Suppose we have the following sample data of reaction times: There are two ways

Question

Suppose we have the following sample data of reaction times: There are two ways to look at these data. Scenario A: as 24 individuals randomly assigned to two groups Scenario B: as 12 individuals who each had to use both their left and right hands One of the scenarios above involves independent samples, and the other involves paired samples. The sample standard deviations are as follows: the standard deviation of the right hand measurements is 0.088, the standard deviation of the left hand measurements is 0.117, and the standard deviation of the paired differences is 0.021. So the standard error for one of the scenarios is 0.0061, and the standard error for the other scenario is 0.0423. (a) The data are treated as independent samples in Scenario _________. For that scenario, the correct standard error is _____. (b) Fill in the blanks in the following statements: 1. Treating the data as independent samples, the standard error is ______ [larger/smaller] than if the data were treated as paired samples. 2. Consequently, treating the data as independent samples would result in a _____ [larger/smaller] test statistic. 3. Therefore, a test for a difference of means will generally have a ____ [larger/smaller] p-value if the data are treated as independent samples.

Explanation / Answer

a) The data are treated as independent samplesin scenario A. For that scenario, the correct standard error is 0.0423

b) 1. Treating the data as independent samples, the standard error is larger than if the data were treated as paired samples.

2. Consequently, treating the data as independent samples would result in smaller test statistic.

3. Therefore, a test for difference of means will generally have a larger p-value if the data are treated as independent samples.

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