A Statistical Analysis of the Gender Gap by Ariel Shin

Introduction

My name is Ariel Shin and I am a Computer Science Major at UC Davis. I have been analyzing trends in debate rounds from the national high school debate circuit in R, a programming language utilized by data analysts and statisticians, with a computer science professor, Norm Matloff. I debated four years for Immaculate Heart and attended the Tournament of Champions my senior year.

For those uninterested in how I created these graphs in R, skip over the italicized parts.

Previous Research

The first step in debate and undergraduate research is reading the topic literature. The only form of debate rankings that currently exists is Kirsch’s ranking on vbriefly, which determines a debater’s ranking on number of rounds won. Secondly, research on tournaments that include pre-elimination rounds and elimination rounds do not exist. A vast majority of the research focuses on elimination tournaments, such as March Madness predictions and tennis rankings. Lastly, there has been previous research conducted on the gender gap. Cai et al1 examined performances during competitive pressure, their specific example being China’s National College Entrance Exam, considered one of the world’s most competitive exam. Cai et al found that gender differences translated to a 15% decline in the likelihood that females are eligible for admission into a Tier 1 university.

Data

I collected my data from tabroom.com and included 24 bid tournaments from the 2015-2016 season. I will continue to add more tournaments and possible more variables to my data set. I recorded school names, debater’s names, pre-elimination records, elimination records, and speaker-points. I was able to generate a list of genders from camp attendance sheets, Facebook, and websites that determine gender from names.

Results

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I generated this first graph by plotting seed frequency by gender. This graph shows that males consistently have better seeding than females, as the blue line, which represents males, is more towards the left than the red line, which represents females. Based on this graph alone, we can extrapolate that male debaters perform better than female debaters.

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For elim rounds, I marked debaters who were not present in an elim round as -1, a debater who lost an elim round as a 0, and a debater who won an elim round as a 1. For instance if I were to lose in quarters, I would be marked as a 0. For octas, I would be marked as a 1 and for semis and finals, I would be marked as -1. This graph charts seed vs. mean elim wins means by gender.

The previous graph told us that boys have better seeding than girls. However, when we look at the same exact seed, for example seed 3, we see that boys won more elim rounds than girls. A seed is supposed to be a non-biased and equal measure of performance. Instead, we see a gender bias. If I were to win the same number of rounds as a boy and get the same speaker-points, I am more likely to lose in elimination rounds because I am a girl. And that’s only if I were to get the same wins and speaker-points, which is less likely because according to the previous graph — girls have worse seeding than boys.

The graph also diverges for smaller seeds. This implies that at higher levels and at more competitive levels, boys perform significantly better than girls. While at lower levels, boys only perform slightly better.

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For this graph, the x-axis is rounds won and the y-axis is frequency of rounds won. This third graph continues to show support for the gender gap. The many bumps are due to the different number of rounds. This graph shows that boys tend to have more winning records than girls. Moreover, girls tend to have more losing records. Out of 6 rounds, boys are winning a majority of rounds, while girls are losing a majority of rounds.

I use lm, which is a tool in R that allows me to perform linear regression analyses. This tool allows me to see the impact a coefficient has on its covariates. In very simple terms, I am able to find the impact of one variable on other variables. I have created a table with the results. My coefficient was the total number of elim wins, which I called totalw. My covariates are the variables in the first column.

Estimate Standard Error Confidence Interval
Male 0.1602454 0.0363653 0.088969412 0.231521388
Speaks 0.0004085 0.0009326 -0.001419396 0.002236396
Seed -0.0093938 0.000394 -0.01016604 -0.00862156

 

Estimate Standard Error Confidence Interval
Male 0.0835484 0.0339467 0.017012868 0.150083932
Speaks -0.0071 0.0009462 -0.008954552 -0.005245448
Seed -0.0018409 0.0005317 -0.002883032 -0.000798768
rWon 0.3695685 0.0189042 0.332516268 0.406620732

 

The first table shows the confidence intervals when we compared total number of elim wins and its impact on gender, speaker-points, and seed. The second table shows the confidence intervals when we added one more variables, rWon which represents the number of prelim rounds won. We compared the total number of elim wins and its impact on gender, speakerpoints, seed, and rWon.

