Check normality in discrete variable

[joan marc]

Hi everyone,

Which would be the more correct way to check the normality of the distribution of a discrete variable?
(range 0-10: 0,1,2,3,4,5,6,7,8,9,10), n=17.000

My best option is swilk but does it understand it is discrete? Other alternatives: plot it with hisogram , kdensity normal or graph box

Thank you in advance

Joan

[daniel klein]

What do you mean by "more correct way"? Strictly speaking, I do not believe a discrete variable can follow a normal distribution as the latter is continuous. Perhaps it would be a good idea to state what your ultimate goal here is.

Best
Daniel

[joan marc]

I want to perform a mean-difference test but I have read ttest needs the variable to be normal

[Nick Cox]

Such a variable can at best be approximately normal. It's clearly bounded as well as discrete.

swilk has precisely no idea that it should think differently if the data are discrete. That would make little or no sense.

Why do you think you should test here for normality? What assumption or ideal condition have you got in mind here?

[daniel klein]

The t-test can be expressed as a simple linear regression model. Normality is assumed for the residuals, but neither for the response nor for the predictors. It also turns out that this specific model is quite robust in case this assumption is violated if the sample is large, large meaning roughly more than 50 cases.

A probably more important assumption is constant variance of the errors. But you can fix this adding the unequal option to ttest (or using vce(robust) with regress).

Best
Daniel

[Nick Cox]

I tend to agree with Daniel. Note that there is also a stronger assumption implied here, that your variable is close enough to counted or measured scales that means make sense.