Question

In: Statistics and Probability

Proficiency of math courses is evaluated using a special departmental assessment. Three different instructors at two...

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

Solutions

Expert Solution

ANSWER:

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

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

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orchestra answered 2 years ago
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