# When I try to use PSM, Should I calculate for normal distribution with Shapiro-Wilk normality test before pair matching or after pair matching?

Suppose there is dataset of 100 patients' including the item "Blood pressure". 45 patients belongs to Group A, and the rest of 55 belongs to Group B.

In consequence, there will be 30 vs 30 patients(60 patients for total) pair matching after using Propensity Score Matching.

I'm trying to find out P-value for "Blood Pressure" with t-test if it is normal distribution, or with Wilcoxon rank sum test if it is non-normal distribution.

To determine which method to use, I have to use Shapiro-Wilk normality test for "Blood pressure" to find out whether if it's normal distributed or not.

Am I supposed to perform Shapiro-Wilk normality test for the dataset after it's pair matched(Calculate for each Group A(30 patients) and Group B(30 patients). 2 times calculation for total)? or for the original dataset?(Group A with 45 patients + Group B with 55 patients. 2 time2 calculation)

You should never use a hypothesis test to assess balance. Balance is achieved by ensuring that the full distribution of covariates is the same between treatment groups. You should compare multiple features of the covariate distribution to determine whether you have achieved balance. Numerical statistics like standardized mean differences and Kolmogorv-Smirnov statistics can be supplemented with visual inspections of the distributions. All this is explained in great detail in the cobalt vignette, including why you should not be using hypothesis tests to assess balance.

Given that you will not be using a hypothesis test to assess balance, there is no reason to use a test to decide whether a covariate is normally distributed. Whether it is or isn't has no bearing on how you should proceed.

• You don't need to perform a normality test ever, but especially with PSM. Where did you read that you should do this?
– Noah
Commented May 11, 2023 at 0:07
• So do you mean I don't need to perform normality test after it's pair matched but I have to perform normality test against the full size of sample, which hasn't been matched up yet?
– nan
Commented May 11, 2023 at 0:09
• I'm using R with user-friendly input interface called "EZR" (jichi.ac.jp/saitama-sct/SaitamaHP.files/statmedEN.html). With this software, I'm asked whether if each continuous variable is with normal distribution or non-normal distribution to calculate for P-value(t-test will be performed if it's normal distribution, and Wilcoxon rank sum test if it's non-normal distribution)
– nan
Commented May 11, 2023 at 0:17
• Are you using p-values to make a balance table? As I say in my answer, don't do that. I will also reiterate that you do not need to test for normality at all in this analysis or most analyses. Please read one of my many guides on best practices for PSM, e.g., this one.
– Noah
Commented May 11, 2023 at 6:27
• Many thanks for the help. I'm using p-value to compare between each group for significant differences in each item. As long as there's no need to test for normality at all in this PSM, it should be okay then. Thanks again!
– nan
Commented May 12, 2023 at 0:24