Importance of Normality Assumption for Hypothesis testing methods

Hello everyone!

Can someone please share their thoughts on the following question with me.

Methods of hypothesis testing usually has a normality assumption for underlying data or for residuals in the case of regression. Why is this assumption important for either case; i.e. for 'Differences in Means' and 'Regression'.

Please let me know if you need any further clarification.

Thank you for your time.


No cake for spunky
The normality values are I believe central to both creation of the confidence intervals and the p values. Without them it is impossible to do statistical tests (well to interpret statistical tests). I am not sure this is what you are asking.