Once again, these results show that gender has a huge impact on number of elimination rounds won. We see that the confidence interval is from 0.089 to 0.23 in the first table. This suggests there is a positive relationship with being male and the number of elim rounds won. The second table also suggests that there is a positive relationship between the male gender and the number of elim rounds won. On top of the graphs, these confidence intervals support the gender gap.

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This graph shows the frequency of speaker-points by gender. The variety of bumps in this graph is due to the different number of rounds since the number of prelim rounds range from 5 to 7. Since I kept the speaker-points given on tabroom, which is a sum and not an average, our graph shows 3 peaks to represent the varying number of rounds and the speaker-points given.

The blue line is slightly towards the right in the right two peaks – indicating that boys tend to have higher speaker-points in tournaments with 6 to 7 rounds. This graph shows that there is a higher density of boys having higher speaks than females. Speakerpoints are important because they determine your seeding and whether or not you will advance to another round. In my personal experience, girls have been told that their voice is too high-pitched and that they should change their natural voice. Moreover, if a girl acts too aggressive, she is marked down for it while a male debater is simply assuming his dominant role.image5image6

As a novice debater, I thought to myself if I had the resources and a team of coaches, I could do just as well as any successful male debater.

When we start debating, we become aware of powerhouse schools. Their teams have a very strong reputation, a lot of funding and support from their school, and they have a strong attendance at the TOC. I defined a powerhouse school, as a school with at least one bid to the TOC each year for the past 6 years. I compiled this list by using NSD’s bid lists from the past 6 years. According to my metric of a powerhouse school, there are 13 schools that are powerhouses.

The first graph compares the number of rounds won among powerhouse schools and non-powerhouse schools. This graphs shows that powerhouse schools tends to have more winning records than non-powerhouse schools.

The second graph compares seeding among powerhouse schools and non-powerhouse schools. This graph further shows the dominance of powerhouse schools as they have higher seeds than non-powerhouse schools. So, my theory was correct – Having resources, coaches, and a strong reputation can aid a debater’s success.

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However, I also assumed my gender would not play a role in my success if I had the resources of a powerhouse school.

So, I compared the different performance of powerhouse school debaters by gender. The first graph shows that males from powerhouse schools won more rounds than the females from powerhouse schools. The second graph shows that male debaters from powerhouse schools had better seeding than females from powerhouse schools.

Among most debate teams, you can easily identify the A debater and the B debater. A majority of times, both the A and the B debaters are males. These graphs are very telling of team dynamics. When you’re on a team that has the resources, the coaches, the funding, there is still a gender gap. Could there be favoritism on the team? In my personal experience, I have witnessed that big teams tend to split up. They send their A debaters to one tournament and the B debaters to an easier local tournament. This means the people who do not gain as much success at the start of the season or the coaches assume will not become successful, are not trained to reach their full potential as a debater.

When there are fewer girls on a team or even none at all, girls are less likely to join debate. Moreover, a female debater faces more obstacles than her male teammate.  For instance, it becomes more expensive as the debater has to pay for her own hotel room and the school must pay for a separate female chaperone. Therefore, I believe that a school has less incentive to groom girls to become the top debaters and may favorite boys. I also believe it’s also easier for schools to hire male debate coaches because not only do males win more, but also they are also more likely to stay in the activity after they graduate.

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When we analyze the different performance among genders from non-powerhouse schools, we still see that males perform better than females.

The first graph shows that males have better seeding than girls. On the second graph, we see that males have more winning records than girls.

As a debater from a non-powerhouse all-girls school, what are we supposed to do when we see that girls systematically lose to boys when we have access to the resources and don’t have access to the resources? This begs the question of what makes a good debater, if its not access to resources or coaches.

Conclusion

My last slide for my presentation at the Undergraduate Research Conference was a collage of the pictures of finalists vbriefly posts when they report tournament results. I asked the audience if they could spot the female. You can scroll through the main website and see how long it takes to spot a female debater. I often joke that female debaters can write on our resumes and college applications that we are one of the top 10 female debaters in the nation. However, we can’t write we are one of the 10 debaters in the nation. The female qualifier allows us to jump to the top 10. In fact, the first girl to appear on Kirsch’s debate ranking is number 15.

While my data provides some insight as to how severe the gender gap is, the question remains: Is there a solution?

References:

[1] Cai, Xiqian, et al. “Gender Gap under Pressure: Performance and Reaction to Shocks⇤.” (2014).

Edited for typos.