I have data for a mental health study with a relatively small sample (N=80).
I have been researching whether I can run a parametric analysis with my non-normally distributed data but am going around in circles. Essentially I have a sample with positively skewed outcome measures data (ie, not very symptomatic ~ 1/3 have no symptoms). I've done a Log10 transform but it's still not reaching normality according to Kolmogorov-Smirnova and Shapiro-Wilk. I'm not sure how strict/conservative K-S & S-W normality tests are in terms of having to abandon T-tests, ANOVAS, ANCOVAs.
Skewness for my main two variables is 1.49 (SE, .267) & 1.46 (SE, .267). Kurtosis for each is 2.02 (SE, .529) & 1.38 (SE, .529)
There are some things we can't answer without a parametric test eg influence of covariates, so obviously we want to be able to run parametric analysis if at all possible, without unduly violating assumptions that would make the inferences/results invalid.
I've run both parametric & non-para analyses and there are very few differences in results (ie, significance), so I'm inclined to think either the para tests are sufficiently robust, or my data is not so badly skewed that it has to be analysed using non-para.
I'm currently writing up the paper and am at a crossroads in analysing this data - do I have to go abandon the parametric analyses and go down the non-parametric path?
Thanks in advance.
Watch this video to understand when to use Non-parametric test, which NP test to run and its effect:
https://youtu.be/Xu6-kU8s-ls
First, remember that the assumption is that the residuals are normally distributed, not the outcome variable. However, IMHO I think you're good to go. I usually want to look at a plot of the residuals before making that call, however.
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hard to give an opinion without a look at the data !
bootstrapping may be a handy third way out of the parametric/non parametric alternative
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