## Student Research Submissions

Spring 4-28-2015

#### Document Type

Honors Project

Hydorn, Debra L.

Helmstutler, Randall

#### Degree Name

Bachelor of Science

Mathematics

Mathematics

#### Abstract

Gender bias is a problem in the workforce at large. In order for society to progress it is important that hiring practices do not use gender as a competitive factor. Hiring practices based on gender can be represented statistically using Bernoulli Random Variables and the Beta and Binomial distributions.Using the moment generating function (MGF) of the Bernoulli and Binomial Distributions, it is possible to calculate the expected value (mean) and variance for the number of women hires for n positions. The probability generating function (PGF) of a sample size n can be used to find the probability of hiring a specific number of women (X). The PGF when solved for P(X = 0) reveals the probability of no women hired for n positions, while P(X less than or equal to 1) gives the probability that one or no women were hired. A computer program was used to run trials to simulate different male/female distributions using recent data on the proportion of women earning a PhD in a variety of disciplines. The simulations were used to represent hiring results for seven faculty positions. Situations where the female proportion is centered at 0.3, 0.5, and 0.7 were studied to account for a range of situations explained by the data researched. Trials that included random proportions of women for each position were run as well. The Chi-Squared Goodness-of-Fit Test will compare the Binomial cumulative distribution function to the sum of Bernoulli cumulative distribution function in order to find a critical value at which it is acceptable to approximate the Bernoulli distribution with a Binomial distribution for various simulations. Simulations will be run to find the average difference between the probabilities that one or more women are hired. Results reveal that it is actually unusual for employers to hire one or no women for seven positions, which could provide evidence of gender bias and that the Binomial distribution approximates each situation fairly well for varying measures of central tendency.

English