Standard error

standard_deviation_diagram.svg

Standard error (SE) is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation. The standard error is an important concept in the field of statistics and is used in various statistical analyses.

Definition

The standard error of a statistic (usually the mean) is the standard deviation of its sampling distribution or an estimate of that standard deviation. The term is used in the context of sampling and inferential statistics.

Formula

The standard error of the mean (SEM) can be calculated using the following formula:

SE = σ / √n

where:

• σ is the standard deviation of the population.
• n is the sample size.

Interpretation

The standard error provides an indication of the reliability of the sample mean as an estimate of the population mean. A smaller standard error indicates that the sample mean is a more accurate reflection of the actual population mean. Conversely, a larger standard error suggests that the sample mean is less reliable.

Applications

Standard error is used in various statistical analyses, including:

• Confidence intervals: The standard error is used to calculate the margin of error for confidence intervals.
• Hypothesis testing: It is used to determine the significance of test results.
• Regression analysis: The standard error of the estimate measures the accuracy of predictions made with a regression line.

Difference from Standard Deviation

While both standard error and standard deviation measure variability, they are used in different contexts. The standard deviation measures the variability within a single sample, while the standard error measures the variability of the sample mean from the population mean.

Related Concepts

• Central limit theorem
• Law of large numbers
• Sampling distribution
• Margin of error
• Bias (statistics)

See Also

• Variance
• Estimator
• Confidence interval
• Hypothesis testing
• Regression analysis