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I'm reading Stephen Senn's book, Statistical Issues in Drug Development, and come across this formula for the expected variance of a randomised clinical trial, with a fitted single continuous covariate, given that a perfectly balanced clinical trial has a variance of 1: 1+1/(2n-4).

I was thinking that the 2n-4 the -4 is for the mean and coefficient of the covariate, but I'm unsure why the inverse is summed with 1?

Thanks

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As a baseline, the variance of a perfectly balanced trial without covariates is 1. There are more sources of variability that must be taken into consideration when a covariate is included to the model. The term $\frac{1}{2n -4}$ refers to the increase in variance that results from calculating the mean and the covariate's coefficient.

As already mentioned if the trial were completely balanced and no covariates were fitted, the variance would be represented by the number "1" in the numerator of the formula. The total number of observations for both groups is indicated by the "2n". The reason for the "4" is that each new parameter you estimate (the mean and slope for the covariate) effectively reduces the degrees of freedom by one. "4" is the result of you losing two degrees of freedom for each of the two parameters you are estimating—the intercept and the slope.

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