How to Choose the Right Statistical Test

Choosing the right statistical test can feel overwhelming. With dozens of tests available, how do you know which one fits your data? This guide will walk you through a systematic approach to selecting the perfect test for your analysis.

The Three Key Questions

Before selecting any test, answer these fundamental questions:

What type of data do you have? (Categorical or continuous)
How many groups are you comparing? (One, two, or more)
Are the groups related or independent?

Your answers will narrow down the options significantly.

A Decision Framework

Step 1: Identify Your Variables

Dependent Variable (what you’re measuring):

Categorical: Categories like yes/no, colors, types
Continuous: Numbers like height, weight, scores, time

Independent Variable (what defines your groups):

One group: Comparing to a known value
Two groups: Comparing two conditions or populations
Three+ groups: Comparing multiple conditions

Step 2: Consider Your Research Design

Are your groups independent or related?

Independent: Different people in each group (e.g., men vs. women)
Related/Paired: Same people measured twice, or matched pairs (e.g., before vs. after treatment)

Quick Reference Guide

For Continuous Data (Comparing Means)

Scenario	Independent Groups	Related/Paired
Compare to known value	One-sample t-test	—
Compare 2 groups	Independent t-test	Paired t-test
Compare 3+ groups	One-way ANOVA	Repeated measures ANOVA

For Categorical Data (Comparing Frequencies)

Scenario	Test
One variable, expected proportions	Chi-square goodness of fit
Two categorical variables	Chi-square test of independence
Before/after, same subjects	McNemar’s test

For Relationships Between Variables

Variable Types	Test
Two continuous	Pearson correlation
Continuous + categorical predictor	Linear regression
Categorical outcome	Logistic regression
Both ordinal or non-normal	Spearman correlation

Detailed Test Selection

When to Use a t-Test

One-Sample t-Test Use when comparing your sample mean to a known or hypothesized value.

Example: Is the average test score in your class different from the national average of 75?

Independent Samples t-Test Use when comparing means between two unrelated groups.

Example: Do students taught with Method A perform differently than those taught with Method B?

Paired t-Test Use when comparing two measurements from the same subjects.

Example: Did students’ scores improve from pre-test to post-test?

When to Use ANOVA

One-Way ANOVA Use when comparing means across three or more independent groups.

Example: Do test scores differ among students taught with Method A, B, or C?

Two-Way ANOVA Use when examining two independent variables and their interaction.

Example: How do teaching method AND class size affect test scores?

Repeated Measures ANOVA Use when the same subjects are measured multiple times.

Example: How do scores change across three testing sessions?

When to Use Chi-Square Tests

Chi-Square Goodness of Fit Use when testing if observed frequencies match expected proportions.

Example: Do customer preferences match the expected distribution across product categories?

Chi-Square Test of Independence Use when testing the relationship between two categorical variables.

Example: Is there a relationship between gender and voting preference?

When to Use Correlation

Pearson’s r Use for linear relationships between two continuous variables with normal distributions.

Example: Is there a relationship between study hours and exam scores?

Spearman’s ρ Use for ordinal data or non-linear relationships.

Example: Is there a relationship between class rank and job satisfaction rating?

Non-Parametric Alternatives

When your data doesn’t meet assumptions (normal distribution, equal variances), consider these alternatives:

Parametric Test	Non-Parametric Alternative
Independent t-test	Mann-Whitney U test
Paired t-test	Wilcoxon signed-rank test
One-way ANOVA	Kruskal-Wallis test
Repeated measures ANOVA	Friedman test
Pearson correlation	Spearman correlation

Checking Assumptions

Most parametric tests assume:

Normality: Data is approximately normally distributed
- Check with histograms, Q-Q plots, or Shapiro-Wilk test
Homogeneity of variance: Groups have similar variability
- Check with Levene’s test
Independence: Observations are not related
- Determined by study design

If assumptions are violated:

Consider non-parametric alternatives
Use robust versions of tests
Transform your data
With large samples, violations often matter less

Common Mistakes to Avoid

1. Using the Wrong Test for Your Data Type

Don’t use t-tests for categorical data or chi-square for continuous data.

2. Multiple Testing Without Correction

Running many tests inflates Type I error. Use Bonferroni correction or control False Discovery Rate.

3. Confusing Correlation with Causation

Finding a relationship doesn’t prove one variable causes changes in another.

4. Ignoring Assumptions

Always check test assumptions. Violated assumptions can invalidate results.

5. Only Reporting p-values

Include effect sizes and confidence intervals for complete reporting.

Flowchart Summary

Start Here: What is your dependent variable?

If CATEGORICAL (counts, frequencies):

One variable → Chi-square goodness of fit
Two variables → Chi-square test of independence

If CONTINUOUS (measurements, scores):

Comparing to a single value → One-sample t-test
Comparing 2 groups, independent → Independent t-test
Comparing 2 groups, paired → Paired t-test
Comparing 3+ groups, independent → One-way ANOVA
Comparing 3+ groups, repeated → Repeated measures ANOVA
Looking at relationship with another continuous variable → Correlation/Regression

Putting It All Together

Let’s walk through an example:

Research question: Do three different fertilizers affect plant growth differently?

Dependent variable? Plant height (continuous)
How many groups? Three (Fertilizer A, B, C)
Independent or related? Independent (different plants in each group)

Answer: One-way ANOVA

If you find significant differences, follow up with post-hoc tests (like Tukey’s HSD) to see which specific groups differ.

Final Tips

Start simple: Use the simplest test that answers your question
Check assumptions: Before running any test
Report fully: p-value, effect size, and confidence intervals
Replicate: One significant result isn’t proof
Consult resources: When in doubt, seek statistical guidance

Choosing the right statistical test is a skill that improves with practice. Use this guide as a starting point, and don’t be afraid to consult additional resources for complex situations.