Pearson vs Spearman: The Short Answer
| Your situation involves... | Consider... |
|---|---|
| Quantitative variables, approximately linear relationship | Pearson |
| Ordinal or ranked variables | Spearman |
| Monotonic but clearly nonlinear relationship | Spearman |
| Influential outliers in raw values | Investigate; Spearman may be more appropriate |
| Clearly curved, non-monotonic relationship | Neither may summarize it well |
| Non-normal data distribution | Do not automatically switch to Spearman — inspect the relationship first |
| Individual Likert-type ordinal items | Often Spearman, but context matters |
| Composite scale scores treated as approximately continuous | Pearson may be reasonable depending on context |
Do not choose between Pearson and Spearman based on normality alone. First consider the measurement scale, the shape of the relationship in a scatterplot, independence, influential observations, and the purpose of the analysis. Non-normal data does not automatically require Spearman.
What Is Pearson Correlation?
Pearson's correlation coefficient, written r, measures the strength and direction of the linear association between two quantitative variables. It was formalized by Karl Pearson in the late 19th century and remains the most widely used correlation measure for continuous data. A full treatment is available on the main Pearson correlation page.
Pearson works by examining whether deviations from the mean in one variable tend to accompany deviations from the mean in the other variable, in the same direction or opposite directions. When both variables tend to be above their means together, and below their means together, r is positive. When one tends to be above while the other is below, r is negative. When there is no consistent pattern, r falls near zero.
- Symbol: r (also written rxy or rP)
- Range: -1 to +1
- Measures: Strength and direction of a linear association
- Data type: Quantitative (continuous or interval-scale) measurements
- Relationship required: Approximately linear
- Uses raw values: Yes — the actual numerical values, not ranks
- Sensitive to: Influential outliers, which can substantially change r
- Parametric: Yes, in the usual inferential sense
What Is Spearman Correlation?
Spearman's rank correlation coefficient, written rₛ or ρ (the Greek letter rho), measures the strength and direction of a monotonic association between two variables. It was developed by Charles Spearman in 1904. The method converts observations to ranks and then computes what amounts to the Pearson correlation between those ranks.
Spearman captures whether, as X increases, Y consistently tends to increase (or consistently decrease), regardless of whether the rate of change is constant. A monotonic relationship does not have to be linear. Spearman can detect a strong association even when the relationship curves, as long as the ordering is consistent.
- Symbol: rₛ or ρ (rho)
- Range: -1 to +1
- Measures: Strength and direction of a monotonic (rank-based) association
- Data type: Ordinal, ranked, or quantitative data
- Relationship required: Monotonic (consistently increasing or decreasing)
- Uses ranks: Yes — converts values to ranks before computing the correlation
- Less sensitive to: Extreme numerical values (though not immune to all influential patterns)
- Nonparametric: Yes, in the rank-based sense — but it still has assumptions
Pearson vs Spearman: Full Comparison
| Feature | Pearson (r) | Spearman (rₛ) |
|---|---|---|
| Common notation | r | rₛ or ρ |
| What it measures | Linear association | Monotonic rank association |
| Works on | Raw values | Ranks of values |
| Data type | Quantitative measurements | Ordinal, ranked, or quantitative |
| Relationship shape | Linear | Monotonic (need not be linear) |
| Range | -1 to +1 | -1 to +1 |
| Outlier sensitivity | Higher | Generally lower; not immune |
| Normality requirement | Relevant to some inference procedures, not a simple raw-variable requirement | Not required |
| Handles ordinal data | Not the first choice | Yes |
| Nonlinear monotonic relationships | May underestimate association strength | Can capture monotonic association |
| Parametric / nonparametric | Parametric in common inferential use | Nonparametric (rank-based) |
| Tied values | Not applicable as a rank issue | Require average-rank treatment |
| Interpretation | Direction and strength of linear association | Direction and strength of monotonic association |
Pearson or Spearman? Interactive Decision Guide
Answer four questions about your data and research context. The tool recommends a starting point and explains the reasoning. Use this alongside visual inspection of your data, not instead of it.
