Statistics – Normality test

 In Statistics & methods

Hi, I got a comment from a SPSS developer person that has a LOT of knowledge. He mentioned after my blog post in August about normality, that it’s also possible to make a test of the normality.

I will just would like to recommend only to use this test when you have small samples. Say under 100 cases, because the tests were created long time ago when samples were smaller. Otherwise the test seems to show wrong conclusion – example that a variable I know is normal has a conclusion that it’s not normal.

So my rule to you as an advice, do this test only if you have under 100 cases.

In this example I have 30 cases and I would like to test if salary and age is normal distributed or not.

Command: Analyze – Descriptive Statistics – Explore

and put in the variables you want to check

Then click on the sub-command-button: “Plots” and tick the box at “Normality plots with tests”

Here is the result:

You get 2 test: Kolmogorov-Smirnov and Shapiro Wilk. The question is which to use?

My old statistician colleague likes Shapiro Wilks best, because more stable result.

Conclusion: “Age” is normal distributed. Detailed info: If we have a look at the Sig-value (significance value or p-value) for Age, it say: 0.056. So because it’s bigger than 0.05 then we cannot reject the null hypothesis (Normality). So we cannot say that age is skewed distributed, it seems to be more normal distributed.

Conclusion: “Monthly salary” is NOT normal distributed. Detailed info:  If we have a look at the Sig-value (significance value or p-value) for Salary, it say: <0.0001 (Obs you can never say that it’s 0). So because it’s much less than 0.05 then we can reject the null hypothesis (Normality). So we can say that salary has a skewed distribution or you can say that it is not normal distributed.


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