In: Statistics and Probability
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
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 |
(OR) TRY THIS IF ANYTHING
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