Decision Guide: Pearson or Spearman?
Formulas: How Pearson and Spearman Are Calculated
Pearson Correlation Formula
xᵢ individual X value
yᵢ individual Y value
x̄ mean of X
ȳ mean of Y
n number of paired observations
What Pearson is doing at each step: it centers X around its mean and Y around its mean. For each observation pair, it multiplies the two centered values together. When both deviations are positive (both above average) or both negative (both below average), the product is positive. When they go in opposite directions, the product is negative. Summing these products gives the covariance, and dividing by the product of the standard deviations scales the result so it always falls between -1 and +1.
Spearman Correlation Formula
The cleanest way to understand Spearman is that it is simply the Pearson correlation applied to the ranks of the data rather than the raw values. If you rank your X values from 1 to n and your Y values from 1 to n, then compute Pearson on those ranks, you get Spearman.
For data with no tied ranks, a convenient shortcut formula exists:
dᵢ rank of xᵢ minus rank of yᵢ
n number of paired observations
The shortcut formula above is only valid when there are no ties. When two or more observations share the same value, assign each observation the average of the ranks they would have occupied. Then compute Spearman as the Pearson correlation between the two columns of average ranks. Using the shortcut formula with tied data gives incorrect results.
Worked Examples
Example 1: Pearson Correlation (Study Hours and Exam Score)
Six students: study hours (X) and exam score (Y). Are they linearly related?
| Student | X (hours) | Y (score) | xᵢ−x̄ | yᵢ−ȳ | (xᵢ−x̄)(yᵢ−ȳ) | (xᵢ−x̄)² | (yᵢ−ȳ)² |
|---|---|---|---|---|---|---|---|
| A | 2 | 58 | -2.5 | -12.33 | 30.83 | 6.25 | 152.03 |
| B | 3 | 63 | -1.5 | -7.33 | 11.00 | 2.25 | 53.73 |
| C | 4 | 67 | -0.5 | -3.33 | 1.67 | 0.25 | 11.09 |
| D | 5 | 74 | 0.5 | 3.67 | 1.84 | 0.25 | 13.47 |
| E | 6 | 78 | 1.5 | 7.67 | 11.51 | 2.25 | 58.83 |
| F | 7 | 84 | 2.5 | 13.67 | 34.18 | 6.25 | 186.87 |
| Mean | 4.5 | 70.67 | Σ = 91.03 | Σ = 17.50 | Σ = 476.02 |
Numerator (covariance term): Σ(xᵢ−x̄)(yᵢ−ȳ) = 91.03
Denominator: √(17.50 × 476.02) = √8330.35 = 91.27
Pearson r: 91.03 / 91.27 = 0.997
r = 0.997. There is a very strong positive linear association between study hours and exam score in this sample. Each additional hour of study corresponds closely with a higher score.
Example 2: Spearman Correlation (Service Quality Ranking)
Five customers rate service quality (1-5 ordinal scale) and overall satisfaction (1-7 ordinal scale). No ties.
| Customer | Quality rating (X) | Satisfaction (Y) | Rank X | Rank Y | dᵢ (Rank X minus Rank Y) | dᵢ² |
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 1 | 1 | 0 | 0 |
| 2 | 3 | 4 | 2 | 2 | 0 | 0 |
| 3 | 4 | 5 | 3 | 3 | 0 | 0 |
| 4 | 5 | 6 | 4 | 4 | 0 | 0 |
| 5 | 5 | 7 | 5 | 5 | 0 | 0 |
| Σd² | 0 | |||||
Apply the formula: rₛ = 1 − (6 × 0) / (5 × (25 − 1)) = 1 − 0/120 = 1.00
rₛ = 1.00. The rank ordering is perfectly consistent: every customer who ranks quality higher also ranks satisfaction higher. Spearman captures this perfectly, regardless of whether the underlying scale intervals are equal.
Why Pearson and Spearman Can Give Different Results
This is the most important concept on this page. Consider data where X increases and Y also consistently increases, but Y rises quickly at first and then levels off. The ordering is perfectly consistent (Spearman will be high), but the relationship is not linear (Pearson will be lower).
