Effective Sample Size Calculator
Compute weight-based effective sample size, normalized weights and the largest normalized weight.
Open toolDesign Effect Calculator
Calculate equal-cluster design effect, effective sample size and sample-size enlargement. Provide Equal cluster size m, Intracluster correlation ρ, Supplied sample size / SRS target to compute results directly in your browser. DEFF = 1+(m−1)ρ and must be positive. Effective n = nominal n/DEFF; enlarged target = supplied SRS target × DEFF. Equal cluster sizes are assumed; this page does not apply a formula for unequal clusters. Numeric output uses up to 12 significant digits; floating-point rounding can occur.
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How the Design Effect Calculator Works & Core Formula
The Design Effect Calculator evaluates Equal cluster size m, Intracluster correlation ρ, Supplied sample size / SRS target in client-side JavaScript using the deterministic rule below and updates the output panel immediately without uploading data to a server.
Calculate equal-cluster design effect, effective sample size and sample-size enlargement.
DEFF = 1+(m−1)ρ and must be positive. Effective n = nominal n/DEFF; enlarged target = supplied SRS target × DEFF. Equal cluster sizes are assumed; this page does not apply a formula for unequal clusters. Numeric output uses up to 12 significant digits; floating-point rounding can occur.
Design Effect Calculator Quick Reference & Input Guide
Review the input parameters, allowed value ranges, and worked reference cases for the Design Effect Calculator below before running your calculation.
| Parameter / Scenario | Default / Sample Value | Rule or Allowed Range | Output / Usage Note |
|---|---|---|---|
| Input: Equal cluster size m | 20 | Range: 1 to 1000000 | Required workspace parameter |
| Input: Intracluster correlation ρ | 0.05 | Range: -1 to 1 | Required workspace parameter |
| Input: Supplied sample size / SRS target | 1000 | Range: 1 to 1000000000 | Required workspace parameter |
| Worked Case 1: Baseline run (Equal cluster size m = 20) | Preloaded / test values | Calculate equal-cluster design effect, effective sample size and sample-size enlargement | Equal cluster size m = 20; Intracluster correlation ρ = 0.05; Supplied sample size / SRS target = 1000. Output: Equal-cluster design effect: 1.95; Effective sample size : 512.820512821; Sample-size multiplier: 1.95; Enlarged sample for supplied SRS target: 1950. |
| Worked Case 2: Comparison scenario (Comparison equal cluster size m check) | Preloaded / test values | Calculate equal-cluster design effect, effective sample size and sample-size enlargement | Equal cluster size m = 10; Intracluster correlation ρ = 0.1; Supplied sample size / SRS target = 100. Output: Equal-cluster design effect: 1.9; Effective sample size: 52.6315789474; Sample-size multiplier: 1.9; Enlarged sample for supplied SRS target: 190. |
Step-by-Step Guide to Using the Design Effect Calculator
Follow these three steps to configure Equal cluster size m, Intracluster correlation ρ, Supplied sample size / SRS target, verify unit and boundary rules, and export your Design Effect Calculator output.
Input and settings
Check units and mode
DEFF = 1+(m−1)ρ and must be positive. Effective n = nominal n/DEFF; enlarged target = supplied SRS target × DEFF. Equal cluster sizes are assumed; this page does not apply a formula for unequal clusters. Numeric output uses up to 12 significant digits; floating-point rounding can occur.
Tool result
Calculate and save
Select Calculate, check the labelled result, then use Copy result or Download result.txt.
Review the details
Practical Worked Examples for Design Effect Calculator
These concrete scenarios illustrate how the Design Effect Calculator processes baseline inputs, comparison checks, and boundary constraints.
Baseline run (Equal cluster size m = 20)
Equal cluster size m = 20; Intracluster correlation ρ = 0.05; Supplied sample size / SRS target = 1000. Output: Equal-cluster design effect: 1.95; Effective sample size : 512.820512821; Sample-size multiplier: 1.95; Enlarged sample for supplied SRS target: 1950.
Comparison scenario (Comparison equal cluster size m check)
Equal cluster size m = 10; Intracluster correlation ρ = 0.1; Supplied sample size / SRS target = 100. Output: Equal-cluster design effect: 1.9; Effective sample size: 52.6315789474; Sample-size multiplier: 1.9; Enlarged sample for supplied SRS target: 190.
Boundary & unit check (Design Effect Calculator)
When solving for 'design effect calculator', verify that Equal cluster size m, Intracluster correlation ρ, Supplied sample size / SRS target use consistent units and stay within the documented scope: DEFF = 1+(m−1)ρ and must be positive. Effective n = nominal n/DEFF; enlarged target = supplied SRS target × DEFF. Equal cluster sizes are assumed; this page does not apply a formula for unequal clusters. Numeric output uses up to 12 significant digits; floating-point rounding can occur.
How to Read and Verify the Design Effect Calculator Output
The output panel reports the exact result derived from Equal cluster size m, Intracluster correlation ρ, Supplied sample size / SRS target alongside any unit or formatting notes.
Every calculation follows the rule: Calculate equal-cluster design effect, effective sample size and sample-size enlargement. Because JavaScript uses IEEE 754 double-precision floating-point arithmetic, numeric outputs display up to 12 significant digits where applicable.
Always cross-check the displayed result against the scope note (DEFF = 1+(m−1)ρ and must be positive. Effective n = nominal n/DEFF; enlarged target = supplied SRS target × DEFF. Equal cluster sizes are assumed; this page does not apply a formula for unequal clusters. Numeric output uses up to 12 significant digits; floating-point rounding can occur) before applying the value to production specifications, financial models, or lab records.
Scope Limits, Accuracy Assumptions & Related Everyday Math Tools
Review these boundary constraints and validation rules before relying on the Design Effect Calculator output.
Operational scope: DEFF = 1+(m−1)ρ and must be positive. Effective n = nominal n/DEFF; enlarged target = supplied SRS target × DEFF. Equal cluster sizes are assumed; this page does not apply a formula for unequal clusters. Numeric output uses up to 12 significant digits; floating-point rounding can occur. Inputs that violate minimum/maximum bounds or required format rules are rejected with a clear diagnostic prompt.
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Open toolFrequently Asked Questions About Design Effect Calculator
Answers about using Design Effect Calculator and understanding its results.
What formula or rule does the Design Effect Calculator use?
The Design Effect Calculator applies the rule: Calculate equal-cluster design effect, effective sample size and sample-size enlargement. Enter Equal cluster size m, Intracluster correlation ρ, Supplied sample size / SRS target into the workspace and the tool computes the exact output in your browser.
What input parameters and units are required for Design Effect Calculator?
Yes. Provide Equal cluster size m, Intracluster correlation ρ, Supplied sample size / SRS target using the documented units and format shown in the quick reference table above. Preloaded default values let you test the workflow immediately.
What are the accuracy limits and boundary assumptions for Design Effect Calculator?
DEFF = 1+(m−1)ρ and must be positive. Effective n = nominal n/DEFF; enlarged target = supplied SRS target × DEFF. Equal cluster sizes are assumed; this page does not apply a formula for unequal clusters. Numeric output uses up to 12 significant digits; floating-point rounding can occur. Confirm that your inputs fall within the allowed ranges before exporting the result.
Is the Design Effect Calculator free and does it keep my inputs private?
Yes. All calculations for the Design Effect Calculator execute 100% locally in your browser's JavaScript runtime. No inputs or results are uploaded to any external server.
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