leschiffres / weighting-survey-statistics

Simplified Weighting Algorithm for Survey statistics

The purpose of this repository is to use a simplified version of the raking algorithm, to showcase its capabilities.

By making use of the titanic dataset, we create a biased sample where there is a slight deviation of the initial distribution. Initially we have the following distribution:

'Pclass': {3: 0.542, 1: 0.247, 2: 0.212},
'Sex': {'male': 0.644, 'female': 0.356},
'FareGroup': {'Cheap': 0.575, 'Average': 0.241, 'Above Average': 0.119, 'Expensive': 0.064}

and the biased sample has the following one:

'Pclass': {3: 0.44, 1: 0.296, 2: 0.264},
'Sex': {'male': 0.568, 'female': 0.432},
'FareGroup': {'Cheap': 0.512,'Average': 0.252,'Above Average': 0.16,'Expensive': 0.076}

Clearly in the biased sample there's a higher than expected percentage of female passengers and a lower percentage of the 3rd class passengers.

Normally in survey statistics we cannot know the actual distribution of all opinion data / population characteristics, so we try to estimate the based on the things we know. Thus, if we have a survey where 70% of the voters were male, we try to balance it out as we know that normally the percentage of men and women in the general population, should be closer to 50%. This is when a weighting algorithm can help.

Here we assume that the Pclass and Sex population data are known and we try to estimate the FareGroup one.

We implement a simple algorithm that:

• In the beginning each row gets a weight equal to 1 and then we adjust it accordingly.
  • For instance if we know that the actual male percentage is 65% but in our sample men are at 32.5% then every male row should get a doubled weight.
• We divide the actual ratio by the observed ratio for each category to get the raking factor.
• Then each row gets their weight multiplied by the corresponding factor of Pclass and Sex to get the final weight.

Thus, we are able to get a final estimation of the FareGroup distribution.

Cheap            0.588861
Average          0.220911
Above Average    0.134534
Expensive        0.060532

Clearly, the this is much closer to the reality that what is observed in the biased sample.