Pearson’s r and Spearman’s rho (ρ, also written rs) both measure how strongly two variables are related, both range from −1 to +1, and both appear constantly in theses. They answer slightly different questions, though, and choosing the wrong one can understate or overstate a relationship. This guide explains the difference, gives clear rules for choosing between them, and shows how to report each in APA style. You can calculate both with the free Pearson correlation calculator and Spearman correlation calculator.
The key difference: linear vs monotonic
Pearson’s correlation measures the strength and direction of a linear relationship between two continuous variables: how closely the points on a scatter plot fall around a straight line. It is calculated from the actual values: the covariance of the two variables divided by the product of their standard deviations.
Spearman’s correlation measures the strength and direction of a monotonic relationship: whether one variable tends to increase (or decrease) as the other increases, not necessarily at a constant rate. It is calculated by converting each variable to ranks and then computing Pearson’s correlation on the ranks (Schober et al., 2018).
Because Spearman uses ranks, it does not care how far apart the values are, only their order. This makes it suitable for ordinal data and much less affected by outliers and skewed distributions.
| Pearson r | Spearman ρ | |
|---|---|---|
| Type of relationship | Linear | Monotonic (consistently increasing or decreasing) |
| Data | Both variables continuous (interval/ratio) | Ordinal, or continuous data that are skewed or have outliers |
| Based on | Raw values | Ranks |
| Sensitivity to outliers | High | Low |
| Distributional assumption | For significance tests and CIs, approximately bivariate normal | None about the shape of the distribution |
| Typical thesis use | Scale totals, test scores, age, income | Single Likert items, rankings, skewed counts |
When to use Pearson’s r
- Both variables are continuous, for example total scores on two multi-item scales, test marks or hours of study.
- The scatter plot shows a roughly straight-line pattern.
- There are no extreme outliers that drive the result.
- For significance testing, the variables are approximately normally distributed. With large samples, the test is fairly robust to moderate departures.
When to use Spearman’s ρ
- At least one variable is ordinal, for example a single Likert item, education level or a ranking.
- The relationship is monotonic but clearly curved, for example scores rise quickly at first and then level off.
- The data are strongly skewed or contain outliers that you cannot justify removing.
- The sample is small and normality is doubtful.
Always look at the scatter plot first
Neither coefficient can describe a relationship that is not monotonic. A U-shaped pattern, for example performance that rises with arousal up to a point and then falls, can give a correlation near zero for both Pearson and Spearman even though the variables are strongly related. Plot your data before choosing a coefficient. Both ScholarCalc calculators draw a scatter plot automatically.
How outliers change the picture
Imagine ten students whose study hours and grades rise together fairly steadily, plus one student who reports 60 study hours and a low grade. That single point can pull Pearson’s r down considerably, because Pearson works with the actual distances from the mean. Spearman only sees that this student has the highest rank for hours and a low rank for grade, so the effect is limited. If the two coefficients differ substantially in your data, investigate why: outliers, skewness or a non-linear pattern are the usual causes (Hauke & Kossowski, 2011).
Likert scale data
This is the most common source of confusion in theses. A sensible approach that most supervisors accept is:
- Single Likert items (one question on a 1–5 scale) are ordinal, so use Spearman.
- Composite scores (the sum or mean of several items measuring one construct, ideally with acceptable Cronbach’s alpha) behave much more like continuous data, and Pearson is widely used for them. If the composite scores are clearly skewed, Spearman is a safe alternative.
Whatever you decide, state your reasoning in the methodology chapter.
Interpreting the strength of a correlation
Cohen (1988) suggested that correlations of about .10, .30 and .50 can be described as small, medium and large effects in the behavioural sciences. Other authors use different labels. For example, Schober et al. (2018) describe .10–.39 as weak, .40–.69 as moderate and .70–.89 as strong. Choose one framework, cite it, and apply it consistently. These descriptions apply equally to Pearson and Spearman coefficients.
The square of Pearson’s r (r²) is the proportion of variance shared by the two variables. For example, r = .50 means the variables share 25% of their variance. Remember that correlation does not imply causation: a strong correlation may reflect a third variable or reverse causality.
Statistical significance and sample size
The p-value of a correlation tests whether the population correlation could plausibly be zero. With large samples, even very weak correlations become statistically significant, so always interpret the size of the coefficient as well. Reporting a 95% confidence interval for the correlation shows how precisely it was estimated. Both ScholarCalc calculators provide one. See also the p-value explained.
