## Significance tester

Determination of sample size on the basis of expected median values

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

Important factors for the calculation are:

1. the expected size of the standard deviation
i.e. the dispersal of the measured values in the sample around the median value.
Where the standard deviation is unknown the following rule of thumb applies:
(Maximum value on the scale – minimum value on the scale)/3.
2. the maximum tolerated fluctuation range of the median values
i.e. how far the actual value of the statistical population may deviate at most from the measured value of the sample.
3. the desired significance level
i.e. with which statistical probability the actual median value of the statistical population is aligned with the measured median value of the sample, within the tolerated fluctuation range. In market research, the target is usually a significance level of 95%.

Sample sizes based on median values

For an expected standard deviation of ##in1## and a maximal tolerated fluctuation range 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 the real median of the population is with a probability of 95% in the range of ±##in2## around the surveyed value.

Requirements

1. The populations are sufficiently large, so that correction factors for finite populations can be neglected.
2. The populations are approximately normally distributed.