Question

Proficiency of several biology sections is evaluated using a special departmental assessment. Three different instructors at two different class times are assessed. The data are below. What can the department conclude with ? = 0.05?

Instructor A Time 1	Instructor B Time 1	Instructor C Time 1	Instructor A Time 2	Instructor B Time 2	Instructor C Time 2
100 88 96 98	85 79 80 90	89 78 89 61	94 81 80 85	72 63 73 77	88 94 96 99

a) What is the appropriate test statistic?
---Select--- na One-Way ANOVA Within-Subjects ANOVA Two-Way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
Time: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Instructor: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Interaction: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Time: ?² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Instructor: ?² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: ?² =  ;  ---Select--- na trivial effect small effect medium effect large effect

Answer 1

a.  Within-Subjects ANOVA because each instructor is assessed in two diffeent times.

b.

Two-way ANOVA:

Source DF SS MS F P
Instructor 2 709.08 354.542 6.54 0.007
Time 1 40.04 40.042 0.74 0.402
Interaction 2 930.58 465.292 8.58 0.002
Error 18 976.25 54.236

Total 23 2655.96

Time: critical value =F_0.05,1,18= 4.41 ; test statistic =   0.74
Decision: Fail to reject H0 since test statistic<critical value
Instructor: critical value =F_0.05,2,18=3.55  ; test statistic =6.54  
Decision:Reject H0 since test statistic>critical value

Interaction: critical value ==F_0.05,2,18=3.55  ; test statistic = 8.58
Decision:  ---Select--- Reject H0 since test statistic>critical value.

c.

Formula for effect size:

Time: w²=(40.04-1x54.236)/(40.04+18x54.236)<0 implies w²=0 ; na

Instructor: w² = (709.08-2x54.236)/(709.08+18x54.236) =0.3564;  --- medium effect
Interaction: w² =(930.58-2x54.236)/(930.58+18x54.236)=0.4311  ;  ---medium effect