Calculators
Effective Sample Size Calculator
Calculate Kish effective sample size, weighting efficiency and weight-only design effect from unequal observation weights in your browser.
Enter one non-negative weight per observation, separated by spaces, commas or semicolons. Weights are normalized automatically. Use 1–10000 values and at most 200000 characters. Nonzero weights must be between 1e-100 and 1e100; at least one must be positive. Calculation runs locally in your browser.
How Kish effective sample size works
Kish effective sample size is ESS = (Σwᵢ)² / Σwᵢ², or 1 / Σpᵢ² after normalizing weights. Enter one weight per independent observation, not one aggregate weight per class. Equal positive weights give ESS equal to the number of observations; weights 1, 2, 3 give 36/14 ≈ 2.57142857143. Scaling all weights by the same positive constant leaves ESS unchanged. Zero weights are allowed and count in entered n but contribute nothing to ESS. Weighting efficiency is ESS/n; the weight-only design effect is n/ESS. This diagnostic accounts for unequal weights only: clustering, stratification, correlations and outcome-specific precision may require a different design effect. It does not calculate autocorrelation-based MCMC effective sample size. Enter 1–10000 non-negative weights separated by spaces, commas or semicolons, up to 200000 characters. Commas separate values, not thousands. Nonzero weights must be between 1e-100 and 1e100 and at least one must be positive. Scaling and compensated sums reduce overflow and rounding error. Results display up to 12 significant digits. Inputs remain in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is the Kish effective sample size formula?
ESS = (sum of weights) squared divided by the sum of squared weights. For weights 1, 2, 3 it is 36/14, about 2.57142857143.
Do I need normalized weights?
No. Multiplying every weight by the same positive factor does not change the result. Enter one weight for each observation.
What do zero weights mean?
They contribute nothing to effective sample size. They count in the entered observation count used for efficiency and the weight-only design effect. At least one weight must be positive.
Does this measure MCMC effective sample size?
No. This is the Kish unequal-weight diagnostic for independent observations. It does not account for autocorrelation, clustering, stratification or outcome-specific precision.
Are my inputs uploaded?
No. Validation, calculation and copying run locally in your browser.