Reporting in APA style
Report the coefficient with its degrees of freedom (N − 2) in parentheses, the exact p-value, and the confidence interval if available. Use two decimal places and no leading zero, because correlations cannot exceed 1 (APA, 2020).
A Pearson correlation showed a strong positive relationship between weekly study hours and exam scores, r(48) = .62, p < .001, 95% CI [.41, .77].
Because the satisfaction item was measured on a single 5-point scale, Spearman’s rank-order correlation was used. There was a moderate positive relationship between perceived teacher support and satisfaction, rs(98) = .38, p < .001.
When you report several correlations, use a correlation matrix table with means and standard deviations in the first columns and the coefficients below the diagonal, with a note explaining the significance markers.
Moving beyond correlation
If you want to predict one variable from another, or control for other variables, use linear regression. For two categorical variables, neither Pearson nor Spearman is appropriate; use the chi-square test with Cramér’s V instead.
Quick decision rules
- Both variables continuous, linear pattern, no extreme outliers → Pearson.
- Any variable ordinal → Spearman.
- Monotonic but curved pattern, strong skew or outliers → Spearman.
- Pattern not monotonic (for example U-shaped) → neither; consider other models.
- Both categorical → chi-square test.
Reporting the choice in your methodology
Examiners want to see that the choice of coefficient was deliberate. A single sentence in the analysis plan is usually enough, for example: ‘Pearson correlations were used to examine relationships between the composite scale scores, which were approximately normally distributed; Spearman’s rank-order correlation was used for single-item ordinal measures.’ If normality checks led you to switch from Pearson to Spearman for some variables, say so in the results chapter and give the reason, such as strong skewness. Reporting both coefficients for the same pair of variables is rarely necessary, but it can be helpful in an appendix when outliers are a concern and the two values differ noticeably.
Sample size for correlations
Correlations estimated from small samples are unstable and have wide confidence intervals. To detect a medium correlation (r = .30) with α = .05 and power = .80, about 84 participants are needed; smaller correlations require larger samples. See sample size for a thesis for how to plan this.
Roman Urdu mein khulasa
Pearson correlation do continuous variables ke seedhe (linear) rishte ko napta hai aur asal values istemal karta hai, is liye outliers se bohat mutasir hota hai. Spearman correlation values ko ranks mein badal kar monotonic rishta napta hai, is liye ordinal data (jaise aik Likert item), skewed data ya outliers ke liye behtar hai. Akele Likert item ke liye Spearman, aur kai items ke total ya mean score ke liye aam tor par Pearson istemal hota hai. Pehle scatter plot zaroor dekhein. APA mein r(48) = .62, p < .001 ki tarah likhein.
Frequently asked questions
What is the main difference between Pearson and Spearman?
Pearson measures linear relationships using raw values; Spearman measures monotonic relationships using ranks, which makes it suitable for ordinal data and robust to outliers.
Should I use Pearson or Spearman for Likert data?
Use Spearman for single Likert items. For composite scale scores (sums or means of several items), Pearson is widely used unless the scores are strongly skewed.
Can Pearson and Spearman give different results?
Yes. Large differences usually point to outliers, skewness or a curved relationship. Check the scatter plot.
What is a strong correlation?
By Cohen’s (1988) conventions, about .10 is small, .30 medium and .50 large. Other frameworks use different labels, so cite the one you use.
How do I report Spearman’s correlation in APA?
Write r_s(df) = value, p = value, for example r_s(98) = .38, p < .001, where df = N − 2.
Related calculators
- Pearson Correlation Calculator
- Spearman Rank Correlation Calculator
- Linear Regression Calculator (Simple & Multiple)
- Test chooser: which statistical test should I use?
References
- American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). https://doi.org/10.1037/0000165-000
- Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
- Hauke, J., & Kossowski, T. (2011). Comparison of values of Pearson’s and Spearman’s correlation coefficients on the same sets of data. Quaestiones Geographicae, 30(2), 87–93. https://doi.org/10.2478/v10117-011-0021-1
- Schober, P., Boer, C., & Schwarte, L. A. (2018). Correlation coefficients: Appropriate use and interpretation. Anesthesia & Analgesia, 126(5), 1763–1768. https://doi.org/10.1213/ANE.0000000000002864
Written and maintained by the ScholarCalc team. Last reviewed: November 2026.