Significance testing - Effective Base
When tstats are specified on weighted tables, Quantum calculates and uses the effective base in the calculation of the test statistics. The following explains why the effective base is used and how it is calculated.
Consider the case in which the data is weighted by sex (male and female), to adjust it to reflect the population being studied, because 30% women and 70% men were sampled when the actual population proportions are 52% women and 48% men.
In this case, the weighting is actually inflating the answers for the women and deflating the answers for the men in order to match the population proportions. In other words, an answer from a woman will count as more than 1 on the tables, similarly, an answer from a man will count as less than 1, to be precise, every woman will count as 1.733 and every an as 0.686.
The effective base is used as a safeguard against making statistical conclusions from a sample that has been drastically adjusted (using weights) to match the population.
The effective base is calculated using the following formula,
effective base = (sum of weight factors) squared / sum of the squared weight factors.
If the data for a particular column is as follows
Total unweighted 40
Total weighted 40
and comes from 12 women and 28 men, then the effective base is
effective base = (12*1.733 + 28*0.686)**2 / (12*(1.733**2)+(28*(0.686)**2)
= 1600 / 49.2162 = 32.509
The effective base is a good criterion to judge how good the weighting is. If the weighting is inflating the answers from a particular group by a large factor, the effective base will end to be much smaller than the unweighted and weighted bases.
The closer the effective base is to the unweighted base, the better the weighting is.
