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Degrees of Freedom Calculator
Select the statistical test (i.e., ANOVA, chi-square) & input the required values such as sample size (N) and number of groups (k). Then Click the Calculate button, this Degrees of Freedom Calculator will compute the result based on entries.
Table of Contents:
Degree of Freedom Calculator
Degrees of Freedom calculator is an online tool that helps to calculate the degrees of freedom for different statistical tests such as:
- ANOVA
- Chi-Square
- 1-Sample
- 2-Sample t-test (samples with equal variances)
- 2-Sample t-test with unequal variances (Welch’s t-test)
It provides the result with a complete step-by-step solution for every test selection. This df calculator allows users to copy and download the result as PDF for easy saving or sharing.
What are Degrees of Freedom?
Degrees of freedom (df) is a statistical concept that shows the finding of independent values that vary in an analysis without violating any constraints. It depends on the sample size of any statistics.
If the sample size is small then there is a small number of degrees of freedom. On the other hand, if the sample size is large then degrees of freedom in large numbers or many pieces of independent values.
Degrees of freedom play an important role in calculating the reliability and accuracy of statistical estimates. It is used in different statistical tests to find the critical values and p-values. These values help in hypothesis testing like T-test, F-test, and Chi-square test.
Df is also used in Regression analysis and ANOVA (Analysis of Variance) to measure the number of independent values, which are used to find the significant differences between two or more groups.
Degrees of Freedom Formula
The numerical value of the degrees of freedom is determined using different formulas according to the different statistical tests or given data set values. These formulas are discussed below:
DF-Formula for ANOVA
In ANOVA, the degrees of freedom are split into two types: between-group and within-group. But total degrees of freedom is equal to the sum of between & within-groups of degrees of freedom. The degrees of freedom formula for ANOVA is given below:
Between groups: df between =k−1
Within groups: dfwithin= N−k
Total degrees of freedom: dftotal=N−1
Where:
- k is a number of groups or cell means.
- N is the total number of observations taken in the test.
Formula for Chi-Square Test
In the chi-square test, the degrees of freedom depend on the number of rows and columns in the contingency table. The chi-square degrees of freedom value can calculated with below formula:
df = (r-1) (c-1)
where
- r is the number of rows in a table.
- c is the number of columns table.
Formula for One Sample T-test
If one sample data is given then the below degrees of freedom formula is used to calculate the df-value:
df = N-1
Where:
- Df = Degree of Freedom
- N = Sample Size
For Two-sample T-tests with Equal Variances
The degrees of freedom value for two sample data having equal variances are calculated by using the below formula:
df = N1+ N2 −2
Where:
- N1 = Number of data values of the first sample data set.
- N2 = Number of data values of a second sample data set.
For Two-sample T-tests with Unequal Variances (Welch’s t-test)
Degrees of freedom for unequal variances can be calculated with the below formula:
df ≈ (σ12/N1 + σ22/N2)2 / [(σ12/N1)2 / (N1 - 1) + (σ22/N2)2 / (N2 - 1)]
Where:
- σ = Variance
- N = Total Number of Sample
All the above formulas are difficult to remember for students or analysts, face difficulty in finding their value. To remove this difficulty use our above online Degrees of Freedom calculator. It provides the answer instantly by just putting the values in the data fields.