Which Statistical Test to Use? Interactive Guide

Statistical Test Selector

1. What is your primary research goal?

2. Study Design & Group Structure

3. Level of Measurement / Data Type

4. Distribution & Parametric Assumptions

Methodology & Research Design Guide

How to Choose the Right Statistical Test

Selecting the appropriate statistical test depends directly on your research question, study design, level of measurement (nominal, ordinal, or continuous), and whether your data satisfies parametric assumptions (such as normality and homoscedasticity).

Choosing an incorrect test can lead to invalid conclusions, inflated Type I errors (false positives), or severely compromised statistical power (Type II errors).

Key Selection Criteria

Research Objective: Are you testing for group differences, measuring association, fitting predictive models, or checking instrument validity?
Sample Independence: Are observations independent (separate groups) or paired/repeated (same subjects measured across conditions)?
Level of Measurement: Continuous data allows parametric testing; ordinal and nominal data require non-parametric or contingency methods.
Distributional Shape: When continuous data is heavily skewed or contains severe outliers, non-parametric rank-based alternatives must be used.

Parametric vs. Non-Parametric Pairing

$$\text{Independent 2-Group: } \text{Two-Sample t-Test} \iff \text{Mann-Whitney U}$$ $$\text{Paired 2-Condition: } \text{Paired Samples t-Test} \iff \text{Wilcoxon Signed-Rank}$$ $$\text{Independent 3+ Group: } \text{One-Way ANOVA} \iff \text{Kruskal-Wallis}$$

Non-parametric tests replace raw scores with relative ranks ($R_i$), eliminating the requirement for Gaussian distribution assumptions.

Decision Scenarios

Scenario 1: Comparing systolic blood pressure between Treatment ($n=25$) and Control ($n=25$) groups with normally distributed data $\implies$ Two-Sample Independent t-Test.

Scenario 2: Evaluating pre- and post-workshop customer satisfaction on a 5-point Likert scale $\implies$ Wilcoxon Signed-Rank Test.

Scenario 3: Testing whether patient recovery rate differs across 4 distinct physical therapy regimens with non-normal recovery times $\implies$ Kruskal-Wallis Test.

Decision Tree Match

Recommended Statistical Test

Primary Recommended Test

Two-Sample Independent t-Test

Direct match for comparing 2 independent normal continuous distributions

Test Family Parametric

Primary Metric Means (x̄₁ - x̄₂)

Distribution Student's t

Direct Alternative Mann-Whitney U

Test Specification & Theoretical Formulation

Key Statistical Assumptions to Verify

How to Report & Execute This Test

Decision Flowchart Hierarchy

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Which Statistical Test to Use? Interactive Guide

Statistical Test Selector

Recommended Statistical Test

Test Specification & Theoretical Formulation

Key Statistical Assumptions to Verify

How to Report & Execute This Test

Decision Flowchart Hierarchy

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