Question

A university also wants to determine if there are significant differences in GPA among students from different majors. They collect data on GPA for four different majors and find the following results: Business Administration (M = 2.9; N = 60), Fine Art (M = 3.3; N = 60), Nursing (M = 3.5; N = 60), and Psychology (M = 3.6; N = 60). They also calculated the between-group and total sum of squares (SSB = 19.8; SST = 303.0). Use a one-way ANOVA (where α = .05) to determine if there are significant differences in GPA by major.

12. Identify the alternative hypothesis (F tests are always nondirectional)

13. List your degrees of freedom (within)

14. List your degrees of freedom (between)

15. List your mean squares between groups

16. List your mean squares within groups

17. List your F test statistic

18. List your critical F value(s)

19. Are there statistically significant differences in GPA by major? (Yes/No)

20. Calculate partial eta-squared (η2) for the effect of major on GPA (list as decimal, 0.xx)

21. Calculate Tukey’s HSD

22. Use Tukey’s HSD to determine if the difference in GPA between Psychology majors and Business Administration majors is statistically significant (Yes/No)

Answer 1

12. for at least one set of (i,j)

13. degrees of freedom (within)= 236

14.degrees of freedom (between)= 3

NOTE : total df = 4*60-1=239

there are 4 groups , df =4-1=3

within df = 239-3 =236

15.Mean square between groups = SSB/df = 19.8 / 3 = 6.6

16.Mean square within groups = SSW/df = 283.2 / 236 = 1.2

NOTE : SS(within) = SST-SSB= 303.0-19.8 = 283.2

17. F statistic = MSB / MSW = 6.6 / 1.2 = 5.5

18.At alpha =0.05 with (3,236) df , critical value of F

F critical = 2.643