How To Calculate Standard Error Of A Sample Proportion

Calculating the standard error of a sample proportion is crucial in statistics to estimate the sampling error and make informed decisions. This calculator helps you determine the standard error of a sample proportion with ease.

1. Enter the sample size.
2. Enter the proportion of the sample.
3. Click the “Calculate” button.
4. View the results and chart below.

The formula to calculate the standard error of a sample proportion is:

SE = sqrt[(p * (1 - p)) / n]

where:

• SE is the standard error,
• p is the sample proportion, and
• n is the sample size.

Comparison of Standard Errors for Different Sample Sizes

Sample Size (n)	Proportion (p)	Standard Error (SE)
100	0.5	0.05
500	0.5	0.02
1000	0.5	0.01

Effect of Proportion on Standard Error

Proportion (p)	Sample Size (n)	Standard Error (SE)
0.1	100	0.03
0.5	100	0.05
0.9	100	0.03

• Larger sample sizes result in smaller standard errors, making the estimate more precise.
• Proportions close to 0.5 have the largest standard errors. As the proportion moves towards 0 or 1, the standard error decreases.

What is the difference between standard error and standard deviation?

Standard error is a measure of the sampling error, while standard deviation is a measure of the spread of the data. Standard error is always smaller than or equal to standard deviation.

Can I use this calculator for a population proportion?

No, this calculator is for sample proportions. To calculate the standard error of a population proportion, you would need to know the population size.

BLS Handbook of Methods – Chapter 9: Sampling and Estimation

StackExchange – Difference between standard error and standard deviation