Short Answer
Correlation analysis is a statistical method that summarizes the direction and strength of the relationship between two variables with a coefficient ranging from -1 to +1. If both variables are continuous and normally distributed, parametric Pearson correlation is used; if one of the variables is not normally distributed, if an ordinal scale (Likert, VAS) is used, or if there are outliers, the rank-based non-parametric Spearman correlation is preferred. The coefficient is roughly interpreted as very weak below 0.20, moderate between 0.40 and 0.59, and very strong above 0.80, and it is reported together with the p value. The two most common mistakes are presenting correlation as if it were causation (a high r does not prove that one variable causes the other, there may be a hidden confounder) and failing to draw a scatter plot before the analysis, thereby overlooking different relationship patterns that the same r value can conceal. When many correlations are tested, a multiple comparison correction such as Bonferroni or FDR should be applied.
Serteser Danismanlik is run by a biomedical engineer (BME MSc) with peer-reviewed publications and PROSPERO-registered systematic reviews; it designs and carries out thesis, article, and clinical research statistics, including Pearson and Spearman correlation and coefficient interpretation, in a manner that is publication-ready and defensible before a jury or reviewer, using SPSS, R, and Python.
Is there a relationship between two variables? Does joint space narrow as age increases? Does complication risk increase as BMI rises? Correlation analysis is used to answer questions of this kind. However, saying "I performed a correlation analysis" is not enough. Pearson, Spearman, or Kendall? The correct choice directly affects methodological reliability.
What Is the Correlation Coefficient?
The correlation coefficient (r) summarizes the direction and strength of the linear relationship between two variables with a number ranging from -1 to +1.
r = +1: Perfect positive relationship (as one increases, the other also increases)
r = -1: Perfect negative relationship (as one increases, the other decreases)
r = 0: No relationship
Interpretation thresholds:
| r value | Interpretation |
|---|---|
| 0.00 - 0.19 | Very weak |
| 0.20 - 0.39 | Weak |
| 0.40 - 0.59 | Moderate |
| 0.60 - 0.79 | Strong |
| 0.80 - 1.00 | Very strong |
Pearson or Spearman?
Pearson correlation:
It is a parametric test. It requires both variables to be continuous and normally distributed. It measures a linear relationship.
Use Pearson if:
- Both variables are continuous (uninterrupted numerical)
- Both variables show a normal distribution
- There are no outliers or they are minimal
Spearman correlation:
It is the non-parametric alternative. It is calculated over rank values. It does not require the assumption of a normal distribution.
Use Spearman if:
- One or both of the variables do not show a normal distribution
- An ordinal scale is used (such as Likert or VAS score)
- There are outliers
- The relationship is monotonic but not linear
Correlation Is Not Causation
One of the most common misinterpretations in medical research is confusing correlation with causation.
There is a strong correlation between ice cream sales and drowning deaths. Ice cream does not cause drowning; both increase in hot weather (confounding).
Similar pitfalls exist in clinical research. An r of 0.70 between two variables does not prove that one causes the other. Causation requires a randomized controlled trial or an appropriate observational design.
Partial Correlation
If you want to examine the relationship between two variables while controlling for the effect of a third variable, partial correlation is used.
Example: Examine the relationship between age and joint space while controlling for the effect of BMI.
SPSS: Analyze → Correlate → Partial
Correlation Analysis with SPSS
Pearson:
Spearman:
The output reports the "Correlation Coefficient" (r value) and "Sig. (2-tailed)" (p value).
Scatter Plot: Visual Inspection Is Mandatory
Always draw a scatter plot before correlation analysis. Because:
The same r value can conceal very different relationship shapes. Anscombe's quartet demonstrates this perfectly: four different data sets have the same correlation coefficient while having very different appearances.
In a scatter plot, outliers, clustering, and non-linear relationship patterns become noticeable.
How Many Correlations Can You Perform?
When many correlations are performed, the multiple comparison problem arises. If you test 20 pairs of variables, at least one is expected to come out significant by chance.
Solution: Determine your primary hypothesis in advance. For exploratory analyses, apply a Bonferroni correction or FDR control and explain this in the Methods section.
Request a free consultation for correlation analysis and its interpretation.
Where Do People Get Stuck Most in This Analysis?
- You got r = 0.45 but you do not know how to express in the article that this is a "moderate correlation."
- You cannot decide whether to use Pearson or Spearman, and the normality test is borderline.
- The correlation came out significant but the reviewer says "correlation is not causation," and it is unclear how you should respond.