Correlation coefficient
Descriptive statistics · Method and input reference
Paired observations of equal length. Pearson, Spearman and Kendall correlations; covariance uses n−1. Synthetic example: 120 matched baseline and week-12 blood pressures (mmHg). Row positions identify the same person; responses vary and some worsen.
Open calculator · Compare methods in the decision matrix
When to consider it
- Estimate monotonic association using rank correlation.
- Estimate a linear association between two numeric variables.
- Estimate concordance using Kendall’s tau-b, which accounts for tied ranks.
Assumptions and scope
- Independent paired observations; inspect the relationship for monotonicity and influential points.
- Rank correlation does not establish causation.
- Independent paired observations; inspect linearity, outliers and sampling assumptions for inference.
- Correlation does not establish causation.
- Independent paired observations. Small sample size alone does not determine the right correlation measure.
Shares the correlation calculator.
Required inputs
- Observations — Numeric observations; preserve the row and column structure described above.
- Second sample — Numeric observations; preserve the row and column structure described above.
Review missing values and data coding before running. Sample inputs are synthetic teaching examples.
Implementation
Lifescio validates inputs and formats results; listed functions are the principal calculation routines, not an exhaustive transitive dependency list.
- scipy 1.15.3: scipy.stats.pearsonr, scipy.stats.spearmanr, scipy.stats.kendalltau
These are pinned library versions; saved results record the versions actually used at runtime.