Quartz | Level 8

## Sample Size for Wilcoxon Signed Rank Test

I am comparing the opioid prescriptions for several providers, 1st Quarter 2017 vs. 1st Quarter 2018. We intend to compare the average MMED (morphine milligram equivalent dosage) per patient (unless anyone knows of a better statistic). I'm assuming this will not be very normally distributed and so am looking at using the Wilcoxon Signed Rank test rather than the paired t test. I have done much googling on the subject but can't find much on how to determine a proper sample size for the Wilcoxon Signed Rank test. I did find some guidance at the link below. Any help on this would be greatly appreciated!

http://www.statisticssolutions.com/wilcoxon-signed-rank-1-tailed/

4 REPLIES 4
Super User

## Re: Sample Size for Wilcoxon Signed Rank Test

One thing about the signed rank tests is they do work for very small samples but may not have the sensitivity you want.

I would suggest looking into Proc Power and the TWOSAMPLEWILCOXON which will allow you to set some parameters such as test, one or two sided test power needed, groupn sizes, some distribution of value assumptions

Quartz | Level 8

## Re: Sample Size for Wilcoxon Signed Rank Test

BallardW,

Thanks for the reply! However I don't see anything in the TWOSAMPLEWILCOXON  documentation about paired analysis. I was wondering since we are looking at the average MMED/patient would the Central Limit Theorem kick in and we could just do a standard paired t test?

Super User

## Re: Sample Size for Wilcoxon Signed Rank Test

You mentioned "average per patient" which would not be a paired test.

If you have two measures per patient you would calculate the difference per patient and then signed ranks on that difference.

The sample size reported from Proc Power would likely be the number of differences not equal to 0.

But you might need to describe what your analysis question is. Are you looking for something like Provider A prescribes more/less than Provider B? Or was more prescribed in 2017 vs 2018?

Quartz | Level 8

## Re: Sample Size for Wilcoxon Signed Rank Test

We want to determine if providers, on average, are prescribing fewer opioids, 4th quarter 2016 vs. 4th quarter 2017. So we are summing up the MME in those time periods and dividing that by # of patients in those time  periods. So each provider is paired with themselves. So the data should look something like this(units = MME/pt):

Provider ID       4Q2016    4Q2017

0001                  55.2          34.3

0002                  65.4          55.5

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