When deciding between parametric or non-parametric forms of statistical analysis, researchers usually consider the assumptions that underpins such statistical analysis type, and when for example the assumptions of a parametric test are violated, the alternate non-parametric equivalent test is used.
Consider this scenario, a researcher wants to compute a paired sample t-test, and checks to see if the assumptions are violated. All but one assumptions of the paired sample t-test are met but the data is not normally distributed. The researcher then goes ahead to use the paired sample t-test and states that although the data is not normally distributed, the assumptions are not markedly violated. Hence, my questions are:
1. What does it mean by the assumptions of a test are not markedly violated?
2. In the scenario above, does it mean that the researcher was wrong in using the parametric pared sample t-test instead of its alternate non-parametric test?
3. If the researcher in the scenario was not wrong, then how do we justify his interpretation of results owing to the fact that the assumptions of the paired sample t-test were not all met?
You can also add a Wilcoxon test in the analysis, in SPSS. Analyze->Non parametric Tests-> 2 Related Samples. Under this procedure, normality is not needed. Try to compare the 2 tests results (.sig values).
Thank you for your feedback, @Sofia and Subrata, are we saying that if the sample size is large enough, the lack of a normal distribution from the data does not affect the use of t-test?
@Shmatis Ntamos...Thank you for your recommendation. I am aware of the alternate non-parametric test for paired samples. I just wanted to know if the practice of utilizing t-test when some of the assumptions are violated is okay.
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