Question

Answer the within-subjects ANOVA questions using the data below. Use α = 0.05.

1	2	3	4
53 49 47 48 51 34 44	44 39 36 34 39 30 41	46 42 39 47 36 34 47	37 35 30 27 33 28 31

a) Compute the preliminary statistics below.
SS_BG =  ; df_BG =  
SS_BS =  ; df_BS =  
SS_E =  ; df_E =  
SS_T =  ; df_T =  

b) Compute the appropriate test statistic(s) 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

d) Make an interpretation based on the results.

At least one week differs on the GRE verbal score.No week is different on GRE verbal score.     

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

Answer 1

Solution

We will solve it by using Excel

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
1	7	326	46.57143	38.95238
2	7	263	37.57143	21.61905
3	7	291	41.57143	28.95238
4	7	221	31.57143	13.28571
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	845.25	3	281.75	3.008787	0.0001	3.008787
Within Groups	616.8571	24	25.70238
Total	1462.107	27

a) Compute the preliminary statistics below.
SS_BG = 845.25 ; df_BG = 3
SS_E = 616.8571   ; df_E = 24
SS_T = 1462.107 ; df_T = 27

b) Compute the appropriate test statistic(s) to make a decision about H₀.
critical value =3.008787  ; test statistic =  3.008787
Decision: Reject H0

d) Make an interpretation based on the results.

At least one week differs on the GRE verbal score.