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I am relatively new to statistics and struggle with the normality assumption (where and how it needs to be assessed). I understand that parametric tests need the data to be normally distributed. The literature seems to be conflicting information on what variables need to be checked.

Could someone suggest a normality-testing process to follow for t-tests, multiple regression and binary logistic regression in terms of what variables/things to check, when and how?

I am getting confused with the below: Before conducting a parametric test:

  1. Do I need to check that each continuous independent variable follows a normal distribution? Do I need to check the dependent variable also?
  2. If any variables do not follow the Normal distribution, is it at this point that I would potentially transform data and restest/assess for normality?
  3. Does any of the above apply to certain types of tests (e.g. t-tests)? After running a test:
  4. Is it only the standardised residuals that need to be assessed for normality? Apologies if any of the above are silly questions!
Codingguy1
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  • Welcome to Cross Validated! I addressed the regression assumptions about normality in an answer a few days ago, and my objections to A and B apply to logistic regression, too. – Dave May 24 '22 at 12:35
  • Thanks Dave- just read your answer. To check my understanding, I do not need to ensure any of my predictors have a normal distibution pre-testing? Is an Ordinary Least Squares Regression applicable to all parametric testing? – Codingguy1 May 24 '22 at 13:18
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    Does this answer your question? Is normality testing 'essentially useless'? That page, and the many links from it, should answer all of your questions. It's only residuals that matter (think of t-tests as very simple regressions), and even then you don't absolutely need normal residuals. See presentations on best linear unbiased estimates and the central limit theorem. – EdM May 24 '22 at 13:22

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