Standard Error of Proportion Calculator

Standard Error of Proportion Calculator calculator can be used to calculate the standard error of a proportion from sample data, which is essential for hypothesis testing and confidence interval estimation in statistics.

Input Parameters

Calculation Results

Calculation Formula

Standard Error (SE) = √[p(1-p)/n]

Where:
p = proportion of successes (x/n)
n = sample size
x = number of successes

Standard Error of Proportion Calculator Calculator Usage Guide

Learn how to use the Standard Error of Proportion Calculator calculator and its working principles

How to Use This Calculator

  1. Enter your sample size (n) - the total number of observations in your sample
  2. Enter the number of successes (x) - the number of observations that met your criterion of interest
  3. Click the "Calculate" button to compute the proportion and its standard error
  4. The calculator will display the proportion (p = x/n) and its standard error (SE = √[p(1-p)/n])

Understanding the Standard Error of Proportion

The standard error of proportion measures the dispersion of sample proportions around the true population proportion. It's an important measure in inferential statistics, particularly when constructing confidence intervals or performing hypothesis tests about population proportions.

Example Usage

Suppose you conducted a survey of 100 people (n=100) and found that 30 people (x=30) support a particular policy. To calculate the standard error of this proportion:

  • Sample size (n) = 100
  • Number of successes (x) = 30
  • Proportion (p) = 30/100 = 0.30
  • Standard error (SE) = √[(0.30 × 0.70)/100] ≈ 0.048

Interpretation

A smaller standard error indicates that the sample proportion is more likely to be close to the true population proportion. This is useful for determining the precision of your sample estimates and for constructing confidence intervals.