Legit catch. I did struggle a bit with the wording of the post. I think it's still fair (based on my read and yours) to say that the survey results represent a lower bound, which is the broader conclusion I drew. I don't think anyone is suggesting that 100% of instances of bad behavior were surfaced by this survey, so the actual number will be higher.

> I don't think anyone is suggesting that 100% of instances of bad behavior were surfaced by this survey, so the actual number will be higher.

In absolute terms it is clear that it's a lower bound. In percentage we cannot say because as stated in the footnote:

> Callisto chose to send the survey to the 125 founders [of 384] who signed up for the YC female founder email list.

It can be argued that being harassed and subscribing to that list may be correlated. Hence, the percentage of harassed women on that list may be higher than in the general population of female founders.

Also, someone may argue that women who were actually harassed are probably more involved in these matters, and hence more likely to respond to such surveys. They got 88 responses out of 125 reach-outs (70%) so there's also the possibility most of that other 30% were not harassed.

Therefore, the true lower-bound in percentage terms would be 19 (that we know were harassed) of 384 (total population), around 5%. As the name implies, this is just a lower bound.

The equivalent upper bound would be 69 (that we know were not harassed) of 384 (total), setting it at 82%. The real number lies somewhere inbetween. Extrapolating "40% of respondents" to "40% of the population" is debatable, and claiming that is a lower bound would be just wrong.

> Also, someone may argue that women who were actually harassed are probably more involved in these matters, and hence more likely to respond to such surveys.

You may argue this, but I wouldn’t say it’s a given. For one thing, especially at the higher end of the scale (“unwanted sexual contact”, or hypothetically even rape), people who have had traumatic experiences may have a strong desire to avoid recalling them – especially for something as (relatively) unimportant as a survey – potentially producing the opposite effect.

>> the true lower-bound in percentage terms would be 19 (that we know were harassed) of 384 (total population), around 5%.

You're mixing a population about which you can make an inference (survey participants) with a population about which you cannot (people who were not even contacted about the survey). The resulting percentage is essentially meaningless.

It is meaningless, if you want an accurate estimate, or even, say, a 95%-confidence lower bound.

But since we like to be pedantic on this forum, I’ll defend the parent: if you want a true, 100%-confidence lower bound (ignoring the possibility of false reports), then that would be 5%. It’s a completely useless statistic, and you shouldn’t use it for anything, but it’s correct for the strictest possible interpretation of “lower bound”.

And if you want a 99.99% confidence upper bound, it's (384-88+19)/384 == 82%. (the .01% is the probability of false negatives in the survey data). Again, pedantic, true, and useless, but cited for balance.