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BTM8106-8-3 Jackson, Even-Numbered Chapter Exercises

Exercises covering statistical and research methods in business.

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    BTM8106 - 8 - 3 1 BTM8106 - 8 - 3 JACKSON, EVEN - NUMBERED CHAPTER EXERCISES, PP. 308 - 310. 2. What is the difference between a randomized ANOVA and a repeated measures ANOVA? What does the term one - wa y mean with respect to an ANOVA? A one - way randomized ANOVA is an inferential statistical test used to compare the means of three or more groups using a between - subjects design and one independent variable (Jackson, 2012). A one - way repeated measures ANOVA is an inferential statistical te st that compares the means of three or more groups using a correlated groups design and one independent variable (Jackson, 2012): a test to detect any overall differences between related means. The participants are either the same individuals tested on thr ee or more occasions on the same dependent variable or the same individuals tested under three or more different conditions on the same dependent variable ( Laerd, 2015). However, randomized ANOVA’s indicate that subjects are randomly assigned to conditions (Jackson, 2012). The one - way ANOVA compares the means between the groups and determines whether any of those means are significantly different from each other. Specificall y, it tests the null hypothesis. T he one - way ANOVA cannot tell which specific groups were significantly different from each other, onl y that at least two groups were (Laerd, 2015). 4. If a researcher decides to use multiple comparisons in a study with three conditions, what is the probability of a Type I error across these comparisons? Use the Bonferroni adjustment to determine the suggested alpha level. The formula 1 - (1 - .05) / 3 is used to determine the probability of a Type I error w hen making multiple comparisons: there is a 14% chance of a Type I error. Using the Bonfer r oni adjustment, the suggested alpha level is .05 / 3. The suggested alpha level is .017. 6. When should post hoc comparisons be performed? Post hoc tests should be performed when there are three or more groups being compared , and the F - ratio is significant (Jackson, 2012). Post - hoc tests are used to control the error rate

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    BTM8106 - 8 - 3 2 (alpha = 0.05 ), similarly the one - way ANOVA ’s are used, and usually after the study has been conducted. 8. Why is a repeated measures ANOVA statistically more powerful than a randomized ANOVA? When the same participants are used in all conditions, their individual differences; factor s contributing to error variance , are removed. Because error variance represents the denominator in the F - ratio, a smaller number is used in dividing and the answer results in a larger final F - ratio (Jackson, 2012). Therefore, repeated - measures ANOVA’s are more sensitive to negligible differences between groups than randomized ANOVA ’s (Jackson, 2012). 10. In a study of the effects of stress on illness, a researcher tallied the number of colds people contracted during a 6 - month period as a function of the amount of stress they reported during that same time period. There were three stress levels: minimum , moderate, and high stress. The sums of squares appear in the following ANOVA summary table. The mean for ach condition and the number of subjects per condition are also noted . Source df SS MS F Between groups 22.167 Within groups 14.750 Total 36.917 Stress Level Mean N Minimal 3 4 Moderate 4 4 High 6 4 10a. Complete the ANOVA summary table. Source df SS MS F Between groups 2 22.167 11.08 6.76 Within groups 9 14.750 1.64 Total 11 36.917 10b. Is Fobt significant at α = .05; at α = .01? Yes, F (2, 9) = 6.76, p < .05.

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