Tokunaga, Fundamental Statistics for the Social and Behavioral

Testing Differences Between Two or Multiple Means

Lisa F. Peters
University of Phoenix

Testing Differences Between Two or Multiple Means
9.11 Exercises 1 thru 24
4. State the null and alternative hypotheses (H0 and H1) for each of the following research questions:
a. Are the average starting salaries for clinical psychologists in private practice the same as or different from that of psychological researchers in business or the government?
b. In Chapter 3, we looked at psychology majors' and non-psychology majors' belief in the myth that we only use 10% of our brains. Do the two groups differ in this belief?

c. Are men paid more than women for doing the same job?
d. Do Republicans and Democrats similarly support a national health insurance program or does one group favor this more than the other?
16. A third-grade teacher is interested in comparing the effectiveness of two styles of instruction in language comprehension: imagery, in which the students are asked to picture a situation involving the word, and repetition, in which the students repeat the definition of the word multiple times. After 6 weeks of instruction, she gives the students a language comprehension test. The following scores are the number of correct answers for each student. Determine whether the two styles of instruction differ in their effectiveness.
Imagery: 12, 13, 11, 11, 13, 13, 15, 12, 9, 12
Repetition: 6, 11, 10, 12, 9, 10, 11, 12, 10, 8
a. For each group, calculate the sample size (N), mean ( ), and standard deviation (s).
b. State the null and alternative hypotheses (H0 and H1).
c. Make a decision about the null hypothesis.
(1) Calculate the degrees of freedom (df).
(2) Set alpha (α), identify the critical values (draw the distribution), and state a decision rule.
(3) Calculate a value for the t-test for independent means.
(4) Make a decision whether to reject the null hypothesis.
(5) Determine the level of significance.
d. Draw a conclusion from the analysis.
e. What are the implications of this analysis for the teacher?
11.11 Exercises 1 thru 24
2. For each of the following, calculate the degrees of freedom (df) and identify the critical value of F (assume α = .05).
a. # groups = 3, Ni = 10
b. # groups = 5, Ni = 26
c. # groups = 4, Ni = 15
d. There are five groups, with 20 participants in each group.
12. Although men and women have been found to perform differently on tests of mental ability, less is known about possible reasons for these differences. A researcher hypothesizes that one's beliefs play a role, such that women who believe they should not perform well on these tests as men will in fact not perform well. To test this hypothesis, a group of women are given a written test of spatial abilities. Three different instructions were included with this test: (1) Women perform better on the test than men, (2) men perform better on the test than women, or (3) women and men perform equally well on the test. It was hypothesized that women who were told that women perform better than men would score higher than women who were told men were better or that women and men were equal. Here are descriptive statistics of the test scores: Women better: N = 11, M = 6.91, s = 2.63; Men better: N = 11, M = 7.45, s = 2.07; Women and men equal: N = 11, M = 9.82, s = 2.23.
a. State the null and alternative hypotheses (H0 and H1).
b. Make a decision about the null hypothesis.
(1) Calculate the degrees of freedom (df).
(2) Set alpha (α), identify the critical value, and state a decision rule.
(3) Calculate the F-ratio (F) and create an ANOVA summary table.
(4) Make a decision whether to reject the null hypothesis.
(5) Determine the level of significance.
(6) Calculate a measure of effect size (R2).
c. Draw a conclusion from the analysis.
d. Relate the result of the analysis to the research hypothesis.
14. Employers seek ways to improve the performance of their employees. Gardner, Van Dyne, and Pierce (2004) hypothesized that performance is influenced by organizational self-esteem, defined as an employee's evaluation of his or her personal adequacy as an organizational member. More specifically, they hypothesized that the higher one's organizational self-esteem, the higher will be one's job performance. The data below (representative of the study's findings) represent the employees' job performance level on a scale from 1 (low performance) to 5 (high performance). Determine whether job performance varies as a function of organizational self-esteem.

a. Calculate the sample size (Ni), mean and standard deviation (si) for each group.
b. State the null and alternative hypotheses (H0 and H1).
c. Make a decision about the null hypothesis.
(1) Calculate the degrees of freedom (df).
(2) Set alpha (α), identify the critical value, and state a decision rule.
(3) Calculate the F-ratio (F) and create an ANOVA summary table.
(4) Make a decision whether to reject the null hypothesis.
(5) Determine the level of significance.
(6) Calculate a measure of effect size (R2).
d. Draw a conclusion from the analysis.
e. Relate the result of the analysis to the research hypothesis.

References
Tokunaga, H. T. (2016). Measures of central tendency. Fundamental Statistics for the Social and
Behavioral Sciences. SAGE Publications, Chptr 7 and 8.