Welch-Satterthwaite equation

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The Welch-Satterthwaite equation is used to calculate the effective degrees of freedom, in uncertainty analysis for use with the Student's t-distribution when combining a number of standard uncertainties with different degrees of freedom.

$\nu_\mathrm{eff} = \frac{u_c^4}{\sum_{i=1}^N \frac{u_i^4}{\nu_i}},$

where ν_eff is the effective degrees of freedom, u_c is the combined standard uncertainty, u_i are the individual standard uncertainties and ν_i are their degrees of freedom.