Testing means from sampling populations with undefined labels

TL;DR

This paper addresses the challenge of testing means from two populations with uncertain labels, linking it to mixture-model testing, and proposes a procedure that performs well despite label uncertainty, comparing favorably to traditional t-tests.

Contribution

It introduces a new testing procedure for means under label uncertainty, connecting it to mixture-model analysis and evaluating its performance against standard methods.

Findings

Proposed a new testing method for uncertain labels.

The method performs well compared to traditional t-tests.

Performance loss is due to the mixing effect.

Abstract

We consider the problem of testing means from samples of two populations for which the labels are not defined with certainty. We show that this problem is connected to another one that is testing expected values of components of mixture-models from two data samples. The underlying mixture-model is associated with known varying mixing-weights. We provide a testing procedure that performs well. Then we point out the loss of performance of our method due to the mixing-effect by comparing its numerical performances to the Welch's t-test on means which would have been done if true labels were available.