## Significance tester

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

Question: How large must my (partial) samples be if I want a median 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 standard deviation
i.e. the dispersal of the measured values in the sample around the respective median value. Where the standard diversion is unknown the following rule of thumb applies: (Maximum value on the scale – minimum value on the scale)/3.
2. the expected median value differences
3. the desired significance level
i.e. the statistical probability with which two median 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 the median value

For an expected standard deviation of ##in1## and an expected median value difference of ##in2## 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 median values with a difference of  ##in2## or higher are significantly different.

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 approximately normally distributed populations.
4. The variances of the populations are equal.