Standard Error

Definition

The standard deviation of the sampling distribution of a statistic. It quantifies how precisely the sample estimate (e.g., a mean or regression coefficient) represents the corresponding population parameter. Standard errors shrink as sample size grows and are the basis for confidence intervals and hypothesis tests.

Why It Matters

Without standard errors, it is impossible to assess the reliability of an estimate. A coefficient of 2.5 could be precise (small SE, narrow confidence interval) or highly uncertain (large SE, wide interval). Standard errors transform point estimates into interval estimates and enable the statistical tests that underpin virtually all empirical research.

Example

A sample mean income is $48,000 with a standard error of $1,200. Using a 95% confidence level, the interval is approximately $45,600 to $50,400. If the standard error were $5,000 instead, the interval would widen to $38,200 to $57,800, reflecting much greater uncertainty about the true population mean.

Related Terms

• Confidence Interval
• Robust Standard Errors
• Standard Deviation

Software Notes

• SPSS: Reported automatically in regression and descriptive output tables
• R: sd(x) / sqrt(length(x)) for a mean; summary(model) or broom::tidy(model) for regression coefficients
• Stata: Standard errors displayed by default in regression output; access via _se[varname]