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Analysis of Variance (ANOVA) and Post-Hoc Comparisons: A Comprehensive Study

This assignment provides an in-depth analysis of ANOVA and post-hoc tests, explaining their applications in research.

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    Analysis of Variance (ANOVA) and Post - Hoc Comparisons: A Comprehensive Study 1. 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 - way mean with respect to ANOVA? The randomized ANOVA design is the parametric inferential statistical test to compare the mean of three or more groups. Whereas the repeated measures ANOVA is almost same as randomized ANOVA but except the fact that here the groups are correlated to each other. So the main difference between a randomized ANOVA and a repeated measures ANOVA is that 1 st one uses uncorrelated groups and 2 nd one uses correlated groups. When we use one way in ANOVA that mean we are considering only one independent variable. 4) If a researcher decides to use multiple comparisons in a study with three conditions, what is the probability of a Type I err or across these comparisons? Use the Bonferroni adjustment to determine the suggested alpha level. Assuming alpha is 0.05 then the probability of a Type I error across these comparisons would be, ( 1 − ( 1 − 0 . 05 ) 3 ) = 0 . 14263 = 14 . 26% With the Bonferroni adjustment, the alpha level is 0.05/3 = 0.0167 for each comparison. 6) When should post - hoc comparisons be performed? The post - hoc comparisons should be performed when we reject the null hypothesis of ANOVA and conclude that at least one groups mean is significantly different than others. The post - hoc test is performed to see which group mean is different. 8) Why is repeated measures ANOVA statistically more powerful than a randomized ANOVA? The repeated measures ANOVA is statistically more powerful than a randomized ANOVA because both uses different method for the analysis. A repeated measures ANOVA divides the total variance into two parts and only the error variance is used to calculate the F value. So the F value becomes larger giving more power. 10) In a study of the effects of stress on illness, a researcher taillied the number of colds people contracted during a 6 - month period as a function of the amount of stress they reported during the same period. There were three stress levels: minimal, moderate, and high stress. The sums of squares appear in the following ANOVA summary table. The mean for each condition and the number of subjects per condition and the number of subjects per condition are also noted. Source df SS MS f Between groups 2 22.167 11.084 6.763 Within Groups 9 14.750 1.639 Total 11 36.917 Stress level Mean N minimal 3 4 moderate 4 4 maximum 6 4 A) Complete the ANOVA summary table

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