Decide whether the random variable you are considering is Quantitative ( numerical, so you will be asking questions about the mean ), Ranked ( ordered, so you will be asking questions about the median ) or Qualitative ( multiple choice, so you will be asking questions about the proportions ). Then decide how many samples you have (it may be better to think of this as asking how many populations you are comparing. In many cases (especially chi-squared) you can think of all the data as one sample from one population, divided into smaller samples by a second qualitative variable).
Note: The ranked tests are often used with quantitative data when the samples are too small or the data too skew to justify the t-test/ANOVA.
Note: an asterisk* indicates the test can compute a comfidence interval as well as hypothesis testing.
The histogram gives a quick histogram of numerical data that is sufficient for assessing overall shape.
| Histogram |
|---|
| Quantitative Variable | Ranked Variable | Qualitative Variable | |
|---|---|---|---|
| One Sample | One Sample t-test* | One Sample Proportion* | |
| Two Sample | Two
Sample t-test* (regular) or One Sample t-test on differences* (matched pairs) | Wilcoxon Rank Sum Test (regular) or Signed Wilcoxon Rank Sum* (matched pairs) | Two Sample Proportion* |
| Many Samples | Anova | Kruskal-Wallis | Chi Squared |
| Simple Linear Regression |
|---|