# Women passing exams: Help with stats please

• tempguy
In summary, the conversation is discussing the statistics of women taking a particular academic test in 2007 and 2009. In 2007, 11 out of 50 candidates were women and only 3 out of 16 successful candidates were women. In 2009, 12 out of 52 candidates were women and only 1 out of 14 successful candidates were women. The percentages show that in 2007, women accounted for 18.7% of successful candidates, while in 2009 they accounted for only 7%. The person speaking wants to calculate the probability of these results, assuming equal chances for men and women and independent events. They suggest using binomial regression and a hypothesis test to check for bias
tempguy
Hello,

I am looking at the stats for a particular academic test:

- In 2007, 11 women out of 50 candidates took the test; there were only 3 women among the 16 successful candidates.
- In 2009, 12 women out of 52 candidates took the test; there was only 1 woman women among the 14 successful candidates.

The same results in percentages:

- Women accounted for 18.7% of successful candidates in 2007, which is more or less normal insofar as they represented 22% of the candidates taking the test that year (11/50).
- However, women accounted for 7% of successful candidates in 2009, whereas they constituted 23% of all candidates taking the test that year (12/52).

I would like to calculate the probability of this last result, assuming the following:

a) Women and men taking the exam are supposed to have equal chances of succeeding (also known as the anti-http://en.wikipedia.org/wiki/Lawrence_Summers#Differences_between_the_sexes"…).
b) The exams are supposed to be independent events (Bernoulli trials?).

My educated guess is that binomial regression is the way to go but my stats skills are too low to actually perform the operation, or to analyse correctly its results.

If the probability of the 2009 results are very low, then one might reasonably assume that there is an anti-women bias at play (the test is basically a face-to-face interview).

Help much appreciated!

Last edited by a moderator:
Well if you assume they have the same probability of passing (say p), then each person is a Bernoulli trial. So you have a binomial distribution (which is the sum of Bernoulli trials) for the amount of people that pass. You want $$\mathbb{P}(\text{someone passes the test, given they were a women})=\frac{\mathbb{P}(\text{they pass the the test and they are a woman})}{\mathbb{P}(\text{they are a woman})}$$.

If you want to check if they are biased then I suggest making a hypothesis test.

## 1. How do women perform on exams compared to men?

There is no definitive answer to this question as it can vary depending on the specific exam and the population being studied. However, some studies have shown that on average, women perform slightly better than men on exams.

## 2. Are there any factors that may affect women's performance on exams?

Yes, there are various factors that may affect women's performance on exams, such as test anxiety, societal pressure, and gender stereotypes. These factors can impact women's confidence and may lead to lower exam scores.

## 3. How can we address the gender gap in exam performance?

There is no simple solution to addressing the gender gap in exam performance. However, some steps that can be taken include promoting a supportive and inclusive learning environment, providing equal opportunities and resources for both genders, and addressing and challenging gender stereotypes.

## 4. Are there any strategies that can help women perform better on exams?

Yes, some strategies that may help women perform better on exams include time management techniques, seeking support from peers and instructors, and utilizing study aids and resources.

## 5. How can we encourage more women to pursue higher education and take exams?

To encourage more women to pursue higher education and take exams, it is important to promote a culture of inclusivity and diversity, provide mentorship and support for female students, and highlight the benefits and opportunities that come with higher education and exam performance. Additionally, addressing and removing any barriers that may prevent women from pursuing higher education can also be effective in encouraging them to take exams.

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