Standard error

Definition

Standard error measures the accuracy with which a sample distribution represents a population by using standard deviation. It is crucial for estimating population parameters and conducting hypothesis tests.

5 Must Know Facts For Your Next Test

1. Standard error decreases as sample size increases, reflecting more accurate estimates.
2. It is calculated as the standard deviation divided by the square root of the sample size: $SE = \frac{\sigma}{\sqrt{n}}$.
3. In comparing two independent population means, the standard error helps determine if observed differences are statistically significant.
4. The formula for standard error of the difference between two means is $SE_{difference} = \sqrt{(\frac{\sigma_1^2}{n_1}) + (\frac{\sigma_2^2}{n_2})}$.
5. Smaller standard errors indicate more reliable sample estimates of population parameters.

Review Questions

• How does increasing the sample size affect the standard error?
• What is the formula for calculating the standard error of a single sample mean?
• Why is standard error important when comparing two independent population means?

Related terms

Population Mean: The average value of all observations in a population.

Sample Mean: The average value of observations in a sample taken from a population.

Hypothesis Testing: A method used to determine if there is enough statistical evidence to support a particular belief or hypothesis about a parameter.