Analysis of Non-Equivalent Control Groups Design

[Hannah State-Davey]

All,

Can anyone provide me with some advice on the following:

I have a non-equivalent control groups design where I have collected
pretest and postest scores from a number of participants representing two
groups - a treatment group (that went through a major organsisational
restrutcure between pretest and posttest) and a conrol group that did not.

At pretest for the treatment group I obtained 80 participants but only 32
were available at posttest. Similarly for the control group I obtained 112
at pretest then only 58 of this group at posttest.

I have conducted an ANCOVA on this data allowing for an unbalanced design,
with pretest as a covariate due to pretest differences. Although my data
meets most of the assumptions of this test - equality of regression
slopes, homogeneity of variance etc, it violates the linearity assumption.
I therefore rank transformed the pretest and posttest scores based on
Conover & Iman's (1981) paper and performed the ANCOVA on this. However, I
am not entirely convinced that this really makes ANCOVA any more
appropriate in this situation? It also makes it more difficult to
interpret.

In the absence of a nonparametric version of ANCOVA is there any other
analysis that would be worth doing on this data as supplementary or
instead of the ANCOVA?

I was going to do a one-way ANOVA of gain scores despite not being able
to 'control' for the pretest differences, although I would have to cut
down my data to enable pretest-posttest differences to be calculated due
to the unequal sample sizes.

Any thoughts on this would be greatly appreciated.

Regards

Hannah

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[Marta Garcia-Granero]

Hannah State-Davey wrote:

> [...] I have conducted an ANCOVA on this data allowing for an unbalanced design,
> with pretest as a covariate due to pretest differences. Although my data
> meets most of the assumptions of this test - equality of regression
> slopes, homogeneity of variance etc, it violates the linearity assumption.
> I therefore rank transformed the pretest and posttest scores based on
> Conover & Iman's (1981) paper and performed the ANCOVA on this. However, I
> am not entirely convinced that this really makes ANCOVA any more
> appropriate in this situation? It also makes it more difficult to
> interpret.
>
> In the absence of a nonparametric version of ANCOVA is there any other
> analysis that would be worth doing on this data as supplementary or
> instead of the ANCOVA?
>
>
>

Just an idea: have you tried to transform the covariate to make the
relationship more linear? Depending on the non-linearity pattern
observed, you could try:

- log transform the pre-test score (or even the post-test score)
- reciprocal transformation (1/pre-test as covariate)
- add a quadratic term as a 2nd covariate (pre-test+squared pre-test)
....


HTH,
Marta García-Granero


--
For miscellaneous statistical stuff, visit:
http://gjyp.nl/marta/

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[Hannah State-Davey]

Thank you Marta, I will give your suggestion a try.
 
One question though - I presume then it is ok to just transform the covariate as you are holding it constant not comparing it with another variable as such? If you were comparing it with another variable then you would have to transform both. Is this right?
 

> Date: Wed, 15 Apr 2009 12:24:29 +0200
> From: [hidden email]
> Subject: Re: Analysis of Non-Equivalent Control Groups Design
> To: [hidden email]
>
> Hannah State-Davey wrote:
> > [...] I have conducted an ANCOVA on this data allowing for an unbalanced design,
> > with pretest as a covariate due to pretest differences. Although my data
> > meets most of the assumptions of this test - equality of regression
> > slopes, homogeneity of variance etc, it violates the linearity assumption.
> > I therefore rank transformed the pretest and posttest scores based on
> > Conover & Iman's (1981) paper and performed the ANCOVA on this. However, I
> > am not entirely convinced that this really makes ANCOVA any more
> > appropriate in this situation? It also makes it more difficult to
> > interpret.
> >
> > In the absence of a nonparametric version of ANCOVA is there any other
> > analysis that would be worth doing on this data as supplementary or
> > instead of the ANCOVA?
> >
> >
> >
> Just an idea: have you tried to transform the covariate to make the
> relationship more linear? Depending on the non-linearity pattern
> observed, you could try:
>
> - log transform the pre-test score (or even the post-test score)
> - reciprocal transformation (1/pre-test as covariate)
> - add a quadratic term as a 2nd covariate (pre-test+squared pre-test)
> ....
>
>
> HTH,
> Marta García-Granero
>
>
> --
> For miscellaneous statistical stuff, visit:
> http://gjyp.nl/marta/
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD

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[Marta Garcia-Granero]

Hi folks:

OK, I have been framed by someone to try to write a SPSS macro for
Passing-Bablok regression. I tried to put the all business off by asking
for the paper (something like "I'd be delighted to help if only you'd
find the paper with the formulas..."). Unfortunately, he sent them....
Just kidding, I always like a challenge, and the maths involved don't
seem particularly hard, but... I haven't been able to find a dataset
(complete) with the expected output (like the one provided by
Analyse-it, for instance). I need to check my macro output with a "gold
standard", to make sure that I don't send to the wilderness a faulty macro.

Can anybody help?

Thank you

Marta

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