Correlation

Pearson vs. Spearman Correlation: Which to Use for Your Thesis Data (2-Question Decision Framework)

Q: Do I need to test normality before running a correlation?

Yes, for Pearson. Run Shapiro-Wilk on both variables. If either is significantly non-normal (p < .05), use Spearman instead. Spearman does not require normality.

Q: Can I use Pearson correlation on Likert scale data?

Strictly, no - Likert items are ordinal. However, many researchers use Pearson on composite Likert scores (averaged across multiple items) and defend this as approximately interval. The conservative and defensible approach is Spearman for single items and Pearson for composites with a note.

Q: What is the difference between correlation and regression in thesis research?

Correlation measures the strength and direction of a relationship between two variables without implying direction of effect. Regression models how one variable predicts another - it specifies which is the predictor and which is the outcome. Use correlation when you want to describe association; use regression when you have a directional hypothesis or want to predict an outcome.

Q: How many participants do I need for a reliable correlation in my thesis?

For a medium effect (r = .30), 80% power, and α = .05, you need approximately 84 participants. For a large effect (r = .50), approximately 28 participants. Run a G*Power analysis before data collection using Test family: Correlation (bivariate normal model). Small samples produce wide confidence intervals and unreliable r estimates.

Q: How do I report a non-significant correlation in APA format?

Report it exactly as a significant one: state the coefficient, degrees of freedom, and exact p-value. Example: "Study time and exam score were not significantly correlated, r(48) = .18, p = .209." Do not omit non-significant correlations from your results - reporting only significant results is a form of selective reporting.

March 20264 min read

Your supervisor will ask in your thesis defense: 'Why did you use Pearson and not Spearman correlation?' The choice follows from exactly two questions about your data - and this guide gives you both, with a decision table, APA templates, and the one rule that prevents the most common thesis correlation mistake.

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Key takeaways

Pearson requires both variables to be metric AND approximately normally distributed - run Shapiro-Wilk on both before deciding.
Spearman works on ranks, handles ordinal data and non-normal distributions, and is always a defensible choice.
The 2-question decision: (1) are both variables metric and normal? (2) is the relationship linear? Only yes to both → Pearson.
APA format: report r(df) = .xx, p = .xxx for Pearson; rs(df) = .xx, p = .xxx for Spearman.
Cohen's benchmarks: small r = .10–.29, medium = .30–.49, large ≥ .50 - always interpret magnitude, not just significance.

What Pearson Correlation Measures (and When to Use It)

Pearson correlation (r) measures the strength of a linear relationship between two metric variables. Both variables must be on an interval or ratio scale and approximately normally distributed.

Pearson r ranges from −1 (perfect negative linear relationship) to +1 (perfect positive linear relationship). A value near 0 indicates no linear relationship.

Use Pearson when: both variables are metric, both pass Shapiro-Wilk (p > .05), and you expect the relationship to be linear.

What Spearman Correlation Measures (and When to Use It)

Spearman correlation (ρ, rho) measures the strength of a monotonic relationship - one that consistently increases or decreases, but not necessarily in a straight line. It converts raw values to ranks first, then correlates the ranks.

Spearman is appropriate when: one or both variables are ordinal (Likert scales), metric data is non-normal (Shapiro-Wilk p < .05), or you cannot assume linearity.

The interpretation is identical to Pearson: values near +1 or −1 indicate a strong monotonic relationship.

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When in doubt, use Spearman - it makes fewer assumptions, works on ordinal and metric data, and is always defensible to supervisors. You are far more likely to be questioned for using Pearson on ordinal data than Spearman on metric data.

2-Question Decision Framework: Which Correlation to Use

Answer both questions in order. The first 'No' sends you to Spearman.

Question	Answer	Decision
Q1: Are both variables metric (interval/ratio scale)?	No (ordinal/nominal)	→ Use Spearman
Q1: Are both variables metric?	Yes → proceed to Q2
Q2: Do both variables pass Shapiro-Wilk (p > .05)?	No (non-normal)	→ Use Spearman
Q2: Do both variables pass Shapiro-Wilk?	Yes → check scatterplot	→ Use Pearson
Bonus: Is the relationship non-linear (curved)?	Yes	→ Use Spearman regardless

APA Reporting Templates for Pearson and Spearman

Pearson - significant:
"There was a significant positive correlation between study time and exam score, r(48) = .62, p < .001."

Pearson - non-significant:
"Study time and exam score were not significantly correlated, r(48) = .18, p = .209."

Spearman - significant:
"There was a significant positive correlation between motivation rank and course satisfaction, rs(48) = .58, p = .003."

Spearman - non-significant:
"No significant correlation was found between satisfaction rank and performance, rs(48) = .14, p = .341."

Always report: coefficient (r or rs), degrees of freedom (N − 2), exact p-value, and direction.

Cohen's Benchmarks for Correlation Strength

Use these benchmarks to interpret the magnitude of your correlation, not just its significance.

r or ρ Value	Effect Size	Practical Meaning
.10 to .29	Small	Weak relationship - may need large N to detect
.30 to .49	Medium	Moderate relationship - noticeable in practice
.50 and above	Large	Strong relationship - clearly visible pattern

Frequently asked questions

Do I need to test normality before running a correlation?

▾

Yes, for Pearson. Run Shapiro-Wilk on both variables. If either is significantly non-normal (p < .05), use Spearman instead. Spearman does not require normality.

Can I use Pearson correlation on Likert scale data?

▾

Strictly, no - Likert items are ordinal. However, many researchers use Pearson on composite Likert scores (averaged across multiple items) and defend this as approximately interval. The conservative and defensible approach is Spearman for single items and Pearson for composites with a note.

What is the difference between correlation and regression in thesis research?

▾

Correlation measures the strength and direction of a relationship between two variables without implying direction of effect. Regression models how one variable predicts another - it specifies which is the predictor and which is the outcome. Use correlation when you want to describe association; use regression when you have a directional hypothesis or want to predict an outcome.

How many participants do I need for a reliable correlation in my thesis?

▾

For a medium effect (r = .30), 80% power, and α = .05, you need approximately 84 participants. For a large effect (r = .50), approximately 28 participants. Run a G*Power analysis before data collection using Test family: Correlation (bivariate normal model). Small samples produce wide confidence intervals and unreliable r estimates.

How do I report a non-significant correlation in APA format?

▾

Report it exactly as a significant one: state the coefficient, degrees of freedom, and exact p-value. Example: "Study time and exam score were not significantly correlated, r(48) = .18, p = .209." Do not omit non-significant correlations from your results - reporting only significant results is a form of selective reporting.

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