What statistical tests can I use on data collected from quota samples?

Answer 1

The simple answer is you cannot use statistical tests on data collected from quota samples.

Unless the sample was collected using a random sampling technique you cannot have any confidence in the results being representative of the population you are sampling. Quota samples are non random.

However this does not stop researchers from using statistical tests on quota samples, even if the results can be taken with a pinch of salt!

Answer 2

You can use statistical tests appropriate for categorical data, such as chi-square tests or Fisher's exact test for associations between variables. For continuous data, you can use t-tests or non-parametric tests like Mann-Whitney U test or Kruskal-Wallis test. It's important to consider the limitations of quota sampling in interpreting the results.