Range Restriction, explained.
Range restriction limits variation in a measured variable through selection and can alter an observed association within the selected sample.
Why it happens
A bivariate Normal teaching population has generating correlation 0.7. The reader retains observations with absolute x below a chosen bound and compares sample correlations before and after restriction.
Range restriction limits variation in a measured variable through selection and can alter an observed association within the selected sample.
Read the result
The same generated points remain in the background. Only the selected x range changes; population correlation and finite-sample correlation are separate quantities.
A worked example
Select a narrow band without changing the process
Begin with a broad absolute-x bound to retain most of the synthetic population.
Narrow the bound and compare the restricted sample size and correlation with the full sample.
Treat the change as conditional on this selection rule and finite sample rather than a universal correction factor.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
A bivariate Normal teaching population has generating correlation 0.7. The reader retains observations with absolute x below a chosen bound and compares sample correlations before and after restriction.
Where this idea is useful
A practical use
Interpret a correlation among selected applicants in light of the range excluded by admission.
A common misconception
“A lower selected-sample correlation proves the original relationship weakened.”
Selection can reduce variable range and alter the observed association while leaving the generating mechanism unchanged.
What this explanation leaves out
- Finite samples fluctuate and selection rules differ. The display is not a universal correction formula, causal claim or estimate of an actual admissions process.
Why is the displayed full correlation not exactly 0.7?
The generator uses population correlation 0.7, but two hundred realised observations have their own fluctuating sample correlation.
Which part of the predictor’s range was excluded before your relationship was measured?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.