## Significance tester

Determination of sample size on the basis of expected proportion value differences

Question: How large must my (partial) samples be if I want a proportional value difference that I have determined between two samples to be significant beyond a certain value?

Important factors for the calculation are:

1. the expected size of the proportional values
Where the size of the proportional values cannot be roughly estimated, a worst case scenario is assumed for the calculation, i.e. one of the two proportional values is set at 50%.
2. the desired significance level
i.e. the statistical probability with which two proportional values actually differ from each other.
In market research, the target is usually a significance level of 95%.

Sample sizes based on expected differences of proportional values

For an expected proportional value of ##in1##% in sample 1 and an expected proportional value of ##in2##% in sample 2, the required sample size per group is:

 90% significance level ##sig90## 95% significance level ##sig95## 99% significance level ##sig99##

This means for a significance level of 95%:
With two samples with a size of  ##sig95## each, one can statistically expect, that the ratios ##in1##% and ##in2##% are significantly different from each other.

Requirements

1. The populations are sufficiently large, so that correction factors for finite populations can be neglected.
2. Both samples are independent.
3. Both samples are drawn from the same population.