# Degree of Freedom:Pooled estimate of variance

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Sinnicks
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Hello-
How does on calculate the degree of freedom for the pooled estimate of variance?Operator 1 – 100,102, 103, 122, 96.
Operator 2 – 129, 132, 134, 118, 112
Operator 3 – 120, 124, 136, 111, 109

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#163420

Doc
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Pooled Var = [V1(n1-1) + V2(n2-1) + V3(n3-1)] / [(n1-1) + (n2-1) + (n3-1))
You can think of this as a weighted average of the variances … weighted using the degrees of freedom for each group. Of course, if the groups all have the same sample size, then the weighting is equal, and the pooled variance is simply the mean of the variances.
Pooled DF = (n1-1) + (n2-1) + (n3-1) = (n1+n2+n3) – g, where g is the number of groups, in this case 3.

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