df.WS {BivRegBLS}

Degrees of freedom by Welch-Satterthwaite

Description

Calculate the degrees of freedom from the Welch-Satterthwaite equation for a linear combination of sample variances.

Usage

df.WS(variances = NULL, k = rep(1, length(variances)), dfs = NULL)

Arguments

variances

a numeric vector for the variances.

k

a numeric vector with the multiplicative constants.

dfs

a numeric vector with the degrees of freedom of each variance.

Details

The variances argument is mandatory while other arguments are optional.

Value

A numeric variable with the degrees of freedom of the linear combination of the variances.

Author(s)

Bernard G FRANCQ

References

Satterthwaite FE. An Approximate Distribution of Estimates of Variance Components. Biometrics Bulletin, 1946, 2: 110-114.
Welch BK. The generalization of "student's" problem when several different population variances are involved. Biometrika, 1947, 34: 28-35.

Examples

df.WS(variances=c(10,15,20),k=c(1.5,2,1.3),dfs=c(8,13,11))