What Is the Sample Size Proportion Calculator?
A sample size proportion calculator estimates the number of survey participants required to achieve dependable statistical inference.
How Does the Sample Size Proportion Calculator Work?
Inverts the binomial standard error formula to solve for n based on acceptable variance bounds.
Sample Size Proportion Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
n₀ = (Z² × p(1 - p)) ÷ E² · n = n₀ ÷ [1 + (n₀ - 1) ÷ N]
Uses standard critical score Z, assumed proportion p, and margin of error E, adjusted for finite population N via finite population correction.
How to Use the Sample Size Proportion Calculator
- Specify desired margin of error, select confidence level, and optionally enter population size.
Step-by-Step Example Calculation
±5% Margin of Error at 95% Confidence
Input Values:
marginOfErrorPct:5
confidenceLevelPct:95
populationProportionPct:50
Understanding Your Result
Outputs minimum completed responses required to uphold advertised precision.
Factors That Affect the Result
- Lower margin of error dramatically inflates sample size requirements due to inverse square relationship.
When Should You Use This Calculator?
- Political polling, market research questionnaires, customer satisfaction surveys, and clinical audits.
Assumptions & Limitations
- Assumes simple random sampling without clustering or non-response bias.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Cochran WG. Sampling Techniques. John Wiley & Sons.