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Standard Error of the Mean (SEM)

Definition

The standard error of the mean (SEM) measures how much sample means vary from one another when randomly drawn from a population. It quantifies the precision or accuracy of an estimate for the population mean.

Analogy

Imagine you have multiple groups of students, and within each group, you calculate their average test scores. The standard error of the mean would represent how much these average scores differ between different groups, giving you an idea about how reliable your estimates are.

Related terms

Sampling Variability: Sampling variability refers to differences in sample statistics that arise due to random sampling. The SEM captures this variability by measuring how much sample means deviate from each other.

Confidence Interval: A confidence interval provides a range within which we believe the true population parameter lies with a certain level of confidence. SEM is used to calculate confidence intervals for population means.

Precision vs. Accuracy: Precision refers to how close repeated measurements or estimates are to each other, while accuracy refers to how close they are to the true value. SEM helps assess precision in estimating population means.