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paired t-test shows no difference between median and Wilcoxon test p value shows that there is a difference between median values ? How to interpret?

Data Science Asked on April 10, 2021

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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