180 is 20% of 900.
Please do the same for the major B in the female population over here.
Of course it’s 80%–80/100.
The same statistic was run for female students. Again, I made up the data to illustrate the effect. Females tended to apply predominantly for major B with 900 applications for major B and just 100 for major A. The university accepted 80 out of 100 applications in major A and 180 out of 900 in … Read more
And the answer is 10%.
In a second major B 100 students applied, of which 10 were admitted. What is the acceptance rate?
Obviously, it’s 50%.
I hope this example made you think and learn to be skeptical, of your own results and the results from others. Moving forward even when you feel very confident about the statistics you use for your analysis, take a moment to reconsider other ways of looking at your data and whether you chose wisely. Stay … Read more
As you’ve seen in this example, on Simpson’s paradox, the way you choose to look at your data can lead to completely different results. And often, you can majorly impact what people believe to be true with how you choose to communicate your findings. You can guess how people intentionally or unintentionally come to false … Read more
The problem I’d like to tell you about is motivated by an actual study the University of California Berkeley, which many years back wanted to know whether it’s admissions procedure is gender biased. I looked at various admission statistics to understand whether than admissions policies had a preference for a certain gender. And while the … Read more
And surprisingly, when you look at both majors together, you find that males have a much higher admissions rate than females. I’m not making this up. These numbers might be fake, but that specific affect was observed at the University of California at Berkley many years ago. But when you look at majors individually, then … Read more
So, across both majors, I’m asking you the same question again now. Who is actually being favored? Males or females?
The answer is 26%.
Now, do the same for the female student population, and we had a 1000 applicants, same number as in the male case, and 260 students admitted. So, what’s the percentage rate for admission?
And the answer is, of course, 46%. It’s 460/1000 x 100%.
So, what is the admissions rate for male students across both majors in percent?
And the answer is 460.
Who is being favored–the male students or the female students? And looking at the data alone, it makes sense to say the female students are favored because for both majors, they have a better admission rate than the corresponding male students. But now, let’s do the trick. Let’s look at the admission statistics independent of … Read more
And I would say yes, in part because the acceptance rate is so different for the different student populations, even though the numbers are relatively large. So, it doesn’t seem just like random deviations. But the thing that will blow your mind away is a different question.
So, just looking at these numbers for the two different majors, would we believe–in terms of the acceptance rate– is there a gender bias? Yes or no?