# Metaphysics of statistical tests and the principles of identity of indiscernibles

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?

Best regards,

Volodymyr

• Can you clarify the question? It looks like you might be expanding the identity of indiscernibles beyond what the principle means. For example, it looks like you might be thinking that it applies to descriptions--that is, if your descriptions of two things are identical then the things are identical. That isn't what it means. It might help to reformulate the principle like this: two different objects can never have every property identical (where "property" includes everything about the object, even things you have no way of knowing). Commented Aug 1, 2021 at 21:48
• "if your descriptions of two things are identical then the things are identical". - I agree that it is appealing to think like this. "two different objects can never have every property identical (where "property" includes everything about the object, even things you have no way of knowing)" - I accept this definition. Commented Aug 1, 2021 at 22:18
• If we return back to Leibnizian PII: media.philosophy.ox.ac.uk/assets/pdf_file/0009/5886/… : 1. Everything must have a reason (PSR). 2. For every x and every y, if x and y are indiscernible, there is no reason why they are numerically different. 3. Therefore, for every x and every y, if x and y are indiscernible, they are numerically the same (PII). Does it mean that the arguments are related to the numerical descriptions of the concrete objects, e.g. size of cells [now]? Commented Aug 1, 2021 at 22:53