Dear Fateme,

You have 2 ways: you should use either non-parametric tests with your primary data or parametric tests with the normalized data. You can make the data normal with some methods such as log-normalizing, Cox-box test, Johnson test. Please keep in mind you have to do normality tests after each attempt to normalize the data to ensure whether they are normalized. Sometimes, you must apply several normality tests on your data to make them normal.

Best regards.

Dear Mohammad Javad,

Thanks a lot for your attention. Your answer is useful for me.

Regards,

If you failed in normality tests then it would be better to try for non-parametric tests. Total sample is large enough to overcome but if you think for 5 groups separately then it might not be enough for normality.

Hello Fateme,

You can:

1. Use Exact/Reseampling/Bootstrap methods. These are increasingly available in statistical software, and help to avoid the issues of specific distributional requirements. If your software does not include them, then the R system has multiple libraries which do (e.g., boot, coin).

2. Use rank-based non-parametric tests. While these allow you to ignore the normality assumption, they frequently require homogeneity in order to yield valid results.

3. Try transforming the data to conform better to the usual parametric assumptions, as suggested by Mohammad. Some data sets can be made "tractable" in this way; others can't. The problem with forging ahead with the parametric methods even though you have evidence that the underlying conditions haven't been satisfied is that you'll not know whether the result is correct (or if robustness has failed with your data set).

Good luck with your work.

@Muhammed Ashraful Alam

@David Morse

Thanks a lot,

I learn from your answers. I check your solutions on my data.

Best Regards,

Fateme

You also can use Welch test for nonequal variances. With sample size of 1184 it will get an asymptotic p-values valid ever for non-normal data.

https://en.wikipedia.org/wiki/Welch%27s_t-test

Dear Ivan,

Thanks a lot about Welch test. I did not know it.

Best Wishes,

You should have to use nonparametric test instead of parametric test because data are not normally distributed

@Arvindkumar Chaudhary 🙏🙏

An option for those who do not wish to have a lack of distribution is to determine the distance of mahalanobis and delete the data with values of .000 and perform the respective analyses again

https://www.youtube.com/watch?v=AXLAX6r5JgE&t=282s

You should be non-parameteric test