Goodman-Kruskal λ — nominal PRE association
Coming soonAdvanced & specialized
This test is implemented and is currently going through StatMinds’ production verification: every statistic is independently checked against a trusted reference (scipy / R), locked with regression tests, and the screen is exercised across assumption-met/violated and significant/non-significant scenarios before it opens up.
See what’s live nowProportional Reduction in Error (PRE) measure for two NOMINAL variables.
λ asks: 'How much does knowing X reduce the error in predicting the MODAL category of Y (and vice versa)?' Reports λ(Y|X), λ(X|Y), and the symmetric λ. Range [0, 1]. Unlike γ / τ, λ is not ordinal — order doesn't matter — but it has the well-known limitation that λ can equal 0 even when the variables are clearly associated, if the modal category of one variable is the same across all levels of the other.
Worked example
How much does one nominal variable predict another?
Lambda is a proportional-reduction-in-error measure — how much knowing one categorical variable improves prediction of another.
Knowing the predictor cut prediction error by 27% (λ = .27).
Goodman-Kruskal lambda showed a 27% proportional reduction in error (λ = .27).
When to use it
- Modal-category predictability between nominal variablesA retailer cross-tabulates store region (4 nominal regions) against most-purchased product category (5 nominal categories) for 2000 customers.
- Asymmetric prediction with explicit directionAn HR researcher cross-tabulates department (4 nominal departments) against attrition reason (5 nominal categories) for departed employees.
When NOT to — use instead
- Two ordinal variables (rank meaningful)λ ignores order entirely — use γ, τ, or Somers' d for ordinal data. → Goodman-Kruskal's \u03b3 (ordinal, ignores ties)
- Need a significance test on the associationλ is descriptive only; pair it with χ² (or G-test) for the inferential null. → Chi-Square Test of Independence
- Continuous outcome with nominal predictorWhen Y is continuous use ANOVA / Kruskal-Wallis, not a nominal-association measure. → One-Way ANOVA (3+ groups)
- Need a multivariable predictive model
Hypotheses
Parameter tested: λ
Assumptions (and what to do if they fail)
Check: min row/col total.
If violated: Empty levels make lambda undefined.
Ready to run a Goodman-Kruskal λ — nominal PRE association on your own data?
Guided setup, automatic assumption checks, effect sizes, figures and an APA write-up.
Run this test →