These are the supplementary calculations for this post. Read that first or you’ll be confused.
Okay, you clicked. Wow. Good for you. Alright….so to solve this problem we have to do a few different things:
1. First, we have to get our two distributions. Normal distributions are noted using this notation N(average, variance). Since the original paper gave standard deviation for each, I had to square it to get the variance. Thus the two below, one for men, one for women.
2. Next we use these two distributions to make a new one that represents the distribution of the difference between the two distributions. The nifty thing about normal distributions is this is weirdly easy to do. We just subtract the averages to get the new average, then add the variances. Not all transformations are this easy, but a simple one like this is nice and simple.
3. We use my Yugo/Cumberbatch equation! Yay! Basically what we are doing here is turning our newly acquired normal distribution and rejiggering it to make it in to the little black dress of distributions….the N(0, 1) distribution. Every stats book you will ever find has probabilities for this distribution, so it’s the gold standard and makes our lives easier to boot. When we do our math, we get that we’re looking for anything over .95. Our handy dandy book tells me that’s .17 or a 17% chance.