alaxies are unique; requiring all members of a subsample to be unique would skew the statistics [@efron81]. By matching our high- and low-density subsamples in stellar mass, redshift, as well as Sérsic index, we are able to effectively study the correlation between galaxy size and environment at fixed stellar mass.

To test whether our high-density subsample and the random low-density subsamples are consistent with being drawn from the same underlying stellar mass distribution, we apply two non-parametric (i.e., independent of Gaussian assumptions) tests, the two-sided Kolmogorov-Smirnov (KS) test [@press86; @wall03] and the one-sided Wilcoxon-Mann-Whitney (WMW) $U$ test [@mann47]. The result of each test is a $P$-value: the probability that a value of the KS or $U$ statistic equal to the observed value or more extreme would be obtained, if the “null” hypothesis holds that the samples are drawn from the same parent distribution. The WMW $U$ test is computed by ranking all elements of the two data sets together and then comparing the mean (or total) of the ranks from each data set. Because it relies on ranks rather than observed values, it is highly robust to non-Gaussianity. The WMW $U$ test is particularly useful for small data sets (e.g., compared to other related tests such as the chi-square two-sample test, @wall03), as we have when selecting galaxies from a narrow stellar mass range and in extreme environments, due to its insensitivity to outlying data points, its avoidance of binning, and its high efficiency. Note that since this test is one-sided, possible $P_{U}$ values range from $0$ to $0.5$ (versus $P_{\rm KS}$ which ranges from $0$ to $1$); for a $P_{U}$ value below $0.025$ (corresponding closely to $2\sigma$ for a Gaussian), we can reject the null hypothesis (that the two samples have the same distribution) at greater than $95\%$ significance.[^5]

In Figure \[fig\_cdists\], we plot the cumulative distribution of stellar masses for the $93$ sources in the high-density subsample alongside that fo