a) Google is about 70% men; and
b) The "error" in pay (eg how under- or over-paid you are) is randomly distributed
Then it will be trivially true that more men than women are underpaid
If you, in addition to this, assume some level of sex discrimination, such that in addition to (b) there is additional 'error' in womens' pay, depending on the relative strengths of each of these errors, the following two things can both be true at the same time:
1) A higher percentage of women are underpaid than are men.
2) Most of the people who are underpaid are men.
If this is surprising to anybody, they should be taking a remedial statistics class immediately.
To illustrate, assume that Google is 100 people: 30 women, 70 men. assume that 25% of men are underpaid, and 50% of women are underpaid.
That means that 0.2570 =~ 18 men and 0.530 = 15 women are underpaid.
That means that more men are underpaid than women.
That means that 18/(18+15)*100 =~ 55% of the people who are underpaid are men.
So in my hypothetical, is Google biased against men? Or is Google biased against women? Or is Google not biased at all?.
The information provided in the article directly contradicts your hypothetical.
It says that the raises resulting from the study disproportionately went to men. Not just in absolute terms, but proportional terms:
> The study, which disproportionately led to pay raises for thousands of men, is done every year [...]
> In response to the study, Google gave $9.7 million in additional compensation to 10,677 employees for this year. Men account for about 69 percent of the company’s work force, but they received a higher percentage of the money.
a) Google is about 70% men; and b) The "error" in pay (eg how under- or over-paid you are) is randomly distributed
Then it will be trivially true that more men than women are underpaid
If you, in addition to this, assume some level of sex discrimination, such that in addition to (b) there is additional 'error' in womens' pay, depending on the relative strengths of each of these errors, the following two things can both be true at the same time:
1) A higher percentage of women are underpaid than are men. 2) Most of the people who are underpaid are men.
If this is surprising to anybody, they should be taking a remedial statistics class immediately.
To illustrate, assume that Google is 100 people: 30 women, 70 men. assume that 25% of men are underpaid, and 50% of women are underpaid.
That means that 0.2570 =~ 18 men and 0.530 = 15 women are underpaid.
That means that more men are underpaid than women.
That means that 18/(18+15)*100 =~ 55% of the people who are underpaid are men.
So in my hypothetical, is Google biased against men? Or is Google biased against women? Or is Google not biased at all?.