Instruction of online calculator

Degrees of Freedom Calculator

Input Data

Test Type

Output

 

Introduction

Degrees of freedom are a crucial concept in statistics, representing the number of independent values or quantities that can vary in an analysis while still satisfying given constraints. This calculator covers five common scenarios in statistical tests:

  1. Analysis of Variance (ANOVA)
  2. Chi-Square Test
  3. 1-Sample Test
  4. 2-Sample T-Test with Equal Variances
  5. 2-Sample T-Test with Unequal Variances

The inputs required for each case are straightforward, making the calculation quick and convenient.

How to Use

  1. Select the case from the dropdown menu or options provided.
  2. Enter the required input data into the fields (specific inputs depend on the selected case, detailed below).
  3. Press the “Calculate” button.
  4. The result will display the degrees of freedom for your chosen case.

Examples

1. ANOVA

Inputs:

  • Sample Size (N): Total number of observations.
  • Number of Groups (K): Total number of distinct groups.

Calculation Formula:

Formula:
  • Degrees of Freedom Between Groups: K-1
  • Degrees of Freedom Within Groups: N-K
  • Total Degrees of Freedom: N-1

Example:

  • N = 20
  • K = 5

Calculation is as follows:

  • Degrees of Freedom Between Groups: 5-1=4
  • Degrees of Freedom Within Groups: 15
  • Total Degrees of Freedom: 20-1=19

The output of this data using online calculator is as follows:

2. Chi-Square Test

Inputs:

  • Number of Columns in the Table
  • Number of Rows in the Table

Calculation Formula:
Degrees of freedom = (Number of Columns in the Table – 1) * (Number of Rows in the Table- 1)

Example:

  • Number of Rows = 4
  • Number of Columns = 3
    Degrees of Freedom = (4 – 1)*(3 – 1) = 3*2 = 6

The output of this data using online calculator is as follows:

3. 1-Sample Test

Inputs:

  • Sample Size (N): Total number of observations.

Calculation Formula:
Degrees of freedom = ( N – 1 )

Example:

  • N = 30
    Degrees of Freedom = ( 30 – 1 = 29 )

The output of this data using online calculator is as follows:

4. 2-Sample T-Test with Equal Variances

Inputs:

  • Sample Size of Group 1 (N1)
  • Sample Size of Group 2 (N2)

Calculation Formula:
Degrees of freedom = ( N1 + N2 – 2 )

Example:

  • N1 = 20
  • N2 = 25
    Degrees of Freedom = ( 20 + 25 – 2 = 43 )

The output of this data using online calculator is as follows:

5. 2-Sample T-Test with Unequal Variances

Inputs:

  • Sample Size of Group 1 (N1)
  • Sample Size of Group 2 (N2)
  • Variance of Group 1 (σ12 or Var1)
  • Variance of Group 2 (σ22 or Var2)

Calculation Formula:

Example:

  • N1 = 15
  • N2 = 20
  • Variance of Group 1 (Var1) = 4
  • Variance of Group 2 (Var2) = 6

Plugging values into the formula will yield the degrees of freedom.

degree of freedom=32

The output of this data using online calculator is as follows:

Feel free to use this calculator for your analyses, and enjoy the simplicity it brings to your statistical calculations! Let me know if you need additional assistance.