# P-Value in Shapiro-Wilk test

I've read that if this p-value is less than 0.05 (for a 95% confidence interval), the null hypothesis that the data comes from a normal distribution must be rejected.

However, in the following website (scroll down to Both R and Python), the p-value is a number in scientific notation (4.4479165357181255e-25) and is still said to be greater than 0.05. Is this accurate?? I would think the scientific notation indicates the number is quite a small value and thus smaller than 0.05.

https://knowledge.safe.com/articles/69103/perform-a-shapiro-wilks-statistical-test-using-r-o.html

Any insight/confirmation would be helpful. Thanks!

• Given the error that you spotted and the ones Nick Cox points out, I'd exercise a deal of caution in relation to the article. You might also benefit from some of the answers at Is normality testing essentially useless?; (I think Harvey Motulsky's answer is deserves an especially careful read.) – Glen_b -Reinstate Monica Mar 16 '19 at 9:50

## 1 Answer

You are correct. A fuller quotation is

If the p-value is less than the significance level (in this case 0.05, a 95% confidence interval), the null hypothesis that the data is normally distributed can be rejected. Put in plain language, if the p-value is less than 0.05, we can assume the data is not normally distributed. So for our data the p-value is 4.44, which is greater than 0.05, so our data is normally distributed.

At best that is a silly slip. The "e-25" is crucial detail. However, it is a fundamental misunderstanding that "the P-value is 4.44". P-values lie between 0 and 1.

Further, it is confused and confusing to equate P = 0.05 and a 95% confidence interval. No confidence interval is being used here at all.