Significance testing - Effective Base

Survey data is often weighted, at times to balance sampling bias (e.g. obtain a market-distribution representation of gender and age) and at other times weighting to obtain a representation of sales, population, etc.

Weighting actually inflates the "number of answers" per respondents, at times by a relatively large factor. When performing significance testing, we ideally wish to utilize the weighted data to capture the intent of the weighting, however, as significance testing is impacted by the scale of the weighted values, weighted significance testing can be impacted adversely by weighting, in particular in cases in which weights represent large factors, say x10 or x100 or more.

In these cases, the effective base calculation can remove the influence of the numerically large weighted values while capturing the intent of the weighting. Basically, effective base is used as a safeguard against making statistical conclusions from a sample that has been drastically adjusted (using weights) to match target values like sales or 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:

Sample Sample% Population% Weight=Pop%/Sam%
women 12 30% 52% 1.7333
men 28 70% 48% 0.6857

then the effective base is:

effective base = (12*1.7333 + 28*0.6857)**2 / (12*(1.7333**2)+(28*(0.6857)**2)

= 1600 / 49.2162 = 32.509

Applying Effective Base:

From mTAB's spreadsheet view, select menu items Data, then Significance Indicators.

Click on the "Effective Base" checkbox from the resultant Significance Indicator dialog.