I have two groups : Infection group (n=26) and healthy control group (n=127). The aim is to see if there is a difference in the mean of T cells absolute count* values between the two groups.
Ho= the infection group’s T cells absolute count mean is no different than the healthy group’s.
Originally the welch’s t test seemed like the straight forward answer to conduct my hypothesis testing. However after running the shapiro wilk test, the healthy group (n=127) turns out to be not normally distributed, which violates the t test’s assumption of the groups being normally distributed. On the other hand the data Infection group (n=26) had a normal distribution according to the shapiro wilk test. Now switching to a non parametric alternative like Mann whitney u doesn’t work either, since both data needs to be not normally distributed to be valid for this test.
In this case which test do you recommend ?
Considering the difference in sample size I wonder if bootstraping for welch’s t test would be any helpful in ignoring the difference in distribution ?
PS: despite the violation, I did run the welch’s t test on spss, with a 95% confidence interval the results were as follow :
t value = -13.733
Alpha(2tailed)= 0.0000 (4.77 e-25)
Mean difference = -4.88
Standard error difference = 36.67
Running welch’s t test with Bootstrapping based on 1000 sample gave pretty close results but with an alpha of 0.001, would this result be reliable for interpretation?
* T cells absolute counts is a continuous numerical data that can range from 0 to 3000 or even more in some rare cases