Question

Can I conduct a t-test between two groups (one variable) with very different sample sizes (assuming equal variances)? One sample N=128, the other N=550.

Answer 1

Yes, you can definitely conduct a t test between two groups with one variable when the sample sizes are different

This is because the analysis part in the t test is not much affected or we can say that it is not dependent only on the sample size, but it considers other values as well.

Having equal sample sizes or close values are more favorable for the calculation part, but very different sample sizes are also valid and applicable.

So, you can use very different sample size (assuming equal variances).