What are the applications of Bayes Theorem on Columbia University Demographics vs Cornell University Demographics?
Bayes theorem is defined as a theorem that describes how the conditional probability of each of a set of possible causes for a given observed outcome can be computed using knowledge of the probability of each cause and the conditional probability of the outcome of each cause.
This is represented by the equation,
P(A|B)=(P(B|A)*P(A))/(P(B))
Where:
A, B= events, P(A|B)= probability of A given B is true, P(B|A)= probability of B given A is true,
P(A), P(B) = independent probabilities of A and B
Besides networks, there are several applications of this theorem in our society. One of them is the comparison among schools as to who is the most diverse. As we know, colleges have a tendency to advertise their diversity, however that will be put to the test in this analysis. We will analyze 2 of the leading schools here in NY, Cornell University and Columbia University. In addition, the race we will analyze is Hispanic and White.
First let’s analyze Cornell and the Hispanic population.
P(Hispanic|Cornell)= .1064
P(Cornell)=total population of Cornell students / total population of Ithaca= 23620/31853= .7415312099
(https://datausa.io/profile/geo/ithaca-ny/) and (https://www.cornell.edu/about/facts.cfm)
P(Hispanic in Ithaca)= .092
(https://www.census.gov/quickfacts/fact/table/ithacacitynewyork/PST040221)
Thus, P(Cornell | Hispanic) = P(Hispanic | Cornell) * P(Cornell) / P(Hispanic in Ithaca) = 0.1064 * 0.7415312099/ 0.092 = 0.8575971958. It means that if we randomly ask an Hispanic in Ithaca, we should expect a probability of 0.858 that he or she is currently studying at Cornell University.
Now let’s analyze Cornell’s White Population.
P(white|Cornell)= .34
P(Cornell)=total population of Cornell students / total population of Ithaca= 23620/31853= .7415312099
(https://datausa.io/profile/geo/ithaca-ny/) and (https://www.cornell.edu/about/facts.cfm)
P(White in Ithaca)= .677
(https://www.census.gov/quickfacts/fact/table/ithacacitynewyork/PST040221)
Thus, P(Cornell |White) = P(White | Cornell) * P(Cornell) / P(White in Ithaca) = 0.34 * 0.7415312099/ 0.677 = 0.372408584. It means that if we randomly ask a White person in Ithaca, we should expect a probability of 0.372 that he or she is currently studying at Cornell University.
Now let’s do Columbia University.
P(Hispanic|Columbia)= .138
P(Columbia University)=total population of Columbia students/total population of New York City=
30165/8,467,513=.0035624392
(https://datausa.io/profile/university/columbia-university-in-the-city-of-new-york) and (https://www.census.gov/quickfacts/newyorkcitynewyork)
P(Hispanic in New York City)= .289
(https://www.census.gov/quickfacts/newyorkcitynewyork)
Thus, P(Columbia | Hispanic) = P(Hispanic | Columbia) * P(Columbia) / P(Hispanic in NYC) = 0.138 * 0.0035624392/ 0.289 = 0.0017010955. It means that if we randomly ask a Hispanic in NYC, we should expect a probability of 0.002 that he or she is currently studying at Columbia University.
Now let’s analyze Columbia’s White Population.
P(White|Columbia)= .34
P(Columbia University)=total population of Columbia students/total population of New York City=
30165/8,467,513=.0035624392
(https://datausa.io/profile/university/columbia-university-in-the-city-of-new-york) and (https://www.census.gov/quickfacts/newyorkcitynewyork)
P(White in New York City)= .413
(https://www.census.gov/quickfacts/newyorkcitynewyork)
Thus, P(Columbia | White) = P(White | Columbia) * P(Columbia) / P(White in NYC) = 0.34 * 0.0035624392/ 0.413 = 0.0029327587. It means that if we randomly ask a white person in NYC, we should expect a probability of 0.003 that he or she is currently studying at Columbia University.
Besides this, there are a plethora of other options that can be investigated with Bayes’ Theorem. It’s up to us to find out. But in this case, we can see that when selecting college, it’s important to validate what city you choose because that can drastically change how you interpret other people and the way diversity amongst the city is distributed.
All sources are included above. But just in case,
- https://www.collegefactual.com/colleges/cornell-university/student-life/diversity/chart-ethnic-diversity.html
- https://datausa.io/profile/geo/ithaca-ny/
- https://www.cornell.edu/about/facts.cfm
- https://www.census.gov/quickfacts/fact/table/ithacacitynewyork/PST040221
- https://www.collegefactual.com/colleges/columbia-university-in-the-city-of-new-york/student-life/diversity/
- https://datausa.io/profile/university/columbia-university-in-the-city-of-new-york
- https://www.census.gov/quickfacts/newyorkcitynewyork
In continuation from this blog post: