Inter-sample variance explained

Question

[christianhinze]

Dear all,

I am working with single-cell gene expression data of N samples on roughly 800 different features (genes).

The cells of each sample come from 4 different clusters (cell types). My hypothesis is that most/a significant part of the inter-sample variance is explained by the cluster composition of the respective sample, e.g. one sample consists of 20% cluster1 cells, 10% cluster2, 15% cluster3 and 55% cluster4, the others might be different.

How can I statistically prove this?

I hope this information is precise enough for now and hope that this is the right spot to ask this question.

Thanks, best, Chris