Question

The whole question has been posted below, but I have answered some of them. I need help with questions B, E, and F. I need the critical value in question B. I need the answers for the differences in question E. I need the answers for test statistics in F. Thank you.

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Answer the one-way ANOVA questions using the data below. Use α = 0.01.

1	2	3	4
53 49 47 42 48 34 44	44 39 36 34 24 30 12	46 42 39 43 36 34 47	25 35 30 27 33 28 22

a) Compute the preliminary statistics below.
SS_BG = 1312.39  ;   df_BG = 3
SS_WG = 1166.57  ;   df_WG = 24
SS_T = 2478.96  ; df_T = 27

b) Compute the appropriate test statistic(s) to make a decision about H₀.
critical value = _______________  ; test statistic = 9.00
Decision: Reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
η² = 0.5294  ; large effect

d) Make an interpretation based on the results.

At least one mean is different from another.  

e) Regardless of the H₀ decision in b), conduct Tukey's post hoc test for the following comparisons:
3 vs. 4: difference = __________    ; significant:  ---Select--- Yes or No
1 vs. 2: difference = __________    ; significant:  ---Select--- Yes or No

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

____

Answer 1

a). The ANOVA table is presented below:

Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1312.393	3	437.4643	9	0.000357	3.008787
Within Groups	1166.571	24	48.60714
Total	2478.964	27

b).

Critical Value : 3.0088 .test statistic = 9.00
Decision: Reject H0

c). Compute the corresponding effect size(s) and indicate magnitude(s).
η² = 0.5294  ; large effect

d) Make an interpretation based on the results.

At least one mean is different from another.  

e) Regardless of the H₀ decision in b), conduct Tukey's post hoc test for the following comparisons:
3 vs. 4: difference = 12.4286 ; significant: Yes
1 vs. 2: difference = 14 ; significant: Yes

f) Regardless of the H₀ decision in b), conduct Scheffe's post hoc test for the following comparisons:
1 vs. 3: test statistic =1.1500 ; significant: No  
2 vs. 3: test statistic = 3.3351 ; significant: Yes