What Is Spearman Correlation?
Spearman's rank-order correlation coefficient (ρ, or rₛ) measures the strength and direction of the monotonic relationship between two variables using their ranked values rather than their raw scores. Unlike Pearson correlation, which assumes a linear relationship and continuous data, Spearman works with ordinal data and can detect non-linear relationships as long as they're consistently increasing or decreasing. The coefficient ranges from -1.0 (perfect negative monotonic relationship) to +1.0 (perfect positive monotonic relationship), with 0 indicating no monotonic association. It's the go-to correlation method when your data involves ranks, ratings, or doesn't meet Pearson's assumptions.
Why Spearman Correlation Matters
Much of the data in market research is ordinal. Likert scales, satisfaction ratings, preference rankings. Pearson correlation assumes continuous, normally distributed data with a linear relationship. When those assumptions don't hold, Pearson can underestimate or misrepresent the true association. Spearman handles these situations gracefully because it operates on ranks, making it strong to outliers and non-normal distributions.
How Spearman Correlation Works
The Formula
When there are no tied ranks, Spearman's correlation is calculated as:
rₛ = 1 - (6Σdᵢ² / n(n² - 1))
Where:
- dᵢ = the difference between the ranks of corresponding values for each observation
- n = the number of paired observations
- Σdᵢ² = the sum of squared rank differences
When there are tied ranks, a correction factor is applied, or the formula is computed using the Pearson correlation formula on the ranked data (which gives the same result).
Worked Example
You surveyed 8 customers, asking them to rank two attributes of your product on importance (1 = most important):
| Customer | Speed Rank | Reliability Rank | d | d² |
|---|---|---|---|---|
| A | 1 | 2 | -1 | 1 |
| B | 2 | 1 | 1 | 1 |
| C | 3 | 4 | -1 | 1 |
| D | 4 | 3 | 1 | 1 |
| E | 5 | 5 | 0 | 0 |
| F | 6 | 7 | -1 | 1 |
| G | 7 | 6 | 1 | 1 |
| H | 8 | 8 | 0 | 0 |
Σd² = 6
rₛ = 1 - (6 × 6) / (8 × (64 - 1)) rₛ = 1 - 36 / 504 rₛ = 1 - 0.071 rₛ = 0.929
A Spearman correlation of 0.93 indicates a very strong positive monotonic relationship, customers who rank speed as important also tend to rank reliability as important.
Interpreting Spearman Coefficients
The same general guidelines used for Pearson apply:
| rₛ Value | Strength |
|---|---|
| 0.00 - 0.19 | Negligible |
| 0.20 - 0.39 | Weak |
| 0.40 - 0.59 | Moderate |
| 0.60 - 0.79 | Strong |
| 0.80 - 1.00 | Very strong |
These apply to both positive and negative values. A coefficient of -0.75 is just as strong as +0.75, it simply indicates an inverse relationship.
Spearman vs. Pearson
| Pearson (r) | Spearman (rₛ) | |
|---|---|---|
| Data type | Continuous (interval/ratio) | Ordinal or continuous |
| Relationship detected | Linear only | Monotonic (linear or non-linear) |
| Distribution assumption | Bivariate normality | None |
| Sensitivity to outliers | High | Low (ranks compress outliers) |
| Typical use | Measured variables (revenue, time, temperature) | Ratings, rankings, Likert scales |
When both methods are applicable (continuous, normally distributed data with a linear relationship), Pearson and Spearman typically produce similar results. The differences emerge when assumptions are violated.
Example where they diverge: Imagine income correlates with satisfaction, but the relationship is logarithmic (satisfaction increases quickly at low incomes and plateaus at high incomes). Pearson would underestimate the association because the relationship isn't linear. Spearman would capture it because the relationship is still monotonic, as income increases, satisfaction consistently increases, just not at a constant rate.
Handling Tied Ranks
When two or more observations share the same value, they receive the average of the ranks they would have occupied. If two respondents tie for 3rd place, both receive a rank of 3.5 (the average of 3 and 4). Most statistical software handles ties automatically, but heavy ties (common with Likert scales) can reduce the range of possible rₛ values. With many ties, consider whether Kendall's tau might be more appropriate.
When to Use Spearman Correlation
- Analyzing Likert scale data where the intervals between response options aren't guaranteed to be equal
- Working with ranked preferences like brand preference rankings or feature importance rankings
- Data with outliers that would distort Pearson correlation
- Non-linear but monotonic relationships where Pearson would underestimate the association
- Small samples where normality can't be reliably assessed
Common Mistakes to Avoid
- Using Spearman when Pearson is appropriate: if your data is continuous, normally distributed, and linear, Pearson is more powerful (more likely to detect a real relationship); Spearman is slightly less efficient with truly continuous data
- Interpreting Spearman as measuring linear relationships: Spearman measures monotonic association; two variables can have rₛ = 1.0 without the relationship being linear
- Ignoring tied ranks in manual calculations, failing to adjust for ties produces incorrect coefficients, especially when ties are frequent
How Quali-Fi Supports Correlation Analysis
Quali-Fi's reporting automatically selects the appropriate correlation method based on your data type. Spearman for ordinal scales and ranked data, Pearson for continuous measures. The platform displays correlation matrices with significance indicators, making it easy to spot meaningful relationships across survey variables.
Explore correlation analysis in Quali-Fi
Frequently Asked Questions
Can Spearman correlation be used with continuous data?
Yes. Spearman works with any data that can be ranked, including continuous variables. It's just less statistically powerful than Pearson for continuous data that meets Pearson's assumptions. If you're unsure whether assumptions hold, Spearman is the safer choice, you sacrifice a small amount of power but gain robustness.
What's the difference between Spearman and Kendall's tau?
Both are rank-based correlation coefficients, but they use different calculations. Kendall's tau counts concordant and discordant pairs, while Spearman uses rank differences. Kendall's tau tends to produce lower absolute values and has better statistical properties with small samples or many ties. For most market research applications, the choice between them doesn't change your conclusions.
Is Spearman correlation affected by sample size?
The coefficient itself isn't biased by sample size, but its statistical significance is. With a large enough sample, even a weak correlation (rₛ = 0.10) can be statistically significant. Always report both the coefficient (for effect size) and the p-value (for significance), a significant but tiny correlation rarely matters practically.