# Normality test: descriptive vs inferential

REVISED ON REQUEST: Is normality test conducted to check sample normality or population normality, most of the times normality test is required to validate the assumptions of parametric test i.e. the population distribution is normal.

ORIGIANLLY POSTED: We have descriptive normality tests like histogram, QQ plot and other graphical methods Skewness and kurtosis numerical measures

Then the inferential methods the Shapiro-Wilk, Anderson-Darling, KS etc

Why would one perform normality test on sample for descriptive results, most of the hypothesis test talks about population being normal which means inferential methods should be used?

Wondering if something is amiss in my understanding.

I am puzzled why and how descriptives are necessary.

• Could you attempt to clarify your question (by editing the text)? It's really not clear to me what you're asking. – Glen_b -Reinstate Monica Dec 13 '15 at 5:35
• When i do histogram on a sample it just represents the sample data normality ie check if the sample is normal or not; where as when i do Shapiro wilk it does test the normality test for the population ie the inferential part....why would i need histogram or simply put why should i care for sample normality when population normality is what should matter – noob Dec 13 '15 at 5:41
• The sample is not normal but a sample might be drawn from a population which is normal. – Glen_b -Reinstate Monica Dec 13 '15 at 7:08
• Is a normality test - if ever - not done to check the normality of regression residuals? Such a test is not "required", generally choosing the analysis based on such a test invalidates the p-values etc. from the final analysis, some non-normality is not an issue for most methods (esp. If N is large) and more commonly the analsis is chosen up-front based on previous knowledge. – Björn Dec 13 '15 at 7:41

Why would you want 'descriptive' methods like plotting an histogram or a QQ plot? Because sometimes the tests can just be 'wrong' and you have to check visually. Remember that in any goodness of fit test, you don't want to reject $H_0$, but if, for example, you have a very large sample size, the power (the probability of rejecting a false null hypothesis) of the test could be too high and you'll find yourself rejecting $H_0$ with a very high probability (because of small deviations), even if the data is not really that different from the theoretical distribution. If that is the case, a histogram with a QQ Plot may help you in deciding that you can work as if the sample was drawn from a normal distribution.