Women and/or technical skills

Many people believe that women are on average less skilled in technical matters than men. Let me tell you a secret about that prejudice:

It's true!

Why yes! It totally is!

The only problem is that people frequently get the interpretation wrong of what that means.

Because you know, it's all about that nasty conditional probability thing once again. Bayes' theorem. Why "the safest way to fly is to take a bomb with you, because it's damn unlikely that there are two bombs on the same plane" doesn't work. Something closely related to and even less understood than the Monty Hall problem, which is why it has deserved to be also demonstrated with three doors.

Well, let me try to enlighten you with some very basic mathematical insights.

Starting directly with that problem would make the discussion rather abstract and theoretical and you would end up not believing me. Let's therefore stick with the lipstick example for starters. Or, since wearing lipstick is a rather binary decision -- you do or you don't --, let's generalize it to wearing make-up. Also, let's restrict it to typical western countries.

Have a look at the following diagram:

(The x-axis gives the amount of make-up usage, and the y-axis gives the number of people for each position on the x-axis.)

There is a small but not insignificant amount of women who would rather die than wear make-up. There is a small but not insignificant amount of men who plaster their faces with make-up as if it could fall apart without. But on average, women still do wear more make-up than men.

So given two random persons about whom we have no information other than one being female and the other male, which person is more likely to be wearing make-up? Answer: Quite clearly the female one.

Let's further assume that the more make-up people wear, the more they know about make-up. Which of the two persons above is therefore more likely to know a lot about make-up? Answer: Again the female one.

Let's take a third person into consideration now. We have no information about that new person other than that he or she likes wearing tons of make-up. Which of the three persons is most likely to know a lot about make-up now? Answer: Obviously the third one. Independently of whether he or she is male or female. Why? Because while we assume that the male person is probably in the lower half of the range and the female person is probably in the upper half, we know the third person to be in the very top few percent and thus, on average, better than either of the other two.

Now that we are already busy introducing new persons, let's introduce two more of them. Person D is female and wears tons of make-up. Person E is male and wears tons of make-up. Who is more likely to have a lot of knowledge about make-up now, person D or person E? Answer: Well, at this point it's pretty much 50:50.

Why is that?

Let's have another look at that diagram. We know that both persons wear [too] much make-up, which means we are only considering persons in the very right part of the diagram any more:

What can we tell about that small subset of the population?

• They all know a lot about make-up. (Keep in mind that make-up usage and thus (by our assumption) knowledge is measured by the position on the left-right axis. All persons in question are on the very right edge of that graph.)
• There are more females than males in that range. (I.e., there are more females than males who really know a lot about make-up.)
• A male and a female person being both within that range are pretty much equally likely to win a make-up knowledge quiz against each other. In this particular graph, it's even slightly more likely for the male, i.e. person E, to know more about make-up. Why? We know about person D that she is female and within the highlighted range. Amongst the females in that range, there are more towards the lower end (at the left) than at the upper end, so the average female from within this range is slightly below the center of the range. Amongst the few males in that range on the other hand, all positions are pretty much equally (un)likely, so the average male from within this range is quite exactly at the center of this range. Therefore, in this graph person E is actually an itsy bitsy tiny bit more likely to know a lot than person D. It's a damn close call though, so with sufficient approximation we can say that they are equally likely to be more knowledgeable about make-up.

(Bonus question: Remember person three from above? We only know that this person wears a lot of make-up. Is person three more likely to be male or female?)

Now let me just re-label and re-colour that graph and we'll transfer our findings to the original problem in no time.

I know that it's extremely unpopular these days to claim that women have on average less technical competence than men, but for the sake of argument, let's assume it's true:

Now let's only look at those people who are successful in technical careers. With few exceptions, people in technical careers are people with high technical skills, and vice versa. (There might be the occasional technically skilled person who still chooses to study medicine, or the occasional person who has no clue about technical matters but got hired into daddy's company anyways, but for simplicity we ignore those for now.) People with technical careers therefore mostly correspond to the right-most part of the diagram:

And now, the same conclusions apply:

• All persons who are successful in technical careers have high technical competence.
• There are more males than females who have high technical skills.
• Males and females from within the shown range are pretty much evenly matched, i.e., given two persons of whom one is a female technician and the other a male technician, it's hard to tell which one does probably know more about technical matters.

In short: It's less likely for women to go for a technical career, but those who do are quite evenly matched with their male colleagues.


What do we learn from that?

Given an entirely random male person and an entirely random female person, it's absolutely fair to assume that the male person has more technical competence. Let's assume you are at a quiz show, are given a question about the inner workings of a car engine, have no idea about the correct answer, and are allowed to use a phone joker. You can only choose whether the person to be called is female or male, and the quiz team will then pick a random (male or female) name from a phone book and call that person. Then it's very reasonable to go for a male helper.

Let's, in contrast, assume that your car broke down with a flat tyre and you don't know how to change a tyre yourself. A second car stops, a young woman gets out and offers you to change the tyre for you. Here, "You can't do that, you're a girl." is a wrong answer. (Not to mention that it's impolite.) Why? Because she already indicated to you that she can. She gave you some extra information about herself, which means that all conclusions you drew before that aren't valid any more. Your conclusions were made at a point where you had to take the entire range into consideration. Now however this new information significantly restricted the range. Therefore, take the new information and re-evaluate.

There's a very similar scenario, and it seems to happen so frequently that I'm willing to dedicate another diagram to it:

So, assume you call the tech hotline of whatever company to get help with a technical problem. A woman picks up. Again, "No, I want to speak to a man." is the wrong reaction. The person works at the tech hotline, so you can assume that she went through job interviews and technical training. It's also very likely that most employees at that tech hotline are roughly within the same skill range. In short, whether male of female, you will get to speak with an averagely skilled technician. (Good technicians usually get better jobs than working at tech hotlines, just for your information.)

This can be generalized to any job, by the way: While on average over the entire population women might be less technically skilled than men, there is virtually no difference between men and women working in the same job.


The moral of the story? There's nothing bad about prejudices. Just remain open to trashing them as soon as you get additional information about a person.

After all, while it's true that only around 20% percent of all people own a dog, there's no point in insisting that someone most likely doesn't have one once you've seen them taking it for a walk.

-- Birgit


P.S.: I admit to having shamelessly simplified away a lot of potentially important facts and factors.