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I have a dataset. I wanted to do paired t test on it. So I carried out normality test and it showed that it does not follow normal distribution. So I used Wilcoxon test in place of paired t test. The descriptive statistics of my data shows median value of 0 but when I ran wilcoxon test, it gave me a p value <0.05 stating to reject null. Could you please tell me why this discrepancy in my test results?

summary(Rel) REL1. REL2. Diff
Min. :1.000 Min. :1.000 Min. :-5.0000
1st Qu.:7.000 1st Qu.:6.000 1st Qu.:-1.0000
Median :7.000 Median :7.000 Median : 0.0000
Mean :6.617 Mean :6.289 Mean :-0.3282
3rd Qu.:7.000 3rd Qu.:7.000 3rd Qu.: 0.0000
Max. :7.000 Max. :7.000 Max. : 3.0000

Wilcoxon signed rank test data: REL1. and REL2. V = 7993.5, p-value = 2.449e-13 alternative hypothesis: true location shift is not equal to 0

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  • $\begingroup$ Have you removed information on missing values by any chance? Descriptives run on each variable separately. Wilcoxon test runs only on the observations which are non-missing for both variables at the same time. $\endgroup$
    – stans
    Jan 21, 2021 at 6:16
  • $\begingroup$ yes.. I have removed missing values. The above output is after removing missing values only. $\endgroup$
    – pinky
    Jan 21, 2021 at 14:29
  • $\begingroup$ paired t-test does not require normality i.e. normal distribution. You may indicate part of sample data to get a valid response. what is your hypothesis ? $\endgroup$
    – Subhash C. Davar
    Jan 29, 2021 at 2:08

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