After looking at the distribution of data and perhaps conducting some descriptive statistics to find out the mean, median, or mode, it is time to make some inferences about the data. As mentioned previously, inferential statistics are the set of statistical tests researchers use to make inferences about data. These statistical tests allow researchers to make inferences because they can show whether an observed pattern is due to intervention or chance. There is a wide range of statistical tests. The decision of which statistical test to use depends on the research design, the distribution of the data, and the type of variable. In general, if the data is normally distributed, parametric tests should be used. If the data is non-normal, non-parametric tests should be used. Below is a list of just a few common statistical tests and their uses.
| Type of Test | Use |
| Correlational: these tests look for an association between variables | |
| Pearson Correlation | Tests for the strength of the association between two continuous variables |
| Spearman Correlation | Tests for the strength of the association between two ordinal variables (does not rely on the assumption of normally distributed data) |
| Chi-Square | Tests for the strength of the association between two categorical variables |
| Comparison of Means: these tests look for the difference between the means of variables | |
| Paired T-Test | Tests for the difference between two variables from the same population (e.g., a pre- and posttest score) |
| Independent T-Test | Tests for the difference between the same variable from different populations (e.g., comparing boys to girls) |
| ANOVA | Tests for the difference between group means after any other variance in the outcome variable is accounted for (e.g., controlling for sex, income, or age) |
| Regression: these tests assess if change in one variable predicts change in another variable | |
| Simple Regression | Tests how change in the predictor variable predicts the level of change in the outcome variable |
| Multiple Regression | Tests how changes in the combination of two or more predictor variables predict the level of change in the outcome variable |
| Non-Parametric: these tests are used when the data does not meet the assumptions required for parametric tests | |
| Wilcoxon Rank-Sum Test | Tests for the difference between two independent variables; takes into account magnitude and direction of difference |
| Wilcoxon Sign-Rank Test | Tests for the difference between two related variables; takes into account the magnitude and direction of difference |
| Sign Test | Tests if two related variables are different; ignores the magnitude of change—only takes into account direction |
Follow this link for a printable PDF version of this table: Common Statistical Tests.