See also:
Formulas for frequency comparison tests are as follows.
N1: Sample 1 size N2: Sample 2 size Eff1: Count n the cell in N1 (weighted) Eff2: Count in the cell in N2 (weighted) ¯x1=Average of weights in the N1 ¯x2=Average of weights in the N2 dP1: Percentage 1 => Eff1/N1 dP2: Percentage 2=> Eff2/ N2 dFo: Estimated percentage => (eff1+eff2) / (N1+N2)
Askiaanalyse offers four frequency comparison tests, as follows:
Student test using an estimator
In order to reduce the weighting effect, we will use the efficiency factor, calculated as follows:
The ‘Unequal Weighting Effect’ (UWE). Leslie Kish has analysed the effect of unequal weights in the accuracy of estimations through the ‘Unequal Weighting Effect’ (UWE). (Kish L., Weighting for Unequal Pi, Journal of Official Statistics, Vol. 8, N°2, 1992, pp. 183-200). If we have wi the weight per individual (weighting sample factor) and n the global size sample, the factor (UWE) of the variance increase of weight per individual, is:
The relative increase of variance is equal to 1+ the squared of the weighting variance factor (CVw²).
To include this UWE in the calculation, we can replace the total count of individuals n by n0 in the the classical formula denominator. n0 is a fictive number which includes a under /over representation of categories in the sample weighted, where:
This new base is named Efficiency base and the ratio 
, efficiency index.
The efficiency base is calculated as follows:
No=No1+No2
The efficiency coefficient = 
Student Test using efficiency coefficient
Student Test using estimator and efficiency coefficient
