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.


Any insight/confirmation would be helpful. Thanks!

  • 4
    $\begingroup$ 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.) $\endgroup$ – Glen_b -Reinstate Monica Mar 16 '19 at 9:50

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.

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.