Parametric & Non-Parametric Tests

Statistical Decision

Why the Right Test Matters in Research

Choosing between parametric and non-parametric tests affects statistical power, validity, and interpretation of results. Understanding assumptions is critical for correct analysis.

Parametric tests assume normal distribution, homogeneity of variance, and interval/ratio data. Non-parametric tests make fewer assumptions and work with ordinal data or non-normal distributions.

Normal Distribution Sample Size Data Scale Outliers Equal Variance
Key Factors in Test Selection
Data Distribution

Check normality using Shapiro-Wilk test, Kolmogorov-Smirnov test, or visual inspection (Q-Q plots, histograms).

Sample Size Consideration

Central Limit Theorem suggests parametric tests are robust with n > 30 per group. Small samples (n < 30) require normality checks.

Measurement Level

Parametric requires interval/ratio data (continuous). Non-parametric can handle ordinal data (Likert scales, rankings).

Common Tests

Frequently Used Statistical Tests

Compare parametric and non-parametric alternatives for common research scenarios

Parametric
Independent t-test

Compares means between two independent groups. Assumes normality, homogeneity of variance, and independent observations.

Use when:
  • Comparing two independent groups
  • Data is normally distributed
  • Continuous outcome variable
Parametric
One-Way ANOVA

Compares means across three or more independent groups. Post-hoc tests (Tukey, Bonferroni) follow significant ANOVA.

Use when:
  • Comparing three or more groups
  • Equal variances assumed (homoscedasticity)
  • One categorical independent variable
Non-Parametric
Mann-Whitney U

Compares distributions/medians between two independent groups. Alternative to independent t-test when assumptions violated.

Use when:
  • Non-normal distribution present
  • Ordinal or continuous data
  • Small or unequal sample sizes
Parametric
Pearson Correlation

Measures linear relationship between two continuous variables. Value ranges from -1 to +1.

Use when:
  • Both variables are continuous
  • Linear relationship expected
  • No significant outliers present
Non-Parametric
Kruskal-Wallis H

Compares medians across three or more independent groups. Alternative to one-way ANOVA.

Use when:
  • Three or more independent groups
  • Non-normal distribution
  • Ordinal or skewed continuous data
Non-Parametric
Spearman's Rho

Assesses monotonic (non-linear) relationship between two variables. Uses ranked data.

Use when:
  • Ordinal or non-normal continuous data
  • Non-linear but monotonic relationship
  • Outliers are present
Decision Guide

How to Decide Which Test to Use

Follow this decision flowchart for selecting appropriate statistical tests

Start Here
What type of data do you have?

Nominal/categorical: use Chi-square • Ordinal/Ranked: consider non-parametric • Interval/Ratio: consider parametric

Step 2
Is your data normally distributed?

Test normality with Shapiro-Wilk (n < 50) or Kolmogorov-Smirnov (n > 50). Check Q-Q plots and histograms.

Step 3
How many groups are you comparing?

Two groups: t-test (parametric) or Mann-Whitney (non-parametric). Three+ groups: ANOVA (parametric) or Kruskal-Wallis (non-parametric).

use Parametric (Higher Power)
t-test / ANOVA / Pearson Correlation
Use Non-Parametric (Robust)
Mann-Whitney / Kruskal-Wallis / Spearman