Hours of practice (X) vs. skill improvement (Y). Fast early gains, slower later gains.
| Observation | X (hours) | Y (improvement) | Rank X | Rank Y | dᵢ | dᵢ² |
|---|---|---|---|---|---|---|
| 1 | 1 | 10 | 1 | 1 | 0 | 0 |
| 2 | 2 | 17 | 2 | 2 | 0 | 0 |
| 3 | 4 | 22 | 3 | 3 | 0 | 0 |
| 4 | 8 | 25 | 4 | 4 | 0 | 0 |
| 5 | 16 | 27 | 5 | 5 | 0 | 0 |
Spearman rₛ = 1.00. Every rank increase in X matches a rank increase in Y. The ordering is perfectly monotonic.
Pearson r ≈ 0.85. The relationship is not straight-line; Y increases rapidly at first and then flattens. Pearson penalizes the deviation from linearity, so it comes out lower even though the pattern is strong.
Neither result is "wrong." They measure different things. Spearman says: the ordering is perfectly consistent. Pearson says: the straight-line fit is good but not perfect. The right choice depends on which question matters for your research.
What If the Relationship Is Non-Monotonic?
Both Pearson and Spearman can fail when the relationship is not monotonic. A U-shaped relationship, for instance, means Y first decreases as X increases and then increases again. Neither coefficient captures this well.
Do not switch from Pearson to Spearman just because Pearson gives a low correlation. Low Pearson alone does not mean you need Spearman. If the relationship is U-shaped or otherwise non-monotonic, Spearman will also give a low coefficient. The correct step is to inspect a scatterplot first.
If you plot your variables and see a clear U-shape, inverted U-shape, or other curve that reverses direction, neither Pearson nor Spearman will adequately summarize the association as a single number. You may need a different analytical approach entirely, such as polynomial regression or a visual description of the pattern.
How Outliers Affect Pearson and Spearman
Pearson's coefficient is computed on raw values. One extreme observation can have a disproportionate influence because its deviation from the mean is large and gets squared in the denominator. Spearman converts values to ranks, so an outlier that was ranked 7th is still ranked 7th whether its raw value was 100 or 10,000. The rank-transformation limits the effect of extreme numerical magnitude.
Monthly income (X) and life satisfaction score (Y), n = 6. One income value is extreme.
| Person | Income ($) | Satisfaction (1-10) |
|---|---|---|
| 1 | 30,000 | 5 |
| 2 | 40,000 | 6 |
| 3 | 50,000 | 6 |
| 4 | 60,000 | 7 |
| 5 | 70,000 | 8 |
| 6 (outlier) | 500,000 | 7 |
Without person 6 (n=5): Pearson r ≈ 0.97. A strong positive linear relationship.
With person 6 (n=6): Pearson r drops to approximately 0.52. The extreme income value distorts the linear fit substantially.
Spearman with person 6 (n=6): rₛ ≈ 0.77. Because person 6 is ranked 6th on income regardless of the exact dollar amount, the rank-based coefficient is much less affected.
The outlier illustrates why the choice of coefficient matters. But note: Spearman being more stable here does not mean you should automatically delete the outlier or ignore it when using Pearson. First check whether it is a data-entry error, a legitimate extreme case, or a genuinely influential observation that changes the scientific interpretation. A sensitivity analysis showing results with and without the influential observation is often the most transparent approach.
Linear vs Monotonic Relationships
Understanding what "linear" and "monotonic" mean in practice is the foundation for choosing between these two methods.
A linear relationship means that a unit increase in X is associated with a constant change in Y throughout the range. Plotted, the points cluster around a straight line. Pearson is designed for this.
A monotonic relationship means that as X increases, Y consistently moves in one direction, but the rate of change does not have to be constant. The curve can bend. Spearman is designed for this. Importantly, every positive-slope linear relationship is also monotonic, but not every monotonic relationship is linear.
