[Jun8]

One thing that annoyed me (and it's typical of writing on gender and racial issues) is that he bends over backwards to state, effectively, "not that having women execs don't drive success". This hyper-careful threading brings to mind the famous Seinfeld "not that there's anything wrong with that" episode ("The Outing").

My approach in these matters is Bayesian: Do having female, black, Asian, Indian, etc. executives drive start-up success? The a priori probability I assign to this statement is 0.5, i.e. may or may not. I also employ the My Human Law of Large Numbers, i.e. any "large enough" human population (i) has a Gaussian distribution of any cognitive skill and (ii) the parameters of this distribution is pretty much independent of the particular population sample. I don't have solid proof of this principle and in certain subdomains it may be wrong (e.g. the great cognitive differences between men and women debate, etc.) but I doubt that population differences would be significant.

Now, armed with the simple Bayesian approach and the MHLLN, we can see that most of these articles are BS. The evidence to move the a priori value of 0.5 up or down should be substantial, e.g "extraordinary claims require extraordinary proof". I would be extremely surprised if any gender, racial, etc. factor would derive success of any size company.

Since the above analysis is rather trivial, one then has to ask why these things continue to be written. I think the motivation is usually benign: One sees the dearth of women in startups and wants to show that "it's a good thing". This approach, however, is misguided in that, by making silly arguments or sub-par statistical analysis, it hurts the cause due to the "the lady doth protest too much" effect: many people politely nod, but see through your sloppiness and internally become convinced of just the opposite cause (especially if they are inclined to do so, i.e. if the prior was less than 0.5).

A quote I like a lot is "To be ideological is to preconceive reality." These authors, rather than being objective, have already decided what their results will be and are just filling up the blanks.

[btilly]

Yeah, I know it is cool to throw the word Bayesian around. But it is a lot cooler when it is done by someone who actually knows enough about statistics to be making sense. You clearly don't. Adding your comments about the sloppiness of others makes it just ridiculous.

First of all 50/50 "better", "equal" is not a valid Bayesian prior. Here is a simple litmus test to demonstrate that. If you have a valid prior, then you can assign an actual probability to particular predictions. The ability to do that is a prerequisite of Bayes' theorem. If you can't generate probabilities, you don't have a prior. Suppose you were shown a random startup with women on board. What would you predict their odds of success to be? You can't give me a figure? Then you didn't have a valid prior!

Here is an actual prior that matches the "50% same or better" description that you gave: We give 50% chance to the theory, "Startups with or without early women have a 10% success rate." And 50% chance to the theory, "Startups with no early women succeed 10% of the time, with succeed 20% of the time." I am not saying that this is a reasonable prior, just a valid one. Though that said, a 2 to 1 advantage for having women on board is roughly in line with the figures in the (admittedly flawed) dataset.

With this prior, what happens if we look at a startup which had early women? Well we assign 50% probability to the theory that there is a 10% success rate, and 50% to the theory that there is a 20% success rate, so we calculate 15% odds of it succeeding. We can calculate probabilities of protection. Litmus test passed.

Now what happens if that startup succeeds? Well from Bayes' theorem, we now would give a 2/3 chance to the theory in which women help and 1/3 to the theory that they do not.

And if it fails? There we move the needle rather less since both theories predict high probability of failure. In fact we'd be giving the women help theory a weight of .4/.85 which is around 47% - so only a 3% shift in our opinions.

Notice something? I came up with a concrete prior that fit your description. And I found that every single data point makes a noticeable shift in the posterior opinions that should be held. This is the exact opposite of your hand waving claim that extraordinary proof is required.

Before you next try to use Bayesian analysis to make your claims seem authoritative, please learn something about the subject. A starting exercise might be to figure out what kind of valid priors actually would result in your extraordinary claims require extraordinary evidence hypothesis.

[Jun8]

So, by throwing big words around and pretending to be an expert I gained a few karma points, fantastic. Please don't get so worked up about sloppy posts and "attribute to malice that which is adequately explained by stupidity" :-)

The 0.5 prior thing was an irrelevant use of the principle of indifference. What I really had in mind was a situation with the null hypothesis that having early women on board has no effect on the success rate of a startup whereas H_1 would be that they do have an effect. However, from my description I think what came out was a prior of the kind P(success | women).

Without using any terminology, intuitively the point I was trying to make (ineptly, as you point out) was this: the likelihood that I assign to the statement that "having women early in a startup increases its succeed rate" is very low, I need to see many cases, form startups working on diverse areas for me to update my likelihood value for this. Why? Because I don't think that a subset of population selected with no clear connection to success will affect the success of a startup. Clearly, if the selection has some obvious connection, e.g. coming from a highly educated family, being good in programming, etc. then it will affect success. It's just not clear to me how being a female or black or gay or Indian, etc. has such a connection. I may, of course, be wrong.

And what about the irony of me calling the kettle black: I don't hold my HN posts to the same standard as research reports from a major company.

[btilly]

First of all, you were the one who started off on a high horse. Don't be surprised if people come back in kind.

Now what you're now admitting is that your real prior isn't 50/50 or anything close. You're starting from the assumption that it is incredibly unlikely that women can make much of a difference, and therefore you really do require extraordinary evidence before you'll even consider the possibility that hiring women could help. In short your mind is so made up that your actual prior can fairly be described as fact resistant.

But is that a reasonable theory to have? Independent estimates are that women make an estimated 85% of all consumer purchases. If having women at the top of your company helps you figure out how to talk to that group, there is a clear potential connection between success and having women involved.

You don't like where this is leading? Well try something a little less biased on for size. If the vast majority of startups do not have women at a high level, but ability is equally divided between women and men, does that mean that startups with women involved early likely have an advantage getting better people?

I'm seeing lots of reasons to see that it could be plausible that having women involved early is beneficial for your startup. (Not necessarily true, only reasonably plausible.) My advice to you is therefore to not be so fast in setting preconceptions that let you reject data out of hand, sight unseen.

[sopooneo]

If you believe the distribution of cognitive abilities to be orthogonal to race/gender, why set your a priori at 0.5? I may be misunderstanding (my stats knowledge is low) but it seems you see no reason a particular statement should be true, yet assume a fifty fifty chance that it is true.

[mjdwitt]

Because there is equally no reason that the statement should be false.

[trhtrsh]

That is completely missing the Bayesian worldview, which says you should assign a distribution to the probabilities. A uniform distribution of probabilities, 0-100%, is not perfect, captures the uncertainty better than a point distribution at 50%.

I am holding a pencil right now. Is the eraser at a higher altidude than the tip? Maybe, maybe not. Is that 50/50? Would you be willing to make a bet from me at 1:1 odds, that the the answer is yes?