Degrees of freedom

Definition

Degrees of freedom refer to the number of independent values or quantities which can be assigned to a statistical distribution. They are crucial in estimating population parameters and conducting hypothesis tests.

5 Must Know Facts For Your Next Test

1. Degrees of freedom (df) for a single sample t-test is calculated as $n-1$, where $n$ is the sample size.
2. In confidence intervals, degrees of freedom affect the critical value from the t-distribution table.
3. When calculating confidence intervals for small samples with unknown population standard deviation, degrees of freedom determine the shape of the t-distribution.
4. Higher degrees of freedom result in the t-distribution approaching a normal distribution.
5. In paired sample tests, degrees of freedom are calculated as $n-1$, where $n$ is the number of pairs.

Review Questions

• How do you calculate degrees of freedom for a single sample t-test?
• Why are degrees of freedom important in determining the critical value in confidence intervals?
• What effect do higher degrees of freedom have on the shape of the t-distribution?

Related terms

t-Distribution: $t$-distribution is a type of probability distribution that is symmetric and bell-shaped but has heavier tails than the normal distribution. It is used when estimating population parameters with small sample sizes.

Confidence Interval: A range around a sample statistic that provides an estimated range where a population parameter lies, based on a specific level of confidence.

Population Standard Deviation: $\sigma$ (sigma) represents how data points in an entire population differ from the mean. When unknown, it is estimated using sample data.