Standard error

Definition

Standard error measures the variability of a sample statistic, typically the mean, from its population mean. It is used to estimate how much a sample mean might differ from the true population mean.

5 Must Know Facts For Your Next Test

1. The formula for standard error of the mean (SEM) is $\text{SEM} = \frac{s}{\sqrt{n}}$, where $s$ is the sample standard deviation and $n$ is the sample size.
2. Standard error decreases as sample size increases, making estimates more precise with larger samples.
3. In hypothesis testing with two samples, standard errors are used to calculate confidence intervals and test statistics like t-scores.
4. The pooled standard error combines the variances from two independent samples when comparing their means.
5. Smaller standard errors indicate that the sample mean is a more accurate reflection of the population mean.

Review Questions

• What does the standard error measure in a statistical context?
• How does increasing the sample size affect the standard error?
• Why is pooled standard error important when comparing two population means?

Related terms

Sample Standard Deviation: A measure of how spread out numbers in a sample are around their mean.

Confidence Interval: A range of values derived from a sample statistic that likely contains the true population parameter.

t-Score: A standardized value used in hypothesis testing to determine if there is a significant difference between group means.