Final answer:
In a t-test, degrees of freedom are determined by the sample size. For one-sample or paired-sample t-tests, they are calculated as n - 1. For tests with two independent samples with different variances or when conducting an F-test for variances, the calculation is more complex but still ultimately based on sample size.
Step-by-step explanation:
In a t-test, the degrees of freedom are a function of the sample size. The concept of degrees of freedom is central to the correct interpretation of tests of statistical significance. When calculating degrees of freedom in hypothesis testing, different scenarios and tests involve specific calculations. For instance:
- In a one-sample t-test or a paired-sample t-test, the degrees of freedom are calculated as n - 1, where n is the number of observations (or pairs).
- For two independent samples with unequal variances, known as the Aspin-Welch t-test, the formula for degrees of freedom is more complex and was specifically developed for this scenario.
- In the case of an F-test used to compare two variances, the degrees of freedom for each group are sample size - 1 and are used in determining the F statistic, with numerator and denominator degrees of freedom depending on the number of groups and observations within each group.
- It is essential for data to be normally distributed for these test statistics to be valid. Additionally, computer software or calculators often handle the computation of these degrees of freedom, as they can be intricate and not always an integer value.
The degrees of freedom are not affected directly by the alpha level (the threshold for statistical significance) or the difference between the means. Variance does play a role in calculating degrees of freedom when conducting tests that evaluate variance, such as the F-test.