I have little background in statistics. For a dozen items, I have vectors of ratings for these items.

I have calculated the variance, and Pearson correlation for these items (using numpy). Now I would like to compare them.

My adviser asked me to see if the differences in variance and correlation were "statistically significant" using the 95% rule. How can I do this?

How does this statistical significance relate to scipy's p-value which is returned with Pearson correlation (it makes no mention of "95%")?

The p-value roughly indicates the probability of an uncorrelated system producing >datasets that have a Pearson correlation at least as extreme as the one computed from >these datasets. The p-values are not entirely reliable but are probably reasonable for >a datasets larger than 500 or so.


1 Answer 1


If difference between two numbers lies within two standard deviations above or below 0, then this result is not 95% statistically significant. Roughly 95% of normal distribution is covered by two std's, this is where it comes from. That is, if your values have standard deviations of $\sigma_1$ and $\sigma_2$, the joint is $\sigma = \sqrt{\sigma_1^2 + \sigma_2^2}$. If $|x_1 - x_2| > 2\sigma$, they are different with 95% probability. This all assumes normality.

p-value relates to the quality of one variable in predicting (correlating to) another, this is a different thing from what you are asked to do.

  • $\begingroup$ This seems to be mixing up standard deviation and standard error. $\endgroup$
    – Dave
    Jun 15, 2021 at 19:58

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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