Interactive Pearson vs Spearman Calculator
Enter paired X and Y values separated by commas, spaces, or line breaks. The calculator computes both Pearson and Spearman coefficients and explains what the difference means.
Pearson & Spearman Correlation Calculator
Decision Framework
Choosing Between Pearson and Spearman
Assumptions: What Each Method Requires
Spearman is often called "assumption-free," but that description is misleading. Both methods have conditions that should be met for the results to be meaningful and for inference to be valid.
| Consideration | Pearson | Spearman |
|---|---|---|
| Independent observations | Required | Required |
| Quantitative data | Expected | Not strictly required |
| Ordinal data | Not preferred | Appropriate |
| Linear relationship | Important | Not required |
| Monotonic relationship | Not sufficient alone | Important |
| Normality of raw variables | Relevant to some inference; not a simple raw-variable requirement | Not required |
| No influential outliers | Important to check | Less sensitive; still worth checking |
| Tied values | N/A as a rank issue | Must use average ranks when ties exist |
A Note on Normality and Pearson
A common teaching point is that Pearson "requires" normally distributed variables. The more precise version: Pearson's coefficient as a descriptive statistic can be computed from any data. Normality becomes relevant when you want to use certain classical inferential procedures, such as using the t-distribution to test whether the population correlation equals zero. The joint bivariate normal distribution is a theoretical condition under which those tests are exact. With large samples, inference is often reasonably robust to moderate departures from normality. What matters more in practice is whether the relationship is approximately linear, whether observations are truly independent, and whether influential observations are present. Inspect the scatterplot before relying on normality alone as a guide.
Does Spearman Require Normal Data?
No. Spearman does not require normally distributed raw variables. That is one reason it is classified as a nonparametric method. However, Spearman still requires:
- Independent paired observations
- A meaningful ranking (the scale must allow ordering)
- A reasonably monotonic relationship if you want the coefficient to be interpretable as a summary of association
- Appropriate handling of tied ranks
Non-normality alone is not a reason to choose Spearman. The shape of the relationship, the measurement scale, and independence all matter more than the marginal distribution of each variable.
Pearson or Spearman for Likert Scale Data?
This question comes up constantly in social science and psychology research, and the honest answer is: it depends on what you are measuring.
Individual Likert-type ordinal items
A single question with responses like 1=Strongly Disagree, 2=Disagree, 3=Neutral, 4=Agree, 5=Strongly Agree is an ordinal variable. The intervals between points are not guaranteed to be equal. For a pair of such individual items, Spearman is generally a natural choice because the data is inherently ranked.
Composite scale scores
When you sum or average multiple Likert-type items into a scale score (for instance, a 20-item anxiety inventory summed to a score of 20 to 100), researchers often treat the resulting score as approximately continuous. In this context, Pearson may be reasonable, depending on the number of response categories, the distribution of the composite, the sample size, and the measurement framework. This is a decision that should be grounded in the research context, not a mechanical rule.
Do not claim that Likert data always requires Spearman or always allows Pearson. Individual ordinal items generally suit Spearman. Composite scale scores are a judgment call based on measurement assumptions, number of categories, sample size, and research context. If in doubt, reporting both coefficients is a transparent and defensible approach.
Can Spearman Be Used for Continuous Data?
Yes. Spearman can be applied to quantitative continuous data whenever the research question concerns the monotonic ordering of observations rather than the precise linear relationship. Consider income and reported stress: the relationship is probably positive and monotonic (higher income tends to associate with lower stress, or vice versa depending on the job), but the income scale is highly skewed and the relationship may not be linear. In this case, Spearman's rank-based approach may better reflect the research question.
Using Spearman on continuous data is a legitimate analytical choice, not a fallback for when assumptions are violated. The question is whether the rank-based summary of association is what you want to know.
Statistical Significance and P-Values
Both Pearson and Spearman can be tested for statistical significance. The null hypothesis is typically that the population correlation equals zero: H₀: ρ = 0 (for Pearson) or H₀: ρₛ = 0 (for Spearman). A p-value answers: assuming no association exists in the population, how likely is it to observe a coefficient as large as the one you got from your sample?
