What is sample size in statistics?

Sample size is the number of observations or data points collected in a study or survey. A larger sample size provides more reliable and accurate results but requires more time and resources. The required sample size depends on the desired confidence level, margin of error, and population variability.

What is a confidence level in a sample size calculation?

A confidence level represents how certain you are that the true population value falls within your margin of error. A 95% confidence level (the most common) means that if you repeated your survey 100 times, the true value would fall within your interval 95 times. Higher confidence requires a larger sample size.

What is a good margin of error for surveys?

A margin of error of ±3% to ±5% is generally considered acceptable for most surveys. A ±3% margin at 95% confidence requires approximately 1,067 respondents. National polls often aim for ±3%, while quick informal surveys might use ±5% to ±10% with smaller sample sizes.

Sample Size Calculator — Survey Sample Size

How Many People Do You Need? A Guide to Sample Size

When conducting a survey or research, it's often impossible to ask everyone in a group a question. Instead, we take a "sample" of that group and use their answers to make inferences about the whole population. But how large does that sample need to be to get a reliable result? That's the crucial question this Sample Size Calculator is designed to answer.

Understanding the Key Concepts

To use this calculator, you'll need to think about a few statistical concepts:

Confidence Level: How confident do you want to be that your sample results reflect the true population? 95% is the most common standard, meaning if you repeated the survey 100 times, 95 of those times the results would fall within the margin of error.
Margin of Error: How much error are you willing to tolerate? A 5% margin of error means you expect your result to be within 5 percentage points of the true population value.
Population Proportion: What percentage of the population do you expect to have a certain characteristic? If you don't know, use 50%. This is the most conservative choice as it gives you the largest possible sample size.
Population Size (Optional): The total size of the group you are studying. This is only necessary if your population is relatively small. If it's very large or unknown, you can leave this blank.

The Formulas Behind the Calculation

This calculator uses Cochran's sample size formulas.

1. Formula for an Infinite Population

This is the starting point for most calculations.

n = (Z² * p * (1-p)) / E²

Z: The Z-score associated with your confidence level (e.g., 1.96 for 95%).
p: Your estimated population proportion (as a decimal).
E: Your desired margin of error (as a decimal).

2. Formula for a Finite Population

If you know the size of your population (N), you can adjust the sample size downward. This is because a sample forms a larger percentage of a small population, giving you more certainty.

n' = n / (1 + (n-1)/N)

Where 'n' is the initial sample size from the infinite population formula. The result is always rounded up to the nearest whole number.

Sample Size Calculator