In the previous post and step 5 of the controlling FDR procedure used to test if the second digits resemble the Benford’s distribution, we used a fixed alpha equal to 0.05. If this alpha is increased, the chi square statistics from the vote counts are less likely to pass the test. In the other hand, if alpha is decreased, then the chi square statistics are more likely to pass the test. Therefore, in order to measure the effect of alpha, we have generated 200 elections using our Policy Based procedure (explained in previous posts) and evaluated FDR in these elections registering wether each election passes the test with the specific alpha being currently used. Then for that alpha, we calculate the percentage of elections that did not pass the Benford test. This percentage we call FPR (false positive rate) because each of the tested elections are genuine elections not containing any manipulation.
We have calculated the FPR for different alphas in the range of 5*10^(-7) up to 0.05 in logarithmic steps of 0.2. The following figure shows the alphas in the logarithmic scale vs the FPR.
The next step will be to generate another 200 new elections using the same Policy Based procedure, include a type of fraud, and calculate the FNR (false negative rate) in order to see the effect alpha on the missed spoiled elections by Benford’s Law.