The Welch's test is a non-parametric test used to compare two means from two independent groups. It was historically used as an alternative to the Student's t-test in case of unequal groups' variances.
Delacre, M., Lakens, D., & Leys, C. (2017). Why Psychologists Should by Default Use Welch’s t-test Instead of Student’s t-test. International Review of Social Psychology, 30(1), 92–101.
Derrick, B., Toher, D., & White, P. (2016). Why Welch’s test is Type I error robust. The Quantitative Methods for Psychology,12(1), 30-38.