I am an imaging facility manager working with high throughput microscopy; we expect to compare different populations based on different statistical tests.
May I ask you for help to suggest how it is possible [if it is possible in general] to build a consistent system of the application statistical tests together with the principles of identity of indiscernibles https://plato.stanford.edu/entries/identity-indiscernible/ ? To be more specific, how can I accept that the two populations have the same variations if PII defines [to the best of my knowledge] that the the two populations can not be numerically identical, and the variation should be [in general] different? Would you be so kind as to suggest to me any publications which cover the robustness of statistical tests in combination with the PII?
Thank you in advance for your time and help.