# Choose proper test for two numerical vectors in different length

I am currently struggling to find the most proper test to serve my needs. The thing is, I have one data matrix. The columns are computational features and each row corresponds to a patient. The last column of the matrix is the label of the patient, which is called 'Outcome'. There are two categories: R (Responder to immuno-therapy) and NR (Non-responder to therapy). Now, I want to select the most informative features and then input to the support vector machine for patient classification. To achieve this goal, I did the followings:

First, for each feature, I split the data to NR-associated values and R-associated values, then I would like to perform a 'test' for these two vectors to see if there is a significant difference. If yes, the feature is maintained, if no, the feature is discarded.

Second, since there are thousands of features, therefore I need to perform the test for thousands of times. So after I calculated the p value, I also performed a Bonferroni correction to obtain adjusted p value.

The adjusted p values are used for feature screening.

Initially, I used Student's t-test. However, I am struggling if this is the appropriate test to fit the scenario here, since:

1. There are only ~150 patients. The number of samples is not that high.
2. The length of Responder's vector and Non-Responder's vector are not the same. For example, there are ~100 responders but only ~50 non-responders.

Can anyone please give me some suggestions and explain the rationale? Thank you!

• I see no difficulty using a two-sample t test with sample sizes 50 and 100, provided that the data are nearly normal. I would use a Welch test instead of a pooled test unless it is somehow clear that the two groups must have equal variances. Aug 2, 2020 at 10:18
• A t-test compares means while I don't see the word "mean" in your question... note that your approach will lead to a very biased classificator performance. Aug 2, 2020 at 11:41

## 1 Answer

As said by @BruceET, you can use the Welch test to identify the differential features among the two groups.

Be careful about overfitting. Feature selection performance can be evaluated by cross-validation, for example. In that case, you have to run the feature selection on the only training set.