A statistically significant p-value does not tell you whether the correlation is practically meaningful. With a large sample (n = 1,000), a correlation of 0.07 can be statistically significant while being practically trivial. Always report the coefficient alongside the p-value. See the full explanation on the p-values page.
Pearson and Spearman can produce different p-values from the same data because they use different test statistics and are sensitive to different aspects of the relationship. If Pearson is significant but Spearman is not, this may indicate that the Pearson result is driven by influential outliers or a linear trend that the rank-based Spearman is not capturing. If Spearman is significant but Pearson is not, this may indicate a monotonic but nonlinear relationship or data where ranks are more informative than raw values.
Confidence Intervals
Confidence intervals for Pearson's r are commonly constructed using the Fisher z-transformation. The procedure transforms r to an approximately normally distributed statistic z, constructs an interval on the z scale, then transforms back. This approach works well for moderate to large samples. For Spearman, exact confidence intervals are more complex; one approach uses the same Fisher z-transformation applied to rₛ as an approximation, acknowledging that this is less exact than for Pearson.
Confidence intervals are more informative than p-values alone. They show not just whether the correlation is compatible with zero, but also the range of plausible population correlation values given the sample. A wide interval in a small sample tells you there is considerable uncertainty even when the point estimate looks strong. The confidence intervals section of this site covers the general framework in more detail.
Pearson vs Spearman vs Kendall's Tau
Kendall's tau (τ) is a third rank-based correlation measure. It counts the number of concordant pairs (where both X and Y rank in the same direction) minus the number of discordant pairs, divided by the total possible pairs. Like Spearman, it is nonparametric and appropriate for ordinal or ranked data. It tends to be more interpretable as a probability statement and can be more robust with small samples or many tied ranks.
| Feature | Pearson | Spearman | Kendall's τ |
|---|---|---|---|
| Based on | Raw values | Ranks | Concordant/discordant pairs |
| Measures | Linear association | Monotonic rank association | Monotonic rank association |
| Ordinal data | Not preferred | Yes | Yes |
| Range | -1 to +1 | -1 to +1 | -1 to +1 |
| Tied values | N/A as rank issue | Average ranks | Tie-adjusted formulas |
| Typical magnitude | r | rₛ ≈ 1.5 τ (roughly) | τ tends to be smaller |
| Best for | Quantitative linear | Ranked / monotonic | Small samples, many ties, probability interpretation |
Software: R, Python, Excel, and SPSS
Compute and test both correlations in R with a single function call:
x <- c(2, 4, 6, 8, 10)
y <- c(3, 5, 7, 9, 11)
# Pearson correlation coefficient
cor(x, y, method = "pearson")
# Spearman correlation coefficient
cor(x, y, method = "spearman")
# Pearson with hypothesis test and p-value
cor.test(x, y, method = "pearson")
# Spearman with hypothesis test and p-value
cor.test(x, y, method = "spearman")
# Output includes: estimate (rho), S statistic, p-value
The cor.test() output gives the coefficient, test statistic, p-value, and a 95% confidence interval (for Pearson). For Spearman with large samples, R uses an asymptotic normal approximation.
SciPy provides functions for both coefficients:
x = [2, 4, 6, 8, 10]
y = [3, 5, 7, 9, 11]
# Pearson: returns (correlation, p-value)
r, p_pearson = pearsonr(x, y)
print(f"Pearson r = {r:.4f}, p = {p_pearson:.4f}")
# Spearman: returns SpearmanrResult(correlation, pvalue)
result = spearmanr(x, y)
print(f"Spearman rs = {result.statistic:.4f}, p = {result.pvalue:.4f}")
# Handle missing data before calling these functions
# Both require equal-length arrays with no NaN values
If your data contains missing values, use pandas to drop incomplete pairs before passing arrays to pearsonr or spearmanr.
