Table 4. Correlation.

Decile	Correlation	n	Null low	Null high
1	0.156366	6703469	−0.000960	0.000976
2	0.156163	7750717	−0.000905	0.000815
3	0.156499	8253044	−0.000812	0.000840
4	0.156321	8552987	−0.000766	0.000832
5	0.157428	8882969	−0.000750	0.000809
6	0.158828	8847712	−0.000815	0.000793
7	0.161030	9041679	−0.000794	0.000709
8	0.163359	9407243	−0.000736	0.000755
9	0.169258	9356494	−0.000788	0.000762
10	0.190253	9122388	−0.000761	0.000785

The estimated correlation between a user's validated turnout and the validated turnout of her friends by decile of user friend interactions. See Figure 5 for a visualization of this relationship. To compare the observed values to what is possible due to chance, we keep the network topology fixed and then randomly permute the voting behavior of friends. We repeat this procedure 1,000 times and measure the correlation. The simulated correlation values generate a theoretical null distribution for the correlation which we would expect due to chance. The Null low and Null high columns display the 95% confidence interval of this null distribution. Note that the observed correlations exist well outside the null distributions.