How do I choose the right quantitative statistical test for my data analysis?
Answer
When choosing statistical tests to answer a research question or hypothesis, it is important to know whether this involves:
- Test of comparison: Comparing a dependent variable across levels/groups of independent variable(s) OR
- Test of association, correlation, or relationship: Establishing whether a relationship exists between two or more variables
Some important considerations when choosing statistical tests:
- For tests of comparison, the number of levels/groups of the independent variable(s) (two or more than two) is important.
- The number of independent variables (one or more than one) across which the dependent variable is being compared is also important.
- The variable type (continuous/scale, nominal, ordinal) for the dependent and independent variables is also essential.
- Parametric assumptions (such as normality, outliers, homogeneity of variance, homoscedasticity, etc.) also need to be checked to decide on whether parametric or non-parametric versions of the inferential statistical tests is appropriate.
After thinking about all of these criteria, you can then use the below tables to choose the appropriate test.
Selection of inferential tests for comparison
|
Parameters being compared: |
Dependent Variable Type |
Independent Variable Type |
Parametric test
|
Non-parametric test |
|
Averages of two INDEPENDENT groups |
Continuous |
Nominal (Binary) |
Independent T-test |
Mann-Whitney test or Wilcoxon Rank Sum test |
|
Averages of 3 or more INDEPENDENT groups |
Continuous |
Nominal |
One-Way ANOVA* |
Kruskal Wallis test |
|
Averages of two paired/matched samples or conditions (e.g., pain level before and after a treatment) |
Continuous |
Time or Condition variable |
Paired T-test |
Wilcoxon Signed Rank test |
|
Averages of three or more matched/repeated samples or conditions (e.g., pain level before, 6 months after, and 1 year after treatment) |
Continuous |
Time or Condition variable |
Repeated Measures ANOVA |
Friedman test |
Selection of inferential tests for relationship or association
|
Parameters being assessed: |
Dependent Variable Type |
Independent Variable Type |
Parametric test
|
Non-parametric test |
|
Relationship between two continuous (or ordinal for non-parametric) variables |
Continuous |
Continuous |
Pearson’s Correlation Coefficient |
Spearman’s Correlation Coefficient or Kendall’s Tau |
|
Relationship between two variables |
Continuous |
Nominal (Binary) |
Point-Biserial Correlation |
Rank-Biserial Correlation |
|
Relationship between two categorical variables |
Categorical |
Categorical |
|
Chi-Square test |
|
Predicting one variable using another predictor variable |
Continuous |
Continuous or Ordinal |
Simple Linear Regression |
Transform the data or use non-parametric regression |
|
Predicting one variable using another predictor variable |
Categorical (Nominal or Ordinal) |
Continuous or Nominal or Ordinal |
Logistic regression |
Classification models |
Selection of inferential tests when several independent variables are involved
|
Parameters being assessed: |
First Independent Variable Type |
Second/Subsequent Independent Variable Type |
Inferential Test |
|
Predicting a continuous dependent variable using two or more predictor variables |
Continuous |
Continuous or nominal (Binary) |
Multiple Linear Regression |
|
Comparing averages of a continuous dependent variable |
Nominal (Independent groups) |
Nominal (Independent groups) |
Between-Subject Factorial ANOVA |
|
Comparing averages of a continuous dependent variable |
Nominal (Paired/Repeated) |
Nominal (Paired/Repeated) |
Within-Subject Factorial ANOVA (or Repeated Measures Factorial ANOVA) |
|
Comparing averages of a continuous dependent variable |
Nominal (Independent groups) |
Nominal (Paired/Repeated) |
Mixed Factorial ANOVA |
|
Comparing averages of a continuous dependent variable |
Nominal |
Continuous |
Analysis of Covariance (ANCOVA) |
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