We hypothesized that student performance when asked to take a test at a different time than the regularly scheduled class would vary by both the difficulty of the test and the time of day that the test is given. This is a test of the interaction. If we set our alpha level to .05, the critical value of the F ratio at 2 and 18 degrees of freedom is 3.56. If we were to lower our alpha to .01, the critical value of the F ratio is 6.01. For either alpha level, we reject the null hypothesis that ab=0 as the sample F ratio of 20.009 is much larger than our critical values (3.56; 6.01)
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Summary Table
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Source
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SS
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df
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MS
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F
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| Main Effect A -- Difficulty of Test |
2.660
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1
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2.660
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0.560
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| Main Effect B -- Time of Testing |
1.083
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2
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0.542
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0.114
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| Interaction AxB -- Difficulty x Time |
190.090
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2
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95.045
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20.009*
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| Within Groups -- Error |
85.500
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18
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4.75
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| Total |
279.333
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23
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We do not interpret main effects in the presence of an interaction. The next step is to graph our results. This will help us with our interpretation.
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