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