Degrees of freedom (df) represent the number of independent pieces of information available to estimate a parameter. In the context of t-tests, df is crucial because it affects the shape of the t-distribution, which is used to determine the p-value. A higher df generally indicates more reliable results. For a one-sample t-test, $df = n - 1$, where $n$ is the sample size. For an independent samples t-test, $df = n_1 + n_2 - 2$, where $n_1$ and $n_2$ are the sample sizes of the two groups.
Understanding how to calculate degrees of freedom is essential for correctly interpreting t-test results and drawing valid conclusions about your data.
Match the terms with their correct definitions:
| Term | Definition |
|---|---|
| 1. Degrees of Freedom | A. A statistical test used to determine if there is a significant difference between the means of two independent groups. |
| 2. Sample Size | B. The number of independent pieces of information available to estimate a parameter. |
| 3. One-Sample t-test | C. The number of observations in a sample. |
| 4. Independent Samples t-test | D. A statistical test used to determine if there is a significant difference between the mean of a sample and a known value. |
| 5. t-distribution | E. A probability distribution that is used when the sample size is small or the population standard deviation is unknown. |
Complete the following paragraph with the correct words:
The degrees of freedom (df) in a ________ t-test is calculated as $n - 1$, where $n$ represents the ________. For an independent samples t-test, the df is calculated as ________, where $n_1$ and $n_2$ are the sample sizes of the two ________.
Explain why understanding degrees of freedom is important when conducting and interpreting t-tests. How does the degrees of freedom affect the outcome of the test?
Please log in to post your answer.
Log InEarn 2 Points for answering. If your answer is selected as the best, you'll get +20 Points! 🚀