Question

A college dean is interested in the performance of students in a English course. After the final, students are randomly selected from three different sections of the English course. What can be conclude with an α of 0.01? The data are below.

section 1	section 2	section 3
84 68 74 65 90 75 64 77 40 78 69	90 82 82 77 75 82 81 91 70 90 82	94 81 87 82 72 77 81 87 67 86 77

b) Obtain/compute the appropriate values to make a decision about H₀.
critical value = ____________ ; test statistic = ____________
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
η² = ____________ ;  ---Select--- na trivial effect small effect medium effect large effect

e) Regardless of the H₀ decision in b), conduct Tukey's post hoc test for the following comparisons:
1 vs. 3: difference =____________   ; significant:  ---Select--- Yes No
1 vs. 2: difference = ____________ ; significant:  ---Select--- Yes No

f) Regardless of the H₀ decision in b), conduct Scheffe's post hoc test for the following comparisons:
2 vs. 3: test statistic =____________   ; significant:  ---Select--- Yes No
1 vs. 2: test statistic = ____________ ; significant:  ---Select--- Yes No

Answer 1

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	772.545	2	386.273	4.288	0.0230	5.39
Within Groups	2702.182	30	90.073
Total	3474.727	32

b) critical value=5.39

test stat = 4.288

decision: fail to reject Ho

c) eta square ,effect size = SSbet/SST=   0.2223 (medium)

e)  

critical value = q*√(MSE/n)

if absolute difference of means > critical value,means are significnantly different ,otherwise not

1 vs. 3: difference =____9.727________   ; significant:  ---NO
1 vs. 2: difference = ______10.73______ ; significant:  ---YES

f)

Test statistic, F'=   (X̅I - X̅j)²/(MSE*√(1ni+1/nj))

2 vs. 3: test statistic =_____0.06_______   ; significant:  No
1 vs. 2: test statistic = _____7.027_______ ; significant: YES