## 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:

**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%.**the desired significance leve**l

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**

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