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THE FEUTEX TOOLKIT

Welch–Satterthwaite Combined Degrees of Freedom

Calculate effective degrees of freedom for a sum of independent estimated variance components.

Statistics workspace● Runs in your browser
01 Your input
02 Your result
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FormulaCombined Variance = v1+v2; Degrees Of Freedom = (v1+v2)**2/(v1**2/df1+v2**2/df2); Combined Standard Uncertainty = sqrt(v1+v2)
Sources and model references

Made for real tasks

  • Calculate effective degrees of freedom for a sum of independent estimated variance components.
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Worked example

Inputs

First variance contribution
0.4 number
First contribution degrees of freedom
9 number
Second variance contribution
0.6 number
Second contribution degrees of freedom
19 number

Expected results

Combined Variance
1 number
Degrees Of Freedom
27.22929936 number
Combined Standard Uncertainty
1 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter first variance contribution, first contribution degrees of freedom, second variance contribution, second contribution degrees of freedom.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "v1": 0.4,
  "df1": 9,
  "v2": 0.6,
  "df2": 19
}

Accuracy and scope

Independent variance contributions already scaled to the same output quantity. Not an additional two-sample means test.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.