Title: Mean Comparisons under Uncertainty or Missing Groups

Author: Timo von Oertzen

Affiliation: Universität der Bundeswehr, München

Abstract:
An overwhelming majority of articles in psychology compare means, often
between multiple groups. However, sometimes we don't know the group membership
exactly, but only as probability to be in one of the groups. Such information
may come from classifiers trained on other data sets, missing group
memberships for some parts of the sample, multi-level situations where the
group membership is only known as a ratio in an upper level, or expert ratings
(e.g., whether a person has a pathological condition or not). We present a
simple method that allows t-test to compare group means in the absence of
exact knowledge about group membership and investigate the loss of information
depending on the probability values theoretically and in a large-scale
simulation.