Standard error

The standard deviation of a statistic’s sampling distribution. It measures how much the statistic typically varies across repeated samples from the same population.

Sampling distribution: The probability distribution of a statistic across repeated samples drawn under the same conditions. Standard error is the spread of this distribution.
Statistic: A numerical function of sample data used to summarize observations or estimate a population quantity. A standard error describes the sampling variability of a particular statistic.
Confidence interval: An interval procedure designed to cover an unknown population parameter at a specified long-run rate. Many confidence-interval formulas use a standard error to set the interval’s width.
Heteroskedasticity: A condition in which a model’s error variance differs across observations or predictor values. Ignoring it can make conventional regression standard errors unreliable.
Standard deviation: A measure of dispersion equal to the square root of variance. A standard error is a standard deviation applied to a statistic’s sampling distribution.
Population parameter: A numerical characteristic of an entire population, such as its mean or proportion. Statistics vary across samples while often serving to estimate a fixed population parameter.
Hypothesis test: A statistical procedure that evaluates data against a specified null hypothesis. Test statistics often compare an estimate’s distance from the null with its standard error.
Cluster sampling: A sampling design that selects groups of units rather than selecting every unit independently. Within-cluster similarity changes sampling variability and requires design-aware standard errors.
Sample size: The number of observations included in a sample or study. Larger samples generally reduce standard errors, often at a rate proportional to the inverse square root of sample size.
Variance: The expected squared deviation of a random variable from its mean. Standard error is the square root of a statistic’s sampling variance.

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