Excel has a built-in formula for Pearson. For Spearman, rank each column first:
=CORREL(A2:A11, B2:B11)
=== Spearman in Excel (two steps) ===
Step 1: Rank each variable (in columns C and D):
=RANK.AVG(A2, $A$2:$A$11, 1) for each cell in column C
=RANK.AVG(B2, $B$2:$B$11, 1) for each cell in column D
Step 2: Pearson on the ranks:
=CORREL(C2:C11, D2:D11)
RANK.AVG assigns average ranks to tied values (correct)
RANK.EQ would give ties the same rank (incorrect for Spearman)
Make sure to use RANK.AVG rather than RANK or RANK.EQ when ties exist. Applying CORREL directly to raw data gives Pearson, not Spearman.
In SPSS, both coefficients are available through the Bivariate Correlations dialog:
Analyze → Correlate → Bivariate
=== In the dialog ===
1. Move your variables into the Variables box
2. Under "Correlation Coefficients", check:
[x] Pearson
[x] Spearman
3. Choose two-tailed or one-tailed test
4. Check "Flag significant correlations"
5. Click OK
=== SPSS Syntax equivalent ===
NONPAR CORR
/VARIABLES = var1 var2
/PRINT = SPEARMAN TWOTAIL SIG.
CORRELATIONS
/VARIABLES = var1 var2
/PRINT = TWOTAIL SIG.
SPSS outputs a correlation matrix with the coefficient, sample size, and p-value for each pair. Pearson is under Correlations; Spearman is under Nonparametric Correlations.
How to Report Results
Good reporting includes the coefficient, the sample size, and the p-value. For publications following APA style:
Pearson correlation example report
A Pearson correlation indicated a strong positive linear relationship between study hours and exam score, r(4) = 0.997, p < .001 (two-tailed). Students who studied more hours tended to score higher on the exam.
Spearman correlation example report
A Spearman rank-order correlation indicated a significant positive monotonic association between service quality rating and customer satisfaction, rs(3) = 1.00, p < .001 (two-tailed).
Note: The degrees of freedom in parentheses is n minus 2. Include whether the test was one-tailed or two-tailed. Prefer reporting actual p-values over inequality statements where possible.
Common Pearson vs Spearman Mistakes
Practice Questions
Spearman is the natural starting choice. Both variables are ordinal, meaning the categories have a meaningful order but the intervals between points are not guaranteed to be equal. Spearman treats the data as ranked, which matches the ordinal measurement scale well.
If the pattern is consistently increasing (monotonic), Spearman may be more informative than Pearson. The curved pattern means Pearson will underestimate the strength of the association because it is penalizing for the non-linearity. Spearman will capture the fact that higher X values consistently pair with higher Y values, regardless of the shape. Investigate whether the curvature is monotonic (always going in one direction) to confirm Spearman is appropriate.
No, and this is a critical point. A U-shaped relationship is non-monotonic. As X increases, Y first decreases and then increases. Spearman captures monotonic relationships. For a U-shaped pattern, Spearman will also give a value near zero, just like Pearson. The correct response is to acknowledge that neither coefficient summarizes this relationship as a single number. Other approaches, such as polynomial regression or a visual description of the curve, may be more appropriate.
First, check whether the observation is a data-entry error (e.g., a mistyped value). If it is a legitimate extreme case, examine what it means scientifically. Does it belong to a different subpopulation? Does it reflect a real boundary condition? Run a sensitivity analysis showing results with and without the observation. Consider whether Spearman is more appropriate for this research question, since it would be less affected by the numerical magnitude of the extreme value. Never remove an outlier purely to produce a larger correlation.
Yes. Spearman can be applied to any data that can be meaningfully ranked, including quantitative continuous variables. If the research question is about whether one variable's ranking consistently mirrors another's, Spearman is appropriate regardless of whether the data is ordinal or continuous. Choosing Spearman for continuous data is a methodological choice, not a workaround for assumption violations.
Frequently Asked Questions
Pearson correlation (r) measures the strength and direction of a linear association between quantitative variables, using the raw values. Spearman correlation (rₛ) measures the strength and direction of a monotonic association by converting observations to ranks first. Both range from -1 to +1, but they measure different things: Pearson asks whether a straight line fits well; Spearman asks whether the rank ordering is consistent.
