# Testing differences

In statistics, there is often interest in comparing the data for two or more variables in order to help determine whether there are 'real' mean differences, and the size of any differences.

Such questions can be tackled using t-tests where the dependent variables are reasonably normal and with similar variances. Alternatively, several non-parametric statistics can be applied when such assumptions cannot be met.

## Types

Sample Parametric Non-parametric
One-sample One sample t-test Chi-Square goodness-of-fit test
Independent samples Independent samples t-test Mann-Whitney U test, Chi-Square test for two independent samples
Dependent samples Paired samples t-test Wilcoxon signed-rank test, Binomial test

## Considerations

If you have access to the population data, then a descriptive approach could well be sufficient for meaningfully reporting on the data.

However, if you only have a sample, then inferential statistics can help in drawing conclusions about possible differences in the target population.