For four groups, I have only their summary statistics (sample size, mean, standard deviation, median, and interquartile range). I do not have access to the raw data. I believe the dataset is non-normally distributed (small sample sizes and discrete numeric data).
Are there any tools/programs/tests that I can use to compare non-normally distributed data if I don't have the raw dataset? I am able to find online versions of the ANOVA where I can get along by inputting mean & standard deviations to get a p-value for differences between the two groups - this would seem the best option for normally distributed data. However, like I mentioned, I suspect my data is non-normally distributed, and a non-parametric test would be most appropriate.
No. The only option you have is to write to the authors of the publication and request them for the dataset. They might be willing to share it with you. All the best!
Given the median and if you have the upper and lower quartiles you could plot a comparative box plot for the four groups which would tell you quite a lot.
Also if the data were a perfect normal distribution the IQ range would be approximately 1.35 standard deviations , so this will give you some handle on non-normality. Comparing the mean and the median will also help with this.
Heaps of raw data is availablle online. Unfortunately, raw data is NEVER normally distributed. For validity and performance of your approach, the need is to perform some data cleaning techniques, e.g., PCA, SVD, Manifold Learning etc., as a first step of data preprocessing. Accordingly you may obtain approximately normalized data for comparatively optimal results. Another step is to use appropriate samples of training and testing data for avoiding overfit and underfit issues.
I can't help but comment data are not nonparametric only some inference methods are. D. Booth
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