why is my shapiro test for normality not normal?

Could it be because I have 400 males and 500 females? my skewness, kurtosis histograms etc are all fine and my levenes test.

I wanted to say in my report a possible why the shapiro said it wasnt normal....

could it be because of possible outliers or something? is there a way to look and see if i can find out why?



Ambassador to the humans
You really didn't tell us much about your data. For instance... what is your data. You don't tell us what the variable is. Also, most data isn't normally distributed and that's alright. What are you trying to do with your data and why do you need it to be normally distributed?

Mean Joe

TS Contributor
Looking at the way that the statistic is calculated, it looks like it places an emphasis on having more observations near the mean.

I've read that the Shapiro-Wilk test "does not work well" when several observations have the same value.
Thank you so much for all the responses!

My data is on gender (more males than females by about 100), belief in astrology which is a set from 1 (not at all) to 7 (totally) and stress which is based on a 14 point likert-type scale score.

I was first looking at whether belief in astrology varies between genders with an independent t test, if belief and stress correlate with a pearsons r correlation test, and if stress varies between genders using an independent t test.

My Shapiro-wilk says none of these tests are normally distributed. BUT my skewness, kurtosis and levenes tests, hostiograms etc are all normal!

Thanks again i soo appreciate it


Ambassador to the humans
Except that it's impossible for your data to be normally distributed. With such a large sample size you'll easily detect this.

A normal distribution is a continuous one. Your data clearly isn't.