1. What is a p-value?
Remember, our interest is in how consistent the observed data are with data taken from a population where gender and promotion rates are delinked.
By permuting the data repeatedly, we can quantify how likely the observed data are to have happened in a situation where the null hypothesis is true.
2. Understanding the null distribution
The null hypothesis is that promotion rates, in the population, do not differ for men and women.
We know what to expect in terms of variability when promotion rates don't differ and we compare that variability directly with the observed data of 0 (point) 2917.
3. Understanding the null distribution
Recall that the (point) 1 quantile is
4. Understanding the null distribution
(point) 125,
5. Understanding the null distribution
the (point) 05 quantile is (point) 208,
6. Understanding the null distribution
and the (point) 01 quantile is (point) 375. So, depending on the level of significance,
7. Understanding the null distribution
we may or may not reject the null hypothesis. To get around the "sometimes reject" problem, we quantify the degree to which the data disagree with the null distribution using something called a p-value.
8. Definition of p-value
A p-value is the probability of observing data as or more extreme than what we actually got, given that the null hypothesis is true.
9. Gender discrimination p-value
In this example, the p-value is the probability of observing a difference of (point) 2917 or greater when promotion rates do not vary across gender.
10. Let's practice!
OK, now it's your turn to practice what you've learned.