Suppose that you want to perform a hypothesis test based on a simple random paired sample to compare the means of two populations. For each part, decide whether you would use the paired t-test, the pairedWilcoxon signed-rank test, or neither of these tests. Preliminary data analyses of the sample of paired differences suggest that the distribution of the paired-difference variable isa. uniform.b. not symmetric; the sample size is 132.c. moderately skewed but otherwise approximately bell shaped

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Asked Jan 27, 2020
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Suppose that you want to perform a hypothesis test based on a simple random paired sample to compare the means of two populations. For each part, decide whether you would use the paired t-test, the pairedWilcoxon signed-rank test, or neither of these tests. Preliminary data analyses of the sample of paired differences suggest that the distribution of the paired-difference variable is

a. uniform.
b. not symmetric; the sample size is 132.
c. moderately skewed but otherwise approximately bell shaped

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Expert Answer

Step 1

a.

In this context, the aim is to show whether to use paired t-test or paired Wilcoxon signed-rank test, or neither of these tests when the paired difference variable is uniform.

Requirements for a paired t-test:

  • The samples must be paired sample and drawn randomly from normally distributed populations.
  • Size of the sample must be large.

Requirements for a paired Wilcoxon signed-rank test:

  • The samples must be paired sample and drawn at random.
  • Symmetric difference of the sample.

It is more appropriate to use paired Wilcoxon signed-rank test than paired t-test for the uniformly distributed samples. Because uniform distribution is symmetric and non-normal.

Step 2

b.

In this context, the aim is to show whether to use paired t-test or paired Wilcoxon signed-rank test, or neither of these tests when the paired difference variable is not symmetric; the s...

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