a. ANOVA Testing: Expand your research question comparing two independent means from Unit 6 and include more than two groups to compare. Write down your question and why you feel that it is appropriate for a one-way ANOVA test. I want to compare the national mean score of schools of 6 countries namely United States, India, Australia, United Kingdom, Africa and Singapore. When I want to compare means among 3 or more groups I use one way ANOVA. b. State Hypotheses: State your null hypothesis and your alternative hypothesis. State the dependent variable, the independent variable and the levels of that variable. Null hypothesis, Ho: there is no significant difference in the mean score of schools of 6 countries namely United States, India, Australia, United Kingdom, Africa and Singapore. Alternative hypothesis, H1; at least one of the mean score of schools of 6 countries namely United States, India, Australia, United Kingdom, Africa and Singapore differs significantly. c. Describe Data: Describe the type of data you would collect. What sample size would you use and what would your data look like? I use the concept of cluster sampling for collected data for each country. I select one top most school from each country and record the scores of top 20 students. There by my sample size becomes, 20*6 = 210. My data would be measured on ratio scale of measurement. I would have 20 observations for each country. d. Predict Results: Predict the results of your ANOVA test and write out the appropriate conclusion. Using alpha of .05, include a pretend p-value that would justify either accepting or rejecting your null hypothesis. What would you expect from a Post Hoc test given your predicted results from your ANOVA test? With F = 14.65 and p-value < 0.05, I reject the null hypothesis and conclude that at least one of the mean score of schools of 6 countries namely United States, India, Australia, United Kingdom, Africa and Singapore differs significantly. To test which pair differs significantly I apply post hoc analysis. Simultaneous comparisons between all pairs of groups can be done by Tukey-Kramer. Critical range = QU ( c, n c ) MSW 2 1 1 nj nj' Where, n = total number of values in all groups combined nj = number of values in jth group And, c = number of groups Here, there are 6 groups, A, B, C and D. Thus, c = 6. And n = 120 With p-value less than alpha (0.05), I conclude that groups (India, Unites States), (India, United Kingdom), (India, Australia) (Africa, Unites States), (Africa, United Kingdom), (Africa, Australia) differs significantly