Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

252 CHAPTER 8 | Introduction to Hypothesis Testing
Cohen’s d measures the
distance between two
means and is typically
reported as a positive
number even when the
formula produces a
negative value.
representative of the population mean and provides the best measure of the treatment
effect. Thus, the actual calculations are really estimating the value of Cohen’s d as follows:
estimated Cohen’s d 5
mean difference
standard deviation 5 M 2m treatment no treatment
s
(8.2)
The standard deviation is included in the calculation to standardize the size of the mean difference
in much the same way that z-scores standardize locations in a distribution. For example,
a 15-point mean difference can be a relatively large treatment effect or a relatively small
effect depending on the size of the standard deviation. This phenomenon is demonstrated in
Figure 8.9. The top portion of the figure (part a) shows the results of a treatment that produces
a 15-point mean difference in SAT scores; before treatment, the average SAT score is μ =
500, and after treatment the average is 515. Notice that the standard deviation for SAT scores is
σ = 100, so the 15-point difference appears to be small. For this example, Cohen’s d is
Cohen’s d 5
mean difference
standard deviation 5 15
100 5 0.15
(a)
Distribution of SAT
scores before treatment
m 5 500 and s 5 100
d 5 0.15
Distribution of SAT
scores after treatment
m 5 515 and s 5 100
s 5 100
m 5 500
(b)
Distribution of IQ
scores before treatment
m 5 100 and s 5 15
d 5 1.00
Distribution of IQ
scores after treatment
m 5 115 and s 5 15
s 5 15
m 5 100
FIGURE 8.9
The appearance of a 15-point treatment effect in two different situations. In part (a), the standard deviation is σ = 100 and
the 15-point effect is relatively small. In part (b), the standard deviation is σ = 15 and the 15-point effect is relatively large.
Cohen’s d uses the standard deviation to help measure effect size.