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I want to conduct Paired t-test for 2 variables that one is normal distributed and the other is not (N = 56)

I've used the Shapiro-Wilk in order to check normality of the variables and these are the results:

Shapiro-Wilk normality test

data: Bq_t1$var

W = 0.98041, p-value = 0.4932

data: Bq_t2$var

W = 0.9261, p-value = 0.002072

As you can see, the second test came sig (p<0.05) so the var is not normal distributed.

Furthermore, the results of the T-test came significant but I'm not sure whether I can use this test.

Paired t-test

t = 7.8132, df = 55, p-value = 1.759e-10

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval: 6.983627 11.802087

sample estimates: mean of the differences 9.392857

what should I do? Thanks a lot.

Phil
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Ido
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    For a paired t-test we only care if the differences are approximately normally distributed. – Dason Mar 23 '21 at 14:31
  • I see, How do I check it? – Ido Mar 23 '21 at 14:31
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    Look at the distribution of the differences. With n of 56 as long as the distribution isn't too non-normal you should be more than fine. – Dason Mar 23 '21 at 14:34
  • you mean to plot a distribution of var3 which is: var3=(var1 - var2)? – Ido Mar 23 '21 at 14:36
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    If you're thinking about doing a paired t-test then what you define as var3 should be the only variable you actually consider. So yes you can plot the histogram or maybe a qq-plot for that variable. Something along those lines just to assess if it's "too" non-normal or not. – Dason Mar 23 '21 at 14:43

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