0
$\begingroup$

Why do Mathematicians like to think about partitioning variances into different components -- the basis of ANOVA? In contrast, why is it not correct to partition the SD into components?

$\endgroup$

1 Answer 1

2
$\begingroup$

Variances add up, when you add two independent variables, while the standard deviation does not. i.e. $Var(x+y) = Var(x) + Var(y)$ , if $x$ and $y$ are independent. This means that if you take a sample, and $x_1, ... , x_k$ are independent, then the variance of the mean is the mean of the variances of the variables. For the standard deviation, this is not true.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.