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How to compare gender proportions in a population?

Cross Validated Asked by New on January 4, 2021

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?

One Answer

  • 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

Answered by user3808268 on January 4, 2021

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