## Significance tester

Determination of sample size on the basis of expected proportional values

Question: How large must my sample be if I want the actual proportional value of the statistical population within a radius I have determined to resemble the measured proportional value of the sample?

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, with an expected proportional value of 50%.
2. the tolerated fluctuation range of the proportional values
i.e. how far the actual value of the statistical population may diverge at most from the measured value of the sample.
3. the desired significance level
i.e. with which statistical probability the actual proportional value of the statistical population is aligned with the measured proportional value of the sample, within the tolerated fluctuation range. In market research, the target is usually a significance level of 95%.

Determination of sample size on the basis of expected proportional values

For an expected proportional value of ##in1##% and a tolerated fluctuation of ##in2##% the required sample size is

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

This means for a significance level of 95%:
With a sample size of ##sig95## one can statistically expect, that a value of ##in1##% in the sample fits a value of the population of about ##in1##% ±##in2##% with a probablity of 95%.

Requirements

1. The population is sufficiently large, so that correction factors for finite populations can be neglected.