Neither is universally better. Pearson is the right tool when the relationship is approximately linear and the data is quantitative. Spearman is better suited to ordinal data, monotonic nonlinear relationships, or situations where a rank-based summary matches the research question. The choice depends on your data and what you want to know, not on which produces a larger coefficient.
Not in the simple way often stated. Pearson's coefficient as a descriptive statistic can be computed from any data. Normality is relevant to certain classical inferential procedures. More important in practice are whether the relationship is approximately linear, whether observations are independent, and whether influential outliers are present. Do not automatically switch to Spearman just because your variables are not normally distributed.
No. Spearman does not require normally distributed variables. However, it still requires independence, meaningful ordering, and a monotonic relationship to be interpretable as a summary of association.
It depends. For individual Likert-type ordinal items (e.g., a single question rated 1-5), Spearman is often a natural choice because the items are ordinal. For composite scale scores formed by summing multiple items, researchers sometimes treat the result as approximately continuous and use Pearson, depending on the number of categories, distribution, and theoretical justification. There is no universal rule.
A discrepancy between Pearson and Spearman is informative, not an error. Common causes include a monotonic nonlinear relationship (Spearman may be higher), influential outliers affecting Pearson, or ordinal structure where ranks are more meaningful than raw values. When they differ substantially, inspect the scatterplot carefully and consider which summary better matches your research question.
No. Spearman measures monotonic association. A U-shaped relationship reverses direction as X increases, so the rank ordering is not consistent. Both Pearson and Spearman will give a value near zero for a symmetric U-shaped pattern. A scatterplot is the only way to detect this kind of relationship.
Spearman is less sensitive to extreme numerical values because it operates on ranks. An observation that is worth 1,000,000 is still ranked the same as if it were worth 100, as long as it remains the largest value. However, Spearman is not immune to influential observations. An observation that is extreme in its rank position can still have a notable effect.
Both are rank-based nonparametric measures of monotonic association, but they count different things. Spearman computes the Pearson correlation on ranks. Kendall's tau counts concordant pairs minus discordant pairs as a proportion of all possible pairs. Kendall's tau tends to produce smaller values than Spearman for the same data. It can be more interpretable as a probability statement and may be preferred for small samples or data with many ties.
No. Both Pearson and Spearman measure statistical association between variables. A strong correlation does not establish that one variable causes the other. The association may reflect a common cause (confounding), reverse causation, or coincidence. Causal inference requires study designs like randomized controlled trials, not correlation coefficients alone.
Key Takeaways
Use Pearson when...
- Variables are quantitative
- Relationship is approximately linear
- Observations are independent
- No major influential outliers
- Inferential assumptions are reasonable
Use Spearman when...
- Variables are ordinal or ranked
- Relationship is monotonic (not necessarily linear)
- Rank-based summary matches the research question
- Influential outliers in raw values are a concern
Consider alternatives when...
- Relationship is non-monotonic
- Observations are not independent
- Data structure violates both methods' requirements
- Research question requires a different model
Draw a scatterplot of your two variables. The visual pattern tells you more than any rule of thumb. A straight-line cloud points to Pearson. A consistently curving pattern points to Spearman. A curve that changes direction suggests neither coefficient will tell the whole story.
Related Topics
The methods on this page connect to several broader areas of statistics covered in detail across this site:
- Pearson Correlation — Full guide with formula derivation, interpretation, and examples
- Pearson Correlation Examples — Worked problems with full calculations
- Spearman Rank Correlation — Detailed treatment of the Spearman method
- Correlation Calculator — Compute Pearson correlation for any dataset
- Scatter Plots and Correlation — Why visual inspection matters
- Outliers — Identifying and handling extreme observations
- P-Values — Understanding statistical significance
- Confidence Intervals — Constructing intervals for correlation estimates
- Normality Tests — Shapiro-Wilk and other checks
- Simple Linear Regression — When correlation is not enough and you need a predictive model
- Hypothesis Testing — The broader framework for statistical inference