Degree of freedom calculator

How to Use the Degree of Freedom Calculator

Our Degree of Freedom Calculator is user-friendly and requires only a few inputs:

Select Degree of Freedom Type:

• Unequal variance
• Equal (pooled) variance
• Conservative
• One sample

Enter Sample Data:

• For unequal variance: input the sample sizes and standard deviations for both samples.
• For equal variance: input the sample sizes for both samples.
• For conservative: input the sample sizes for both samples.
• For one sample: input the sample sizes.

Calculate:

Click on the 'Calculate' button to compute the degrees of freedom.

How to Find the Degree of Freedom for a T Test

Understanding how to find the degree of freedom for a t-test is essential for accurate statistical analysis. Degrees of freedom are a key component in determining the critical values and p-values for your t-test results. Here’s a guide to help you calculate the degrees of freedom for different types of t-tests:

1. Two-Sample T-Test with Equal Variance (Pooled Variance)

For a two-sample t-test where the variances are assumed to be equal, use the following formula:

Formula:

\( \mathrm{df = n_1 + n_2 - 2} \)

Where:

• \( \mathrm{n_1 } \) is the sample size of the first sample
• \( \mathrm{n_2 } \) is the sample size of the second sample

2. Two-Sample T-Test with Unequal Variance (Welch's T-Test)

For a two-sample t-test where the variances are not assumed to be equal, use Welch's approximation for the degrees of freedom:

Formula:

\( \mathrm{df = \frac{ \left( \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} \right)^2 }{ \frac{ \left( \frac{s_1^2}{n_1} \right)^2 }{n_1 - 1} + \frac{ \left( \frac{s_2^2}{n_2} \right)^2 }{n_2 - 1} }} \)

Where:

• \( \mathrm{s_1 } \) is the standard deviation of the first sample
• \( \mathrm{s_2 } \) is the standard deviation of the second sample
• \( \mathrm{n_1 } \) is the sample size of the first sample
• \( \mathrm{n_2 } \) is the sample size of the second sample

3. One-Sample T-Test

For a one-sample t-test, use the following formula:

Formula:

\( \mathrm{df = n - 1} \)

Where:

• \( \mathrm{n } \) is the sample size of the single sample

4. Paired T-Test

For a paired t-test, use the following formula, which is similar to the one-sample t-test:

Formula:

\( \mathrm{df = n - 1} \)

Where:

• \( \mathrm{n } \) is the number of pairs

Example Calculations

Here are some example calculations for better understanding:

• Two-Sample T-Test (Equal Variance): If \( \mathrm{n_1 =15} \) and \( \mathrm{n_2 =20} \), then \( \mathrm{ df = 15 + 20 - 2 = 33} \)
• Two-Sample T-Test (Unequal Variance): If \( \mathrm{n_1 =10} \), \( \mathrm{s_1 =3.2} \), \( \mathrm{n_2 =12} \), and \( \mathrm{s_2 =2.8} \), the degrees of freedom can be calculated using Welch's formula.
• One-Sample T-Test: If \( \mathrm{n =25} \), then \(\mathrm{ df = 25 - 1 = 24 }\).
• Paired T-Test: If you have \(30\) pairs, then \( \mathrm{ df = 30 - 1 = 29}\).

Using our Degree of Freedom Calculator, you can easily input your sample data and select the type of t-test to automatically calculate the degrees of freedom for your analysis.