Degrees of freedom (df)

Definition

Degrees of freedom (df) are the number of independent values or quantities which can be assigned to a statistical distribution. In hypothesis testing for two population means with unknown standard deviations, df are crucial for determining the critical value from the t-distribution.

5 Must Know Facts For Your Next Test

1. Degrees of freedom for two-sample t-tests often use the formula $df = n_1 + n_2 - 2$, where $n_1$ and $n_2$ are the sample sizes.
2. The calculation of degrees of freedom affects the shape of the t-distribution curve used in hypothesis testing.
3. In cases where sample sizes are unequal, a more complex formula called Welch-Satterthwaite equation might be used to calculate df.
4. Higher degrees of freedom result in a t-distribution that more closely approximates the normal distribution.
5. Degrees of freedom impact the critical t-value needed to determine whether to reject the null hypothesis.

Review Questions

• How do you calculate degrees of freedom for a two-sample t-test with equal sample sizes?
• Why are degrees of freedom important when using the t-distribution in hypothesis testing?
• What happens to the shape of the t-distribution as degrees of freedom increase?

Related terms

t-Distribution: A probability distribution used in hypothesis testing for small sample sizes or when population variance is unknown.

Critical Value: A point on a statistical distribution that represents an established threshold for rejecting the null hypothesis.

Welch-Satterthwaite Equation: A method to approximate degrees of freedom when comparing two means with unequal variances and sample sizes.