relatedness or association between two sets of data,
X andY, 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 inverse; as one variable increases the
other variable decreases. If the correlation coefficient (r) is +1, that perfect relationship 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 relationship at all
between the two variables. As the correlation coefficient approaches +1 or −1, the relation-
ship between variables gets stronger. Correlation coefficients are useful because they enable
psychologists to make predictions about Ywhen they know the value of Xand the correla-
tion coefficient. For example, if r=.9 for scores of students in an AP Biology class and for
the same students in 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 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 isa relation-
ship between variables, not how the relationship came about.
The strength and direction of correlations can be illustrated graphically in scattergrams
orscatterplotsin 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 in Figure 6.2a. The slope of the line for a perfect negative
correlation is r=−1, as in Figure 6.2b. Where dots are scattered all over the plot and no
appropriate line can be drawn, r=0 as 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 psychologists
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 between
groups results from a real difference between the two groups rather than from chance alone.58 ❯ STEP 4. Review the Knowledge You Need to Score High
TIPKEY IDEA