Using Spearman’s Rank Correlation for Data Analysis: A Practical Guide for Researchers

Introduction

Spearman’s rank correlation is a widely used non-parametric statistical technique for examining the relationship between two variables. It is particularly useful when data are measured on an ordinal scale, when variables are not normally distributed, or when the relationship between variables is expected to be monotonic rather than strictly linear.

In academic research, Spearman’s rank correlation can be used in business, economics, agriculture, education, public health, social sciences and development studies.

For example, a researcher may want to determine whether:

• access to credit is associated with business performance;
• education level is associated with household income;
• employee training is associated with productivity;
• market access is associated with farm income;
• customer satisfaction is associated with customer loyalty;
• service quality is associated with customer satisfaction.

The technique can be performed using SPSS, Stata, R and Python.

1. What Is Spearman’s Rank Correlation?

Spearman’s rank correlation coefficient, commonly represented by ρ (rho) or rₛ, measures the strength and direction of the monotonic association between two variables based on their ranks.

Unlike Pearson’s correlation, Spearman’s correlation does not require the variables to be normally distributed.

A useful way to understand it is that the observations are converted into ranks, and the correlation between those ranks is then assessed.

For example, if respondents who have higher levels of access to credit generally also report higher levels of business performance, Spearman’s correlation would tend to be positive.

2. Understanding the Spearman Correlation Coefficient

The Spearman coefficient ranges from:

−1 to +1

Positive correlation

A coefficient greater than zero indicates a positive association.

For example:

rₛ = 0.72

This indicates that higher values of one variable tend to be associated with higher values of the other variable.

Negative correlation

A coefficient below zero indicates a negative association.

For example:

rₛ = −0.65

This indicates that higher values of one variable tend to be associated with lower values of the other.

Little or no association

A coefficient close to zero indicates little evidence of a monotonic association.

For example:

rₛ = 0.04

3. Interpreting the Strength of Spearman’s Correlation

There is no single universally accepted classification system for correlation strength. Researchers should therefore identify the interpretation guideline they are using.

A commonly used descriptive guide is:

These categories should be treated as descriptive conventions, not universal statistical rules.

The sign indicates direction, while the absolute magnitude indicates strength.

For example:

rₛ = −0.71

represents a strong negative association under this classification.

4. Example of Spearman Correlation in Research

Suppose a researcher is studying:

The relationship between access to credit and SME performance.

The researcher collects data from 100 businesses.

The variables are:

Variable 1: Access to credit

Variable 2: SME performance

Suppose the analysis produces:

rₛ = 0.64, p < 0.001

The result indicates a positive association between access to credit and SME performance.

The p-value indicates that the observed association is statistically significant at conventional significance levels.

A suitable interpretation would be:

The findings indicate a statistically significant positive association between access to credit and SME performance (rₛ = 0.64, p < .001). This suggests that businesses reporting higher levels of access to credit also tended to report higher levels of performance.

5. Why Use Spearman’s Rank Correlation?

Spearman’s correlation is particularly useful when:

5.1 Data are ordinal

For example, respondents may rate satisfaction as:

1. Very dissatisfied
2. Dissatisfied
3. Neutral
4. Satisfied
5. Very satisfied

Such data are naturally ranked.

5.2 Data are not normally distributed

Spearman’s correlation does not require the same normality assumption as Pearson’s correlation.

5.3 There are outliers

Because Spearman’s method works with ranks rather than the original numerical values, it can be less sensitive to extreme values than Pearson’s correlation.

However, extreme observations can still affect the analysis, particularly if they alter the ordering of observations.

5.4 The relationship is monotonic

The relationship does not have to form a straight line.

A monotonic relationship means that as one variable increases, the other generally tends to increase or decrease, even if the rate of change is not constant.

6. Spearman Correlation Versus Pearson Correlation

The choice should depend on the characteristics of the data and the research question rather than simply choosing Spearman because it produces a more convenient result.

7. How to Conduct Spearman Correlation in SPSS

SPSS makes Spearman correlation relatively easy to perform.

Step 1: Enter the data

Each respondent should occupy one row.

For example:

Step 2: Open the correlation procedure

Go to:

Analyze → Correlate → Bivariate

Step 3: Select variables

Move the variables you want to examine into the Variables box.

For example:

• Access to credit
• Business performance

Step 4: Select Spearman

Under Correlation Coefficients, select:

Spearman

You can deselect Pearson if you only require Spearman’s correlation.

Step 5: Select the significance test

Usually select:

Two-tailed

unless you have a justified directional hypothesis and an appropriate pre-specified testing strategy.

Step 6: Click OK

SPSS will generate a correlation table.

8. Understanding the SPSS Output

A typical output might look like:

The important information is:

Spearman correlation coefficient

rₛ = 0.640

This indicates a positive association.

Significance

p < .001

This indicates strong statistical evidence against the null hypothesis of no association.

Sample size

N = 100

The correlation was calculated using 100 observations.

The asterisks in SPSS indicate the significance level according to the software’s convention. The exact p-value should be reported where available.

9. How to Interpret a Spearman Correlation

Suppose the results are:

rₛ = 0.58, p = 0.002, N = 100

A suitable interpretation is:

Spearman’s rank correlation analysis revealed a statistically significant positive association between access to credit and SME performance (rₛ = 0.58, p = 0.002). This indicates that businesses with higher reported levels of access to credit tended to report higher levels of business performance.

The interpretation should not automatically say:

“Access to credit causes business performance to increase.”

Correlation by itself does not establish causality.

10. Testing a Research Hypothesis

Suppose the researcher develops the following hypotheses:

H₀: There is no significant relationship between access to credit and SME performance.

H₁: There is a significant relationship between access to credit and SME performance.

If:

p < 0.05

the researcher rejects the null hypothesis at the 5% significance level.

If:

p > 0.05

the researcher does not reject the null hypothesis at the 5% significance level.

It is preferable to say “fail to reject the null hypothesis” rather than “accept the null hypothesis.”

11. Using Spearman Correlation for Likert-Scale Da