# st: Design Effect via -loneway- and -svymean-

 From Garry Anderson <[email protected]> To [email protected] Subject st: Design Effect via -loneway- and -svymean- Date Thu, 19 Feb 2004 20:28:53 +1100

Hi,

I am trying to figure out why there is a slight discrepancy between the value of the design effect (deff) as reported by -svymean- and that calculated from using the intraclass correlation coefficient from -loneway- and the adjusted mean cluster size.

I have an example where the discrepancy is larger than the following example, but I have chosen the following for demonstration because of the availability of a data file via Stata

use http://www.stata-press.com/data/r8/auto7.dta

-svyset,psu(manufacturer_grp)-
-svymean mpg-
reports the deff as 1.836013

Using -loneway mpg manufacturer_grp-
reports the intraclass correlation as 0.36827

A formula to obtain the intraclass correlation coefficient from loneway is

rho = (MSB-MSW) / (MSB + (n_o - 1) MSW) = 0.36827

where n_o = 1/(k-1) [N - sum_i (n_i^2/N] = 3.1584767
k = number of groups = 23
N = total sample size = 74

Variance Inflation Factor = 1 + (n_o - 1) rho
= 1 + (3.1584767 - 1) * 0.36827
= 1.7949

The 1.7949 derived from -loneway- does not equal the value of 1.836013 that is reported for Deff from -svymean-.

Any clues would be much appreciated.

Kind regards, Garry
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