Due to data that is not normally distributed, non-parametric (Wilcoxon) stats have been implemented. However, I would like to know the best way to represent the variability of the data. Is it best to simply use the inter-quartile range or is an equation such as IQR/Median more representative of the variability?
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see the following discussions :
http://stats.stackexchange.com/questions/243453/what-does-the-iqr-median-mean
http://stats.stackexchange.com/questions/38635/a-robust-non-parametric-measure-like-coefficient-of-variation-iqr-median-o
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Start out with a box and whiskers plot, Alexis. It will graphically show the spread of the data, in addition to identifying any existing outliers. If the data looks "OK", I would use the regular measures of variability, such as the standard deviation. It is tricky to distinguish between "real outliers" and "high variability". Rank based metrics lower the usefulness of variability information. The normality requirements are for the test but not for the data visualization.
I think if the variable is understandable to the audience, it is better to use statistics in the original scale, that is, IQR, etc. without dividing it.
My best recommendation is to report the whole 5-number summary (min, Q1, median, Q3, max), or show these in a box plot.
Let me give an example.
Those of us who are used to grading students on a 0-100 point scale will understand, "The median for class A was 80 with the middle 50% of students getting between a 75 and 90"
It's more difficult to make sense of, "The median for class A was 80 (IRQ/m = 0.1875)."
Best is to just report:
Class A:
Min 65
25th Percentile 75
Median 80
75th Percentile 90
Max 93
Yes, exactly. My recommendation is to either report the 5-number summary in a table or show them with a box plot. In most cases, I _think_ that is best way to report both the median and the spread of the data.
I'm not opposed to reporting IRQ or IRQ divided by median, but I think they are less helpful.
Thank you all for your insightful responses to my question. I now have a much clearer idea of how to proceed with my data. I appreciate you taking the time to provide your suggestions.
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