Standard Error Calculator
This simple standard error calculator provides full details of the calculation, including sample size, mean, standard deviation, and standard error.
Further Information
The standard error (SE) is the standard deviation of the sampling distribution of a statistic. The standard error of the mean is a measure of the dispersion of sample means around the population mean.
What is Standard Error?
The standard error tells us how much the sample mean is likely to vary from the true population mean. A smaller standard error indicates that the sample mean is likely to be a more accurate estimate of the population mean.
When to Use
- When reporting the precision of a sample mean
- When constructing confidence intervals
- When conducting hypothesis tests about the population mean
- When comparing means across different samples
Equation
SE = SD / √n
or equivalently
SE = √[Σ(x - x̄)² / (n - 1)] / √n
Where SD is the sample standard deviation, n is the sample size, x represents each data point, and x̄ is the sample mean.
Interpretation
The standard error decreases as the sample size increases. This makes intuitive sense: with more data, our estimate of the mean becomes more precise. The standard error is always smaller than the standard deviation.
