Tutorial: a priori estimation of sample size, effect size, and
  statistical power for cluster analysis, latent class analysis, and
  multivariate mixture models
Edwin S Dalmaijer
Before embarking on data collection, researchers typically compute how many
individual observations they should do. This is vital for doing studies with
sufficient statistical power, and often a cornerstone in study
pre-registrations and grant applications. For traditional statistical tests,
one would typically determine an acceptable level of statistical power,
(gu)estimate effect size, and then use both values to compute the required
sample size. However, for analyses that identify subgroups, statistical power
is harder to establish. Once sample size reaches a sufficient threshold, effect
size is primarily determined by the number of measured features and the
underlying subgroup separation. As a consequence, a priory computations of
statistical power are notoriously complex. In this tutorial, I will provide a
roadmap to determining sample size and effect size for analyses that identify
subgroups. First, I introduce a procedure that allows researchers to formalise
their expectations about effect sizes in their domain of choice, and use this
to compute the minimally required number of measured variables. Next, I outline
how to establish the minimum sample size in subgroup analyses. Finally, I use
simulations to provide a reference table for the most popular subgroup
analyses: k-means, Ward agglomerative hierarchical clustering, c-means fuzzy
clustering, latent class analysis, latent profile analysis, and Gaussian
mixture modelling. The table shows the minimum numbers of observations per
expected subgroup (sample size) and features (measured variables) to achieve
acceptable statistical power, and can be readily used in study design.