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I am starting some quantitative analysis of a dataset. My sample size is just over 100 (approx 110) and before doing the descriptive stats I attempted some normality testing to determine if I should present my descriptive stats as mean (SD) or median (IQR). I read several papers on the topic and then ran the following analysis in SPSS: histograms, skewness and kurtosis, Shapiro-Wilk and K-Smirnov tests so I could get an overall idea of if the different variables were normally distributed. The SW and KS tests both were non-significant for all variables and skewness and kurtosis stats also indicated normal distribution. However, some of the histograms clearly showed non-normal distribution. I am confused about what to do at this point. Which results should I trust to determine if I can should present my descriptive stats as mean (SD) or median (IQR)? Any direction would be appreciated! Thank you!

Matt B.
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  • 1) Can you post the plots? (Maybe you're working with confidential or proprietary data and can't, but maybe you can.) 2) Why not give mean, median, standard deviation, and IQR? – Dave Sep 09 '21 at 15:02
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    You don't choose your descriptions based on a preliminary distributional test! That's almost the opposite of what "description" means (because the test is imposing a preconceived model on the data). You describe the properties that matter to you, period. Thus, obtaining good advice in this matter requires more information abut what kinds of analyses, decisions, or actions you plan to make with these data. – whuber Sep 09 '21 at 15:14
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    I can't post the plots unfortunately. But okay thank you that is good advice. I could just present all in my descriptive stats. Someone had advised me previously to check the normality to know how to describe the results in terms of mean SD/median IQR... maybe I interpreted what they said wrong. After I present the descriptive stats of my sample then I will be doing multiple linear regression... In that case, if I understand correctly, I will need to ensure that the residuals are normally distributed... – Matt B. Sep 09 '21 at 15:33
  • It is rare that a regression analysis requires normally distributed residuals. You can read a great deal about this by searching our site for [normal* test* distribut* regression](https://stats.stackexchange.com/search?q=normal*+test*+distribut*+regression). One top hit at https://stats.stackexchange.com/questions/130775 contains a very thoughtful discussion. – whuber Sep 10 '21 at 13:50

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