Kieran McCaul <[email protected]>:
I'm not sure to whom this email is addressed, but let me suggest that
these points were implicit in the first sentence of my post: "The only
way to verify randomization is to observe the randomization
mechanism." I.e. while it is true that "If the study has demonstrably
been randomized, then all differences, no matter how extreme, are due
to chance," the only way for a study to have been `demonstrably
randomized' is for the details of random assignment to be made public.
If they are not, or there is no claim of randomization (but the
analyst want to treat categories of treatment as having been randomly
assigned), a test of balance is the usual crutch to fall back on. It
is also the standard test of any matching model. So yes, "Statistical
tests test a null hypothesis against an alternative" and the null in a
test of balance is that some treatment is randomly assigned. Whether
that is or is not what the original poster was looking for, I do not
know.
On Tue, Sep 30, 2008 at 10:36 PM, Kieran McCaul
<[email protected]> wrote:
> If the purpose is to check "balance" after randomization, I can't see how any statistical testing will help.
>
> Statistical tests test a null hypothesis against an alternative.
>
> The null is essentially "any differences are no greater than would be expected by chance alone'. The alternative is "differences are so large that they are unlikely to be due to chance".
>
> If the study has demonstrably been randomized, then all differences, no matter how extreme, are due to chance.
>
> Lack of balance, which some people seem to obsess about, is not an indication of failure of the randomization process. Lack of balance will occur. It will occur. Always.
>
> The purpose of randomisation is to remove bias, not achieve balance.
>
> Lack of balance will be a problem if it biases comparison between arms of the study. So adjust for the lack of balance in the analysis.
>
>
>
> -----Original Message-----
> From: [email protected] [mailto:[email protected]] On Behalf Of Austin Nichols
> Sent: Wednesday, 1 October 2008 10:05 AM
> 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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