same range, but a different standard deviation, that are plotted on the same axes show a dif-
ference 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.
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 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 zscore 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% 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,
Xand 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
relationship is direct; as one variable increases the other variable increases, and as one vari-
able 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 relationship between variables gets stronger. Correlation coefficients are useful
because they enable psychologists to make predictions about Ywhen they know the value
ofXand the correlation 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 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 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 between58 STEP 4. Review the Knowledge You Need to Score High
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