Where does your "50%" number come from? If the number was 50%, then the number of underpaid women would be the same as men, which invalidates the entire headline.

The 50 and 76 percentages are not compatible because they're based on different denominators. That means you can't assume it's 50 of out 76 (especially as then 50 out of 24 women would be being underpaid, more than all of them...).

What I said is mathematically correct.

For the sake of completion:

Suppose there are N employees.

76% = 0.76N are men; 24% = 0.24N are women.

Suppose also that n men being underpaid for their work.

The stat as quoted suggests there are n women being underpaid. (Or, sufficiently close to n, that a stronger stat can't be quoted)

Chance of men being underpaid: n/0.76N

Chance of women being underpaid: n/0.24N

Chance of women being underpaid is therefore (n/0.24N)/(n/0.76N) = 19/6 > 3.1 times higher.

I rounded conservatively to conclude "women are three times more likely to be underpaid".

The source [Google post](https://www.blog.google/inside-google/company-announcements/...) says “ men were flagged for adjustments because they received less discretionary funds than women” so your 50/50 split of n is the most aggressive way to interpret that information.

More likely, we should interpret that to mean that men were found to be more likely to be underpaid (n_men > N_men), and that the appropriate comparison of variance (finding outliers) among men versus women was performed.

> your 50/50 split of n is the most aggressive way to interpret that information.

I'm satisfied with that choice.

Given that Google are here quoting this stat in the press (with the 50/50 implication) to defend themselves against an inequality suit, without actually giving us the figures, I assume that this is the best spin that Google can put on it.

That's fine, but it tells you very little about Google because N and n are both informative and you cancelled them out.

It's entirely possible that only 1 man and 3 (3.1) women are underpaid. That would make Google about the fairest employer in the history of the world despite being 3.1 times more likely to under pay women.

On the other hand every woman could be underpaid AND a third of all the men. That would be terrible (and profitable).

Which is it? 3.1 doesn't tell you. So it's not useful. At best it's noise, at worst it's deceptive.

I'll leave you with your 3.1 and I don't object to the mathematics above so much as the logic underlying them. I don't think it's fair for someone to be down voted without explanation so at least you know the "other side" :)

Did you actually read the article? Direct quote refuting your point:

"Men account for about 69 percent of the company’s work force, but they received a higher percentage of the money."