Question

Answer the within-subjects ANOVA questions using the data below. Use α = 0.01.

1	2	3	4
53 49 47 30 51 34 44	44 39 36 25 39 30 12	46 42 39 37 36 34 22	25 35 48 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

Answer 1

applying ANOVA:

Source of Variation	SS	df	MS	F	P-value
subject	1020.7143	6	170.1190	3.6043	0.0159
groups	641.4286	3	213.8095	4.5300	0.0156
Error	849.5714	18	47.1984
Total	2511.7143	27

a)

SS_BG =641.4286 ; df_BG =3
SS_BS = 1020.7143 ; df_BS =6
SS_E =849.5714 ; df_E =18
SS_T = 2511.7143 ; df_T =27

b)

critical value =5.0919 , test statistic = 4.5300

Fail to reject H0

c)

η² = 641.4286/2511.7143=0.2554

large effect