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

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Analysis of Variance (ANOVA) and Post-Hoc Comparisons: AComprehensive Study1.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 meanwith respect to ANOVA?The randomized ANOVA designis theparametric inferential statistical test to compare the mean of three ormore groups. Whereas the repeated measures ANOVA is almost same as randomized ANOVA but exceptthe fact that here the groups are correlated to each other. So the main difference between a randomizedANOVA and a repeated measures ANOVA is that 1stone uses uncorrelated groups and 2ndone usescorrelated 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 erroracross these comparisons? Use the Bonferroni adjustment to determine the suggested alpha level.Assuming alpha is 0.05 thenthe probability of a Type I error across these comparisonswould be,(1−(1−0.05)3)=0.14263=14.26%With the Bonferroni adjustment, the alpha level is0.05/3 = 0.0167for 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 onegroups mean is significantly different than others. The post-hoc test is performed to see which group mean is different.8) Why isrepeated 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 forthe analysis. A repeated measures ANOVA divides thetotal variance into two parts and only the error variance is used to calculatethe 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-monthperiod 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 andthe number of subjects per condition and the number of subjects per condition are also noted.SourcedfSSMSfBetween groups222.16711.0846.763Within Groups914.7501.639Total1136.917Stress levelMeanNminimal34moderate44maximum64A) Complete the ANOVA summary table

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