Date:         Fri, 12 Nov 2010 09:34:05 -0800
Reply-To:     Bruce Weaver <bruce.weaver@hotmail.com>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Bruce Weaver <bruce.weaver@hotmail.com>
Subject:      Re: non-SPSS: appropriate statistical test
In-Reply-To:  <5ECE5C2E20A9439896E0EE64032FC981@NARAYAM>
Content-Type: text/plain; charset=us-ascii

As usual, Mike is giving solid advice.  The only point at which I did a
(small) double-take was where he said, "If you cannot calculate "r", you
have to assume that it is equal to zero".  I was reminded of situations
where I did not know the value of some parameter, and was therefore advised
to do a "sensitivity analysis".  I.e., do the computation a few times with a
range of plausible values plugged in for the unknown parameter to determine
how sensitive the result was to the value of that parameter.  That was when
I was working for people doing medical research, and it seemed that the term
"sensitivity analysis" was well known in those circles.  I had never heard
of it prior to that (my background to that point had  been in experimental
psychology).  The obvious potential problem here is convincing other people
that the values you plugged in are plausible.  ;-)

HTH.



Mike Palij wrote:
>
> Not sure I'm a greater mind but here goes:
>
> (1) Simple stuff first:  if you are doing t-tests, the general formula
> for the t-test is the following:
>
> Obtained t=(M1 - M2)/sqrt[VarErr1 + VarErr2 - 2*r*SE1*SE2]
>
> Where M1=mean group1, M2=mean group2,VarErr1=Variance error group1,
> VarErr2=Variance error group2, r=Pearson r between group1 and group2
> valaues, SE1=standard error group1, SE2=standard error group2, and
> 2=constant (the number 2).
>
> If you cannot calculate "r", you have to assume that it is equal to zero
> which makes the t-test denominator = sqrt [ VarErr1 + VarErr1].  This
> denominator will be larger than the denominator if "r" is known.  The
> good news is if the t-test is significant under the assumption of r=0.00,
> then it has to be significant if you can calculate r (NOTE: r is typically
> a positive value -- a negative r should cause you to re-examine your
> data).
> The bad news is if the t-test is non-significant, it could be so because
> there is no real difference or you failed to find a significant difference
> because you could not adjust (reduce) your denominator appropriately.
>
> So, treating your data as independent groups makes the test more
> conservative
> or less powerful.  I am open to correction on these points.
>
> (2)  It seems to me that you should be able to get an estimate of the
> Pearson r through bootstrapping or some other simulation procedure.
> If there is a positive correlation between time 1 and time 2, then,
> assuming
> data consisting only of 0 and 1, time1 zeros should co-occur with time2
> zeros at a greater than chance level and the same holds for ones. even if
> they are not matched up properly.  I haven't thought this through but
> perhaps someone more familiar with bootstrapping with correlation
> has more wisdom.
>
> -Mike Palij
> New York University
> mp26@nyu.edu
>
>
>
>   ----- Original Message -----
>   From: J P
>   To: SPSSX-L@LISTSERV.UGA.EDU
>   Sent: Friday, November 12, 2010 9:19 AM
>   Subject: non-SPSS: appropriate statistical test
>
>
>   Colleaguees,
>
>   This is not a SPSS question (at least not yet).
>
>   I am seeking advice on the appropriate test for comparing two
> non-independent samples when the non-independence cannot be modeled.
>
>   The proportions are drawn from the same employees pop  (~ 700, response
> rate of ~50%) employee population, surveyd one year apart. An example of
> an actual comparison is 98.4% vs 96.1% between time1 and time2.
>
>   The problem, as I see it, is the two samples are not independent but
> there is no ID so neither a dependent t-test nor a mixed model can be
> used. I found a test for comparing proportions from two independent
> groups.
>
>   What is the risk of violating the assumption of independence? inflated
> type 1 error?
>
>   As far as I know there is no appropriate test for this situation, but I
> thought I'd check with minds greater than mine...
>
>   Thank you,
>
>   John
>
>
>
>
>
>


-----
--
Bruce Weaver
bweaver@lakeheadu.ca
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.

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