Network Comparison of Delaware Litigation

Results

A two-sample proportion test is conducted to test whether the proportion of females in the network after 2019 increases relative to the network before 2019. The proportion of females before 2019 is 0.26 and the proportion of females after 2019 is 0.262. The Chi-Squared test-statistic is 0.07 with a p-value of 0.6, suggesting that the proportion of female attorneys in the post-2019 network is not greater than pre-2019 network.

Similar results show for a two-sample proportion test on whether the proportion of Whites in the post-2019 network is smaller than the pre-2019 network. These proportions are 0.82 and 0.823 respectively, showing that the proportion of Whites actually increases in the network. The test-statistic is 0.06 with a p-value of 0.4.

Table 1: Mean Network Measures by Gender and Period
Gender	Betweenness Centrality		Degree Centrality		Eigenvector Centrality
	Pre-2019	Post-2019	Pre-2019	Post-2019	Pre-2019	Post-2019
female	2461.046	2127.325	80.420	32.761	0.006	0.021
male	5219.153	3298.531	101.784	37.896	0.008	0.028

Next, we test whether the network densities are equal in both networks. Network density is a measure of how connected the nodes in a network are and reflects the cohesion and information flow in a network. The density measures for the network are 0.02 and 0.01. The test whether the two densities are equal has a p-value of 0.9994 with bootstrap standard errors (Snijders and Borgatti, 1999). This result suggests that there is no evidene that the two networks have unequal densities.

Table 2: Mean Gender Assortativity on Pre- and Post- 2019 Networks with Standard Errors using the Vertex Bootstrap Technique (Snijders and Borgatti, 1999; Chen et al. 2018)
	Pre-2019	Post-2019
Mean	-0.00146	-0.00067
Standard Deviation	0.00422	0.00411

Finally, we compare the network assortativity on gender for the networks before and after 2019. These results are shown in Table 2. Both networks show slight disassortativity. The pre-2019 network has an assortativity on gender of -0.00146, and the post-2019 network has an assortativity on gender of -6.7^{-4}. The standard errors are calculated using the vertex bootstrap technique (Snijders and Borgatti, 1999; Chen et al. 2018).

Discussion

References

The following R packages were used in the analysis.