The tests Dr. Nichols notes assume normality - not much of an issue for univariate issue unless there is bad skewness. The multivariate test based on Hotelling could be an issue as it isn't quite as robust to non-normality.
The testing of balance after randomization is often done in the pharmaceutical industry but Senn had a good article in Statistics in Medicine on this about 10 years ago. It's not sensible, as all it does is verify if you did the job right, and if you didn't what then?
Others have suggested using the test to determine if you should adjust for the variables that aren't balanced. This is allowing the data to determine the analysis, and is completely exploratory. If you are planning to adjust for covariables, you should specify these a priori - and usually these are based on their potential effect on the response.
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Tony
Peter A. Lachenbruch
Department of Public Health
Oregon State University
Corvallis, OR 97330
Phone: 541-737-3832
FAX: 541-737-4001
-----Original Message-----
From: [email protected] [mailto:[email protected]] On Behalf Of Austin Nichols
Sent: Tuesday, September 30, 2008 7:05 PM
To: [email protected]
Subject: Re: st: Verify randomization in a large sample
Jos� Luis Ch�vez Calva <[email protected]>:
The only way to verify randomization is to observe the randomization
mechanism. But you can check the balance by comparing means of
several variables in the dataset like age, gender, language, etc.
across categories. For example, if you have treatment and control
groups defined by a variable t (=0 for control and =1 for treatment),
you can do
hotelling age gender language etc, by(t)
or
reg t age gender language etc
to get an F test of the null that all means are the same. Assuming
variances may differ, you can
reg t age gender language etc, r
and for alternative models you can run logit or probit instead (to get
a chi2 test). Presumably, for a categorical t you could run
mlogit t age gender language etc
or -mprobit- assuming a specific error distribution under the null of
randomization (in which case the X vars should not help you predict
t). All of that is just for comparisons of means; for higher moments
you will need tests of equality of distributions (e.g. -ksmirnov-) or
graphical methods (e.g. -qqplot-).
On Tue, Sep 30, 2008 at 8:18 PM, Jos� Luis Ch�vez Calva
<[email protected]> wrote:
> Dear Stata users:
>
> I have a dataset on household income with a large number of
> individuals. The set contains one variable indicating the locality
> where each individual lives and another one indicating the household
> to which this individual belongs to. I would like to know how to
> verify randomization both at locality and household level using
> several variables in the dataset like age, gender, language, etc.
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