[Rasch] Standard error of combined measures

Stuart Luppescu slu at ccsr.uchicago.edu
Tue May 12 08:38:58 AEST 2015

Hello Raschies, This is a general measurement question rather than a
Rasch question, but I hope someone can help me.

I have two measurements x_1 and x_2 with known standard errors, se_1 and
se_2, respectively, which we can assume are independent. The
measurements are correlated with a correlation coefficient of r(x_1,
x_2) > 0. I calculate a weighted mean using normalized weights w and
(1-w): \sum{w*x_1 + (1-w)*x_2}. What is the combined standard error of
the weighted mean?

Since the measurements are correlated I would expect that the combined
standard error would be less than the combined standard error if the
measurements were uncorrelated, which would be something like
\sqrt(w^2*se_1^2 + (1-w)^2*se_2^2).

Can someone provide an actual formula?

Thanks.
--
Stuart Luppescu -=-=- slu <AT> ccsr <DOT> uchicago <DOT> edu
CCSR at U of C ,.;-*^*-;.,  ccsr.uchicago.edu
(^_^)/    才文と智奈美の父
[Crash programs] fail because they are based on the theory that,
with nine women pregnant, you can get a baby a month.
-- Wernher von Braun