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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.

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    $\begingroup$ Could you attempt to clarify your question (by editing the text)? It's really not clear to me what you're asking. $\endgroup$ – Glen_b Dec 13 '15 at 5:35
  • $\begingroup$ 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 $\endgroup$ – noob Dec 13 '15 at 5:41
  • $\begingroup$ The sample is not normal but a sample might be drawn from a population which is normal. $\endgroup$ – Glen_b Dec 13 '15 at 7:08
  • $\begingroup$ 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. $\endgroup$ – Björn Dec 13 '15 at 7:41
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The normality tests are conducted on a sample to test if the sample was drawn from a normal population.

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.

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  • $\begingroup$ when i use spss >>explore>>descriptives for normality then histogram , qq , boxplot are suggested by book, where i was wondering does sample data plot showing normality will automatically imply the population normality?? why do literature talk about these ?? $\endgroup$ – noob Dec 13 '15 at 10:12
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    $\begingroup$ @noob Nothing automatically implies population normality. As well explained in this answer, all you have is the sample and a situation in which significance need not mean practical importance. $\endgroup$ – Nick Cox Dec 13 '15 at 12:40
  • $\begingroup$ I can understand that significance is just statistical and might not mean a practical significance . however this shouldn't mean that ...in the realm of hypothesis testing for thesis or other research work ...I can never state that... because inferential statistics might not be robust I abandon them or downplay them...by stating ...descriptives are of practical significance and robust...thus I do inferential if the result is not favorable... I will use descriptives as substitute for inferential... $\endgroup$ – noob Dec 15 '15 at 17:13
  • $\begingroup$ From this can I interpret that when inferential fails to prove we should use descriptives. My further question is why can't we use more robust methods $\endgroup$ – noob Dec 15 '15 at 17:32
  • $\begingroup$ It is not that when inferential fails you should use descriptives. Is just that you can't rely just in one of them $\endgroup$ – toneloy Dec 15 '15 at 19:32

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