[thaumasiotes]

They certainly aren't independent statements.

Share of homelessness due to an abusive relationship + share of homelessness due to drugs + share of homelessness for all other reasons = 1.

If one of those variables goes higher, one or both of the others must go lower. On the assumption that one of those reasons gets more common "all else equal"... both of the others will go lower.

[msinclair]

The OP didn't say that women were homeless due to abuse and not drugs and that men were homeless due to drugs/PTSD.

In fact if you read what they wrote, they didn't specify sex at all. A man can be homeless due to an abusive relationship, they never said they couldn't. Hence independent statements. nsnick was the one assuming something.

[mjevans]

You are correct in the zero sum outcome for the //ENTIRE// homeless population; however you are not correct in the sense of a hypothetical subject being homeless.

A singular case subject/family could be homeless for MULTIPLE reasons or None (other than other of course) outlined above.

[thaumasiotes]

> You are correct in the zero sum outcome for the //ENTIRE// homeless population; however you are not correct in the sense of a hypothetical subject being homeless.

This is wrong. What's correct as a description of the entire female homeless population is equally correct as a probability assignment for one element of it.

Your second sentence is unrelated to your first, and also applies equally well to the entire population as to an individual sample from it. It is arguing that the sum I describe is in fact more than 1. That is defensible, but it won't make the statements independent; they aren't.

[cabalamat]

> Share of homelessness due to an abusive relationship + share of homelessness due to drugs + share of homelessness for all other reasons = 1.

No, because someone can be homeless for multiple reasons.

[thaumasiotes]

I already acknowledged this in a cousin comment. As long as they can also be homeless for a single reason, the statements are not independent. A population of women who are homeless due to domestic abuse, but not for any other reason, simultaneously drives the share of women-homeless-due-to-domestic-abuse up and the share of women-homeless-for-reasons-other-than-domestic-abuse down.