What Is the Probability of Scoring in the 88th Percentile for a Trait as a Male?

[James Brady]

I scored in the 88th percentile in a certain personality trait and am trying to figure out the probability of that given that I'm male. I'm trying the likelihood that I would land in the 88th percentile given that I'm male.

Definitions: T = trait, M = males, F = female.
Given:
P(T|M) = 0.3
P(T|F) = 0.6

I'm actually having trouble formulating this in mathematical terms even. I'm not sure where the 0.88 comes into play.

 

[Dale]

P(T) doesn't make sense for a continuous trait, and percentiles don't make sense for a binary trait.

 

[James Brady]

So it looks like I'm having to mix binary (male vs female) and continuous (percentile) probabilities and I'm not sure where to starts.

 

[Dale]

The male vs female part is not problematic. It is P(T) that is problematic. Let's say that T is IQ. Then it makes sense to say "I scored in the 88th percentile on IQ", meaning that IQ is a continuous trait and yours is larger than 88% of the population.

But what doesn't make sense is P(IQ). Everybody has an IQ, it isn't a probabilistic thing. What is probabilistic is the score. So you might say P(IQ>100), but you would never say P(IQ)

 

[James Brady]

Oh... So I would formulate it as P(IQ>0.88|M)?

 

[mfb]

0.88 is not a realistic IQ value.
You can ask for P(IQ>yourIQ|M) but that's what you want to get, not what you have given.

Given:
P(T|M) = 0.3
P(T|F) = 0.6

Where does that come from?

 

[James Brady]

@mfb That's completely made up. I'm just trying to get a grasp on how to work with the numbers.

 

[mfb]

Ideally you have the full distribution for males and females, or at least some way to estimate that. Otherwise it will be a lot of guesswork.

 

[FactChecker]

Oh... So I would formulate it as P(IQ>0.88|M)?

That is close. You can have the probability of one event given another event. That would be like P( In88Percentile | M ). If you know the fraction of males in the 88th percentile, that is the answer.

 

[Dale]

Oh... So I would formulate it as P(IQ>0.88|M)?

Pretty close. If x is IQ for the 88th percentile then you would write it as P(IQ>x|M).

So, for convenience (I am on a mobile device) let's say X is "a person has a score for T which is in the 88th percentile or higher". Then your question is to find P(X|M). The way to do that is with Bayes theorem:

P(X|M) = P(M|X) P(X)/P(M)

Can you work it out from there?