I administered pre and post-achievement tests on one sample (N=16), where I obtained two paired variables and intended to run a paired sample T-test. However, while pre-test data are normally distributed, post-test data are not. Should I go for the Wilcoxon signed-rank test on SPSS?
Hello, yes indeed. Given the normality conditions of the post test group, the proper analysis to conduct is the Wilcoxon text. Best wishes in your research :)
Both the paired t-test and the signed rank test are conducted on the paired differences. All assumptions for the tests apply to the these differences. No assumptions apply to the pre- group or post-group separately. The tests --- and the assumptions --- are exactly the same as the one-sample versions of these tests on the differences.
If you have any references that suggest that the assumptions apply to pre- and post- groups separately, you can throw them in the garbage.
Hope that helps...
It is stated that the pre test data are normally distributed but posttest data are not. This means the intervention whatever you have done to the subjects have resulted in varying responses.
It is shown [1] that t-test, against the popular belief and claim, is not sensitive in picking up the expected significant differences. At alpha = 5%, for the selected sample sizes of 18, the validity remained around 53% for the t-test and the Mann Whitney test. It is concluded therefore that the t-test and Mann Whitney test are not suitable when the sample size is below 20. However, by raising the alpha level to 10%, a rise of about 15% is observed in the validity of both the tests.
In general, the statement that the non-parametric tests are suitable for any non-normal sample comparisons is not correct and should be used with due caution [2]. When the samples are following a Uniform distribution or an Exponential distribution, At alpha = 5%, the Mann Whitney test showed a validity, below 15% [2].
Coming to your questions, the sample size appears to be less. In case, still you want to use the data results with pair t-test (which is valid to be used) use alpha=10% not 5%.
[1]. Takiar R (2023): The Validity of t-test, Mann-Whitney test and Z test for testing the Significant differences between two sample means when the sample size is between 10 and 30; Bulletin of Mathematics and Statistics Research, Vol. 11(3), Page 1-12.
[2]. Takiar R (2023): The Validity of Mann-Whitney test for comparing two sample distributions following Uniform or Exponential distribution; Bulletin of Mathematics and Statistics Research, Vol. 11(3), Page 45-57.
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