I have problem with real basics. I have variable that has p=.000 in Shapiro-Wilk. As I looked on the histogram it appears that the cause is natural limit for this measurement (value 0, skewness > 1,5).I'm wondering what whould be the best way to present this data as descriptives. What parameters of descriptive & non-paramteric statistics would be the best to present data like this? Is there equivalent of 95%CI for non-normal distribution ? (for example interquartile range)

Thank you in advance!


There's two questions here really. The first is whether you can use a 95% confidence interval for the mean of a non-normal population. And you can, with several options:

(1) If the sample size is large the mean will be approximately normally distributed anyway

(2) Fit a specific distribution & calculate confidence intervals for the mean based on your fit

(3) Calculate bootstrap confidence intervals for the mean

The second question is about whether the mean is an appropriate descriptive statistic for a skewed distribution. There's no definite answer to this; it depends what information you want to get across to your audience, & of course what they can understand.

(1) Report mean, standard deviation, and skewness. But skewness won't mean much to non-statisticians

(2) Use the median as a location parameter - you can calculate a confidence interval for it too. Reported together, mean & median give some idea of skew.

(3) Make a short table of percentiles. Very easy for anyone to make sense of.

(4) Why not a graph? A histogram or kernel-smoothed density estimate.

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