How to Choose a Statistical Test by Dr Kiran Kakade

Choosing the right statistical test is crucial for analyzing data accurately and drawing meaningful conclusions. The decision depends on several factors, including the type of dependent and independent variables, the number of groups being compared, and the distribution of data.

1. Understanding the Variables

Before choosing a test, it’s essential to identify the following:

Dependent Variable (Outcome Variable): The variable you are measuring or predicting.
Independent Variable (Predictor Variable): The variable you manipulate or use to explain changes in the dependent variable.

The dependent variable can be continuous (e.g., height, weight, income) or categorical (e.g., gender, disease status, satisfaction level).

2. Choosing a Test for Continuous Dependent Variables

A. One Continuous Independent Variable

Assessing a Relationship:
- Parametric Test: Pearson’s correlation (if data is normally distributed).
- Non-Parametric Test: Spearman’s correlation (if data is not normally distributed).
Predicting a Dependent Variable:
- Simple Linear Regression (after checking residuals for normality).

B. Two or More Continuous Independent Variables

Multiple Regression: Used when multiple predictors influence the dependent variable.

C. One Categorical Independent Variable

Comparing Two Independent (Unmatched) Groups:
- Parametric Test: Independent samples t-test (if normally distributed).
- Non-Parametric Test: Mann-Whitney test (if not normally distributed).
Comparing More Than Two Groups:
- Parametric Test: One-way ANOVA (for normal data).
- Non-Parametric Test: Kruskal-Wallis test (for non-normal data).
Repeated Measures (More Than One Observation Per Subject):
- For Two Groups:
  - Parametric Test: Paired t-test.
  - Non-Parametric Test: Wilcoxon signed-rank test.
- For More Than Two Groups:
  - Parametric Test: Repeated measures ANOVA.
  - Non-Parametric Test: Friedman test.

D. Two or More Categorical Independent Variables

Factorial ANOVA: Used when two or more categorical independent variables are involved.
Factorial Repeated Measures ANOVA: Applied when repeated measures exist within groups.

E. Two or More Categorical and Continuous Variables

Multiple Regression: Used when independent variables include both continuous and categorical variables.
ANCOVA (Analysis of Covariance): Applied when controlling for a continuous covariate.

3. Choosing a Test for Categorical Dependent Variables

A. One Categorical Independent Variable

Contingency Table Analysis:
- Chi-Square Test: Determines the relationship between categorical variables.
- Fisher’s Exact Test: Used for small sample sizes in 2×2 tables.

B. Categorical Dependent Variable with Two Outcomes

Prediction of Dependent Variable:
- Logistic Regression: Used for binary (yes/no, success/failure) outcomes.

4. Special Considerations for Ordinal Data

If the dependent variable has many levels, it can be treated as a non-parametric continuous variable.
If the independent variable is ordinal, non-parametric tests are typically preferred.
If both the dependent and independent variables have small groups, they may be treated as normal.

Final Thoughts

Selecting the right statistical test ensures accurate analysis and valid conclusions. Here’s a quick summary of how to make the right choice:

Identify the type of dependent variable (continuous or categorical).
Determine the number and type of independent variables (continuous or categorical).
Check for normality to decide between parametric and non-parametric tests.
Use the appropriate test based on the number of groups and observations.

This structured approach helps researchers and analysts choose the best statistical test for their data, ensuring reliable and meaningful results.