If you want to know whether the difference between the scores in two group or conditions is statistically significant…
and your data is at least ordinal (meaning it could also be interval or ratio but NOT nominal) you can do one of the following two tests:
If you have an independent measures design you should do a: Mann-Whitney U
If you have a repeated measures design you should do a: Wilcoxon signed ranks test
- if your hypothesis is directional you need to check the p value for a one tailed test.
- if your hypothesis is non-directional you need to check the p value for a two tailed test.
If your p value is…
- less than or equal to 0.05 (5% or 1 in 20) you can accept your experimental hypothesis (p<0.05 and reject your null hypothesis
- more than 0.05 (5% or 1 in 20) you must reject your experimental hypothesis and accept your null (p>0.05).
Why would you use a non-parametric test if your data was interval or ratio?
Sometime if is not possible to carry out a parametric test because your data does not meet all of the parametric assumptions, having interval/ratio data is just one of these assumptions. The data in both groups/conditions also needs to be normally distributed AND you have to have homogeneity of variance, meaning the standard deviations are very similar.
Your data is unlikely to be normally distributed if you have a small sample. However, if you have a relatively large sample then you can safely assume that it is. You may wish to check this by plotting your data on a pair of histograms 😀
In most cases it is wiser to stick to a non-parametric test if you are unsure of whether your data meets parametric assumptions.