Sampling Error Calculator

Calculate the sampling error (margin of error) for a survey or study based on sample size, confidence level, and observed proportion.

SAMPLING ERROR (MARGIN OF ERROR)
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Standard Error
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Z-Score
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Lower Bound
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Upper Bound
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What Is Sampling Error?

Sampling error is the difference between a sample statistic and the true population parameter it estimates. It arises because a sample is only a subset of the population. The margin of error quantifies the maximum expected sampling error at a given confidence level and is commonly reported in polls and surveys.

Unlike non-sampling errors (bias, measurement error), sampling error is a natural consequence of random sampling and can be precisely quantified. It decreases as sample size increases and is the basis for constructing confidence intervals around survey estimates.

Formula

Margin of Error = Z × √(p(1-p)/n)
Confidence Interval = p̂ ± Margin of Error

Factors Affecting Sampling Error

FactorEffect
Larger sample sizeReduces sampling error
Higher confidence levelIncreases sampling error
Proportion near 50%Maximizes sampling error
Simple random samplingStandard formula applies

Frequently Asked Questions

What does a 3% margin of error mean?

It means the true population value is expected to be within 3 percentage points of the sample estimate. For example, if a poll shows 52% support with a 3% margin of error at 95% confidence, the true support is likely between 49% and 55%.

How can I reduce sampling error?

The most effective way is to increase sample size. However, the relationship follows a square-root law: to halve the margin of error, you need to quadruple the sample size. Using stratified sampling or other efficient designs can also help reduce error for a given sample size.