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Let's say I have a given sample population $P$, that describes the traits of a group of people as a predictor variable, and whether or not they are CEOs as a response variable. I am trying to determine using a decision tree whether or not females are being discriminated against. That is, all else being equal, being a woman makes you less likely to be a CEO.

Would this fall under the category of inferential or descriptive statistics.

I am of two schools of thought here...

Descriptive: I have two distributions, male and female. I would like to see if all else equal, females have a lower "CEO rate". This seems like I'm describing the data.

Inferential: The way I would do this, is that I would make a decision tree and look at how it breaks up the data. In order to check and see if this tree is not overfitting, I would need to use test data results. This leads me to believe it is an inferential problem.

I am leaning more towards the latter, but I do not have enough experience to definitively say it is one or the other. Thoughts?

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If you have a large dataset with many CEO's and many non-CEO's that contains individual-specific characteristics, you could estimate a binary probit/logit to look at the determinants of being a CEO. In this case, you could test whether gender significantly affects the probability an individual becomes a CEO and also look at whether marginal effects of other regressors are different for men and women. My concern would be that there are too few CEO's in the dataset.

In general, if you are conducting hypothesis tests, it is considered inference, not descriptive analysis.

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  • $\begingroup$ Ok, that is fair. I think the dataset is fairly comprehensive. It contains around 10000 individuals with around 1000 CEOs. $\endgroup$ – QuantumHoneybees Mar 18 at 23:30

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