Explanation of First-Year Housing Race Statistics
For more information on these statistics, please contact Robert_Letzler@brown.edu
Explanation of the Statistical Methods Used:
I was running a series of binomial hypothesis tests.
The null hypothesis was that each unit was sampled from the population
proportion of the class of '02. The alternate hypothesis is that the unit is sampled from some other
distribution.
For several units and for the Mo-Champ, Emery-Woolley, New Pembroke region,
we rejected the Null hypothesis in favor of the alternate hypothesis at the
5% or smaller confidence level.
Explanation of the Statistics' Significance
The Brown ACLU has been looking into the racial distribution of first-year
students. We found that African-American students are over-represent in
certain Pembroke dorms. Our statistical analysis shows that this trend is
unlikely to be a chance occurrence. Thus we would like Res Life to explain
how Brown assigns first years to units and the rationale behind this method.
ACLU memberts, led by David Brock, Andrew Dupuy and Damali Campbell,
compiled data from counselors about the size and racial composition of each
unit. Applied math concentrator, Rob Letzler used statistical analysis to
test the hypothesis that students of color were uniformly distributed
around campus. (I ran binomial analyses which assessed the probability
that the proportion of students of color in a given unit is the same as the
proportion on the whole campus.) Our data and our results are enclosed.
The analysis suggests that:
- Asian-American students are uniformly distributed around campus. The
distribution is consistent with a random assignment of these students to
dorms.
- African-American students are over-represented in Emery-Woolley, New
Pembroke, and Morris-Champlain. They are underrepresented elsewhere on
campus. Statisticians reject the hypothesis that a result is a chance
variation if the probability that it would happen by chance is less than 5%
or 1 in 20. The probability that the student population of Emery-Woolley
and Morris-Champlain (32 out of 319, or 10% of whom are Black) was randomly
drawn from the 6.8% Black freshman class is about 1 in 165. Similarly, the
chances that the proportion of Black students in Units 20 and 27 reflects a
randomly selected sample of the first year population as a whole are both
less than .8%. The difference in populations is very statistically
significant and unlikely to reflect a random variation in the distribution
of students.
- Latino students are uniformly distributed in most units. However, Unit 20
in New Pembroke and Unit 25 in Emery-Woolley have major concentrations of
Latino students. Unit 20 has 15 Latino students, which are 25% of its
population. The class of '02 is only 6.3% Latino. The probability that a
group of 58 that is randomly selected the class of '02 include 15 or more
Latinos is less than 1 in 2,000,000. The probability that Unit 25, which
includes 6 Latinos among 44 first years, is randomly assigned from a
population that is 6.3% Latino is 4%.
The first page shows the racial composition of each unit. The second page
shows the probability that each group in a unit would be at least as over
or under represented as it is if it were drawn randomly from the group's
proportion in the campus as a whole. These numbers range from 0% to
slightly more than 50% (the maximum value would be exactly 50% if we could
assign fractions of students to a unit -- dealing with whole numbers of
people makes the math slightly less elegant). For instance, Unit 1 has 26
students, of whom 5 are of color. The second page reports that the
"Probability of Color" is 32% -- which means that randomly sampling from
the class of '02 that is 25.3% of color, I would get 5 or fewer students of
color in a 26 person unit 32% of the time. This result is consistent with
sampling randomly from the class of '02. There are 15 Latinos out of 58
total first years in unit 20. The probability that there would be between
15 and 58 Latinos if we were drawing randomly from a population that is
6.3% Latino is .00005% -- which means that if Brown assigned 30 units a
year randomly from a population that is 6.3% Latino, this would occur on
average once every 67,000 years. The large number of results, like this
one, with probabilities less than 5% suggests that first years were not
randomly assigned to units.
All else being equal, if a trend continues in a larger data set, it is
much more statistically significant. Consider flipping a coin. We would
not be very surprised if we came up with a few consecutive heads (the
probability of 1 toss coming up heads is ½, 2 consecutive heads is ¼, 3
consecutive heads is 1/8, etc.) but if it came up heads 100 times in a row,
the applied math concentrators in the room would faint (the probability is
roughly 1 in 10^29 -- unimaginably small). The same principle means that a
small proportion overrepresentation throughout a large building is much
stronger evidence than overrepresentation in a single unit. Thus many of
the statistically significant results are on regional total lines.
The Pr. Latino NB and Pr. Black NL columns control for the possibility
that nonrandom assignment of one group might lead to incorrect conclusions
about the other group. These columns should be slightly more accurate,
there is not much evidence that this effect is an issue in this analysis.
In short, we have strong evidence to suggest that African American
students are disproportionately assigned to the Pembroke campus and that
the mechanism that assigns first years is not colorblind.
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