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Implementation of FDR

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.

 

 

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