the researcher finds the data are not exactly normally distributed. He can still use the paired t test because there are at least pairs of measures
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If you have a paired group design and cannot assume a normative distribution, which test do you use?
Prabhakar K.
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 paired Wilcoxon 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. approximately normal. b. highly skewed; the sample size is $20 .$ c. symmetric bimodal.
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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 and you know that the paired-difference variable has a symmetric distribution that is far from normal. a. Is use of the paired $t$ -test acceptable if the sample size is small or moderate? Why or why not? b. Is use of the paired $t$ -test acceptable if the sample size is large? Why or why not? c. Is use of the paired Wilcoxon signed-rank test acceptable? Why or why not? d. If both the paired $t$ -test and the paired Wilcoxon signed-rank test are acceptable, which test is preferable? Fxplain your answer.
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