Difference between revisions of "Significance testing - Effective Base"
(Created page with "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 effectiv...") |
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| − | + | 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 test 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 | + | 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 the population. |
| + | The effective base is calculated using the following formula: | ||
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effective base = (sum of weight factors) squared / sum of the squared weight factors. | effective base = (sum of weight factors) squared / sum of the squared weight factors. | ||
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= 1600 / 49.2162 = 32.509 | = 1600 / 49.2162 = 32.509 | ||
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Revision as of 14:08, 27 November 2013
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 test 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 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
