The problem mentioned in the previous blog of having the false positives as 10% was able to reduced to 0.04%. This was made possible with the help of concept called as False Discovery Rate (FDR) which is used for the removal of Type 1 error (False positives) more details is explained in the paper “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing.” This actually helps in modulating the critical value which is used as the basis for the criterion for the rejection of the Hypothesis (which in our case is the deviation from 2BL). By modulating the critical values properly we were able to reduce the number rejections significantly which in the previous versions was fixed as 0.05 goes on changing depending upon the number of counties the state exists.
Along with that the other gain we made was we scale our system to do the election and verification for the multiple states instead of just one. Right now we had 8 states involved in our experiment which are Alaska, Delaware, Washington D.C. , Hawaii, North Dakota, South Dakota, Vermont and Wyoming. There are some difficulties faced in collecting the census data for other states but we are trying to collect more data samples.
After this step now we are trying to modulating and extending the work done in our Module2-phase1 by improving the quality of frauds in such a way that they would go unnoticed by the 2BL.
Some of our earlier samples of results:
Pmanu : 0.2062639 Pchelsea : 0.9531511 Parsenal : 0.1787494 threshold was: 0.01 for state : Hawaii
Pmanu : 0.6252274 Pchelsea : 0.1884166 Parsenal : 0.8031289 threshold was: 0.001724138 for state : Alaska
Pmanu : 0.4862842 Pchelsea : 0.8163978 Parsenal : 0.5799487 threshold was: 0.0009433962 for state : North Dakota
Pmanu : 0.9049317 Pchelsea : 0.5891186 Parsenal : 0.1960104 threshold was: 0.0007575758 for state : South Dakota
Pmanu : 0.08608333 Pchelsea : 0.8747973 Parsenal : 0.4532776 threshold was: 0.003571429 for state : Vermont
Pmanu : 0.498102 Pchelsea : 0.04824834 Parsenal : 0.09058552 threshold was: 0.002173913 for state : Wyoming
Pmanu : 0.9393464 Pchelsea : 0.3613848 Parsenal : 0.08792899 threshold was: 0.01666667 for state : Delaware
Pmanu : 0.05444741 Pchelsea : 0.005691999 Parsenal : 0.2015466 threshold was: 0.001282051 for state : Washington, D.C.
Tries Passes MANU-FAILED CHELSEA-FAILED ARSENAL-FAILED
1 1 1 0 0 0
where Pxxxx is the critical value for the party in state: xxxx and its goes below threshold: **** 2BL is triggered, but right now every value is far very high then the threshold and so no False Positives are observed.