correlation
Let an agent report correlations with their coefficient, sample and method, and never present a correlation as evidence of cause without further grounds.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent report correlations with their coefficient, sample and method, and never present a correlation as evidence of cause without further grounds.
In statistics, a relationship between two variables in which they tend to vary together, and the coefficient that measures the strength and direction of that relationship.
What it is for: Describing association between variables, as a first step in analysis and prediction.
It can be compute it, with Pearson, Spearman or other coefficients; test it, for statistical significance; visualise it, with a scatter plot; misread it as causation, which is the main error.
Distinguishing features
Measures association, not causation
Pearson measures linear association; rank correlations measure monotonic association
Sensitive to outliers and to restricted ranges
Spurious correlations arise from confounders and chance
What it looks like
A scatter of points trending up or down, and a coefficient between -1 and 1.
Physical character
coefficient range: -1 to 1 dimensionless - 0 means no linear association
How it is recognised
A coefficient r or rho between -1 and 1
A scatter plot with a visible trend
Phrases such as "associated with" or "linked to" in reports
Related models
is confused with - the classic error
is a kind of - descriptive statistics
is related to - regression models the relationship
is affected by - a third variable can produce the association
In practice
Families and kinds
Pearson product-moment correlation
Spearman and Kendall rank correlations
partial and autocorrelation
correlation matrices
Standards and regulation
ISO 3534-1 statistics vocabulary
Reporting guidelines such as STROBE for observational studies
Failure modes and hazards
Inferring causation from correlation
Outliers producing or hiding a correlation
Multiple comparisons producing chance correlations
Ecological fallacy when group correlations are applied to individuals
Also called
+41
Where this came from
wikidata · CC0 1.0
Also registered as vr.tr.correlation
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Measure Which coefficient and what it means.
Different coefficients answer different questions.
Coefficient
Pearson, Spearman, Kendall.
Coefficient used
The coefficient and its value.
- Which coefficient was used, and what is its value? measurement
- Is the relationship linear, or only monotonic? definition
Uncertainty
Confidence interval and significance.
Uncertainty
Interval, p-value and sample size.
- What is the confidence interval and sample size? measurement
- How many comparisons were made? measurement
Data What was measured, on whom.
Correlations are only as good as the data behind them.
Sample
Population and selection.
Sample description
The sample and how it was chosen.
- Which population does the sample represent? provenance
- Could selection have created the association? boundary
Data quality
Outliers and range.
Data checks
Checks for outliers and range restriction.
- Are there outliers driving the result? measurement
- Is the range of either variable restricted? boundary
Interpretation What can be concluded.
The limit of correlation is the main thing to communicate.
Causation
Whether cause is supported.
Causal evidence
Evidence beyond the correlation.
- What evidence beyond correlation supports a causal claim? provenance
- Which confounders were considered? boundary
Level
Group or individual.
Level of inference
Whether conclusions apply to individuals.
- Does the correlation apply to individuals or only to groups? boundary
- How should that be stated? action
Reporting How to communicate it.
Language about correlation is often stronger than the evidence.
Wording
Associated with vs causes.
Wording used
The wording and its strength.
- Does the wording match the strength of evidence? boundary
- What wording should an agent use? action
Replication
Has it been found again.
Replication status
Other studies finding the same.
- Has this correlation been replicated? provenance
- Were there failed replications? provenance
What the second pass must settle
- Should each correlation coefficient be a separate entry?
- How should agents phrase findings based only on correlation?
- The registry entry has merged aliases such as risk factor and virulence factor; should they be split off?