Degrees of freedom

Definition

Degrees of freedom refer to the number of independent values or quantities that can vary in an analysis without breaking any constraints. In statistical calculations, they help determine the accuracy of variance estimates.

5 Must Know Facts For Your Next Test

1. Degrees of freedom are typically calculated as $n - 1$ where $n$ is the sample size.
2. They are critical when using the Student's t-distribution to estimate population parameters.
3. The concept helps adjust for sample size and ensures appropriate variability in estimates.
4. Higher degrees of freedom result in a t-distribution that more closely approximates a normal distribution.
5. In confidence intervals for a single population mean using the t-distribution, degrees of freedom influence the width of the interval.

Review Questions

• How are degrees of freedom calculated in a sample?
• Why are degrees of freedom important when using the Student's t-distribution?
• What effect do higher degrees of freedom have on a t-distribution?

Related terms

Student's t-Distribution: A probability distribution used to estimate population parameters when the sample size is small and/or population variance is unknown.

Confidence Interval: A range of values derived from sample statistics that is likely to contain the value of an unknown population parameter.

$t$-Statistic: A value computed from sample data used in hypothesis testing with the Student's t-distribution.