Table of Contents
What Is Standard Error?
The standard error (SE) is a measure of the statistical accuracy of an estimate. The most commonly reported standard error is the standard error of the mean (SEM), which estimates how far the sample mean is likely to differ from the true population mean. It is calculated by dividing the sample standard deviation by the square root of the sample size.
Standard errors are used to construct confidence intervals and perform hypothesis tests. A smaller standard error indicates a more precise estimate. Standard errors can also be calculated for other statistics such as proportions, regression coefficients, and differences between means.
Formula
Standard Error vs Standard Deviation
| Feature | Standard Deviation (SD) | Standard Error (SE) |
|---|---|---|
| Measures | Spread of individual values | Precision of the mean |
| Depends on n? | No (approaches population value) | Yes (decreases with larger n) |
| Formula | s = √(Σ(x-x̄)²/(n-1)) | SE = s/√n |
| Use | Describe data variability | Infer about population mean |
Frequently Asked Questions
How do I interpret the standard error?
The standard error tells you the typical distance between your sample mean and the true population mean. If the SE is small relative to the mean, your sample mean is a precise estimate. Multiplying the SE by about 2 gives an approximate 95% margin of error for the population mean.
Can the standard error be larger than the standard deviation?
No. Since SE = SD/sqrt(n) and n is always at least 1, the SE is always less than or equal to the SD. When n = 1, SE = SD. As sample size increases, SE becomes progressively smaller than SD.