In an independent measures t-test, one group has 20 participants and the other has 16 participants. What is the degrees of freedom for this test?
A. 36
B. 2
C. 35
D. 34
The correct answer and explanation is:
The correct answer is D. 34.
In an independent measures t-test, degrees of freedom (df) is calculated using the formula: df=(n1−1)+(n2−1)df = (n_1 – 1) + (n_2 – 1)
Where:
- n1n_1 is the number of participants in the first group
- n2n_2 is the number of participants in the second group
Given:
- Group 1 has 20 participants (n1=20n_1 = 20)
- Group 2 has 16 participants (n2=16n_2 = 16)
Plugging these values into the formula: df=(20−1)+(16−1)=19+15=34df = (20 – 1) + (16 – 1) = 19 + 15 = 34
So, the degrees of freedom for this independent measures t-test is 34.
The degrees of freedom represent the number of independent pieces of information available to estimate the population parameters. In the case of an independent t-test, the degrees of freedom reflect the number of data points in each group that are free to vary. Subtracting one from each group size accounts for the fact that one value from each group is used to estimate the sample mean, reducing the available independent data points.
For hypothesis testing, the degrees of freedom are used to determine the critical value from the t-distribution, which is essential for calculating the p-value and deciding whether to reject or fail to reject the null hypothesis. Higher degrees of freedom lead to a more normal distribution and thus affect the sensitivity of the test.