Question

Proficiency of math courses 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 an α of 0.01?

1			2
A	B	C	A	B	C
100 88 96 98	85 79 80 90	89 95 89 61	94 81 80 85	72 63 73 77	88 94 96 87

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Obtain/compute the appropriate values 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: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Instructor: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect


d) Make an interpretation based on the results.

1)There is a time difference in the assessment.

2)There is no time difference in the assessment.    

1)There is an instructor difference in the assessment.

2)There is no instructor difference in the assessment.    

1)There is a time by instructor interaction in the assessment.

2)There is no time by instructor interaction in the assessment.    

Answer 1

a) What is the appropriate test statistic?
two-way ANOVA

b) Obtain/compute the appropriate values to make a decision about H₀.
Time: critical value = 7.636 ; test statistic = 2.359
Decision: Fail to reject H0

Instructor: critical value = 5.453 ; test statistic = 5.746
Decision: Fail to reject H0

Interaction: critical value = 5.453 ; test statistic = 3.859
Decision: Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
Time: η² = 0.060 ; small effect
Instructor: η² = 0.290 ; medium effect
Interaction: η² = 0.195 ;  small effect

d) Make an interpretation based on the results.

2)There is no time difference in the assessment.    

2)There is no instructor difference in the assessment.    

2)There is no time by instructor interaction in the assessment.    

Source	SS	df	MS	F	p-value	F critical	n²
Time	150.00	1	150.000	2.359	.1419	7.636	0.060
Instructor	730.75	2	365.375	5.746	.0117	5.453	0.290
Interaction	490.75	2	245.375	3.859	.0403	5.453	0.195
Error	1,144.50	18	63.583
Total	2,516.00	23