Please do you know how to test normality in the sample of 191?
I read for medium-sized samples (50 < n < 300), reject the null hypothesis at absolute z-value over 3.29, which corresponds with a alpha level 0.05, and conclude the distribution of the sample is non-normal. In my sample, using z-scores are over 3,29, therefore, the distribution should not be normal.
The issue is that my skewness values fall in the interval , and therefore, the distribution should be considered normal...
What do you think?
Can you suggest any sources that talk about this interval between -1 and 1?
The data are from psychology tests.
Thank you for your advice :)
Maria
Why are you using skewness to test Normality? If you cube all the values of a Normally distributed variable it will still be symmetric. There are tests of Normality. But before addressing this, why are you testing for Normality? Is there a particular substantive theory that makes the argument the variable is Normally distributed? Testing for assumptions in this way has issues.
Dear Mr. Wright,
thank you very much for your answer. You are much more experienced in the psychology research (I consider myself a beginner). I am trying to check normality in order to choose the right correlation coefficient and tests (parametric or non-parametric) to make further research for my theses. I thought this was first step (after invstigating the sample), which tells me how to proceed. I checked the reliability of the inventories/questionnaires and it seems to be OK.
Am I totally lost? :)
Testing for normality is advicable AND mostly used when you want to run a Monte Carlo simulation for SEM to confirm if your data is normally distributed. But if you still want to do a normality test, use z-score from parametric data gotten where u have the mean SD and the variance.
Hi Maria Strenacikova Jr. , the difficulty with testing for Normality (and this would be bivariate normality, but there are tests for that too, e.g., Royston's) is that finding a non-significant statistic doesn't mean you have bivariate normality since you don't accept the null hypothesis. There will always be some variation from it. The question is how much, and if it will make a difference. Tukey, one of my stats heroes, said "all assumptions are wrong" (1986), but you should ask how much this affects the inference. So if you did not want to assume it, you can use alternatives. If you are still interested in the fit of the straight line, you would still use Pearson's correlation, just you might use a different technique to get your confidence interval (like bootstrapping). I think there is a bootstrapping option in SPSS. I only have a copy of that in my office and with covid I am not there (and I don't use it much).
Maria Strenacikova Jr. wrote that the "absolute z-value over 3.29...corresponds with a alpha level 0.05". The critical value of z for alpha = .05 (two-tailed) = 1.96, not 3.29. 3.29 is the critical value of z for alpha = .0005 one-tailed or .001 two-tailed. Try it in any good online calculator--e.g., this one:
- http://onlinestatbook.com/2/calculators/normal_dist.html
Use "Above 3.29" to get the one-tailed result, and Outside -3.29 and 3.29 to get the two-tailed result.
PS- I agree with the other posters who have advised that testing for normality is not helpful. Tests of normality have too little power when samples are small, and too much power when samples are larger. I have a presentation on this issue which you can find by searching under Presentations on my profile page.
EDIT: Here's the link to that presentation on testing for normality.
Presentation Silly or Pointless Things People Do When Analyzing Data: 1. ...
Dear Mr. Bruce Weaver, thank you very much for your thorough explanation. It is much clearer now... Thanks.
Dear Mr Daniel Wright , thank you for you explicit answer... I do not need the fit of the straight line. I saw this bootstraping option, but never tried it before. Thank you.
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