# How to compare gender proportions in a population?

I want to test if more women are graduating from high school than men, the last ten years. I want to use percentages, not raw data. (2007-2017 percentages of women who graduated from high schools versus men) And I also want to test if proportionally more women than men are graduating from high school than university. I can not use median because more people graduate from high schools than universities. I can use percentages (2007-2017 percentages of women who graduated from high school versus university) What tests are the right ones?

• 1. It stands to reason that more women are graduating from high school than university, as you have to graduate from high school in order to go to university except in exceptional cases. 2. With population totals, which it seems you may have, you don't need to do any statistical tests, because you have the actual numbers. – jbowman Dec 27 '17 at 15:12
• I want to test if proportionally more women than men are graduating from high school than university. I need to see if the difference is statistical significant. – New Dec 27 '17 at 16:29
• If you have the population figures, there's no need to test. – jbowman Dec 27 '17 at 16:30
• How about using a chi-square test? Nice and simple... en.wikipedia.org/wiki/Pearson%27s_chi-squared_test – John Dec 27 '17 at 18:05

• For testing if (percent of women graduating) > (percent of men graduating)

Consider total number of data points to be $N$.

$p_w$ = proportion of women graduating in Sample.

$p_m$ = 1- $p_w$ = proportion of men graduating in Sample.

$\sigma_{sample}$ = Standard deviation of the sample data = $\sqrt{p_w*p_m}$

$\sigma_{pop}$ = Standard deviation of the population = $\frac{\sigma_{sample}}{\sqrt{N}}$

The null Hypothesis $H_0$ : $p_{w} = p_m$

The null Hypothesis $H_A$ : $p_{w} > p_m$

$Z = \frac{p_w-p_m}{\sigma_{pop}}$

If $abs(Z)$ value is greater than 2, then the percent of women is greater than men.

• Similarly, test for high school and university. Create the new dataset where only women are present. So, repeat the above steps.

$N$ = Total number of women

$p_h$ = percent of women in high school

$p_u$ = percent of women in university