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

254 CHAPTER 8 | Introduction to Hypothesis Testing
Notice that Cohen’s d simply describes the size of the treatment effect and is not influenced
by the number of scores in the sample. For both hypothesis tests, the original population
mean was μ = 50 and, after treatment, the sample mean was M = 51. Thus, treatment
appears to have increased the scores by 1 point, which is equal to one-tenth of a standard
deviation (Cohen’s d = 0.1).
LEARNING CHECK
1. Which of the following is most likely to reject the null hypothesis even if the
treatment effect is very small?
a. A small sample and a small value for σ.
b. A small sample and a large value for σ.
c. A large sample and a small value for σ.
d. A large sample and a large value for σ.
2. A treatment is administered to a sample selected from a population with a mean of
µ = 80 and a standard deviation of σ = 10. After treatment, the sample mean is M = 85.
Based on this information, the effect size as measured by Cohen’s d is _____.
a. d = 5.00
b. d = 2.00
c. d = 0.50
d. impossible to calculate without more information
3. If other factors are held constant, then how does the size of the standard deviation
affect the likelihood of rejecting the null hypothesis and the value for Cohen’s d?
a. A larger standard deviation increases the likelihood of rejecting the null hypothesis
and increases the value of Cohen’s d.
b. A larger standard deviation increases the likelihood of rejecting the null hypothesis
but decreases the value of Cohen’s d.
c. A larger standard deviation decreases the likelihood of rejecting the null hypothesis
but increases the value of Cohen’s d.
d. A larger standard deviation decreases the likelihood of rejecting the null hypothesis
and decreases the value of Cohen’s d.
ANSWERS
1. C, 2. C, 3. D
8.6 Statistical Power
LEARNING OBJECTIVES
13. Define the power of a hypothesis test and explain how power is related to the
probability of a Type II error.
14. Identify the factors that influence power and explain how power is affected by each.
Instead of measuring effect size directly, an alternative approach to determining the size or
strength of a treatment effect is to measure the power of the statistical test. The power of a