# Presenting the results: Continuous variables, Normally distributed vs non normally

#### Elha

##### New Member
Hi

My question is most probably simple but I can't find an answer to it.

According to my stats textbook one should report continuous variables as follows:
- Mean +/-Standard deviation (SD)if the variable is normally distributed
- Median +/-Interquartile range (IQR) if the variable is not normally distributed

Now we were given as a self study exercise a data set and the exercise asks to create some independent groups and compare them. The aim is to practice in applying two sample t-test and the non parametric Mann Whitney.

But what happens when it comes to presenting the results? For the two sample t test one can write "The group A (mean+/-SD) had significantly higher values of the variable compared to the group B (mean+/-SD) p value <...." and the reader can see for themselves.

What is the most efficient way to do this for the Mann Whitney test though?
Can one write something in lines of "The group A (mean+/-SD) had significantly higher values of the variable compared to the group B (median+/- IQR), p<..."?
Or do we report only means and SDs for both groups? Or do we report Medians and IQRs for both groups?

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#### CB

##### Super Moderator
Re: Presenting the results: Continuous variables, Normally distributed vs non normall

The Mann-Whitney test isn't really testing a null hypothesis of equal means or equal medians, so there's no obvious answer as to which descriptive statistic to employ. But certainly you'd want to report the same statistic(s) for both groups. Probably the median would make most sense.

By the by, I think the advice that one shouldn't report means and standard deviations for non-normal variables is a bit silly, though I know this idea gets tossed around a bit. The sample mean is just as good an estimate of the population mean for a non-normal variable as a normal one, and ditto for the standard deviation. A mean doesn't somehow become "broken" if the variable is non-normal.

#### Elha

##### New Member
Re: Presenting the results: Continuous variables, Normally distributed vs non normall

Thank you very much for taking the time to answer my question.

I looked up some papers in the medical field (the field I am interested in) and I saw that there is a huge diversity in the way they report their results. Others report only means + SDs no matter, others means+SD and medians+IQRs and others only medians and IQRs. It's a bit mind boggling for me.

For my exercise I had to accept the textbook rule that I should report continuous variables depending on their distribution. So I presented the results in a table with markers indicating where the numbers are means+SDs and where they are medians+IQRs. In the text I wrote (t=..., p=...) for two sample t-test and (U=...,Z=..., p=...) for Mann Whitney.
I am not sure at all if this is an acceptable way of reporting results and it irks me that I will probably never get an answer from the course because it was a self study exercise and I am categorized as an observer for that class. :/

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