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Sample Size for Multiple Logistic Regression: Omnibus Model Test

Plan a likelihood-ratio test of whether a prespecified predictor set collectively improves a binary-outcome model over an intercept-only model.

1. Information obtained from previous studies or literature

Enter Cox–Snell R², not Nagelkerke, McFadden, Tjur, or ordinary R².

Help convert reported Nagelkerke R²

Used to verify the attainable Cox–Snell range and provide event-balance warnings.

2. Inputs decided by the researcher for the new study

Exclude the intercept. Count dummy variables, interactions, polynomial terms, and spline basis columns separately.

3. Results

Enter the planning assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A cohort study tests whether age, blood pressure, renal function, troponin status, and treatment group collectively improve prediction of 30-day mortality over an intercept-only logistic model.

Formula and methodological note

The omnibus likelihood-ratio test evaluates H₀: β₁=⋯=βₘ=0. Cox–Snell R² is converted to the likelihood-ratio effect D=−ln(1−R²). For N analysable participants, the noncentrality parameter is λ=ND; the critical value is the upper-alpha central chi-square quantile with m predictor-column degrees of freedom. The smallest integer N attaining the requested noncentral chi-square power is reported.

The analysable sample is rounded up before dropout adjustment. Event and non-event counts are diagnostics only. The method assumes independent observations, a prespecified correctly specified model, credible population inputs, and a sample large enough for likelihood-ratio asymptotics. It is not for one coefficient, incremental blocks, variable selection, prediction-model development, clustered/matched/repeated data, or penalized rare-event models. This tool supports research planning and does not replace statistical consultation.

Technical results

Method references

  1. Cox DR, Snell EJ. The Analysis of Binary Data. 2nd ed. Chapman and Hall; 1989.
  2. Faul F, Erdfelder E, Buchner A, Lang AG. Statistical power analyses using G*Power 3.1. Behavior Research Methods. 2009;41:1149–1160.
  3. Riley RD, et al. Minimum sample size for developing a multivariable prediction model: Part II. Statistics in Medicine. 2019;38:1276–1296.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Omnibus Multiple Logistic Regression (LOG-OM).” Web calculator. NajibMY, 2026. https://najibmy.netlify.app/tools/sample-size/regression/multiple-logistic-regression-omnibus/.