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# Re: st: Re: z-score diff plots

 From Nikos Kakouros To statalist@hsphsun2.harvard.edu Subject Re: st: Re: z-score diff plots Date Thu, 11 Apr 2013 11:13:31 -0400

```Dear Prof Cox,

Although the tests are meant to measure the same factor they do so
differently and hence with vary different resultant values.  This is
why I standardized into z-scores and then plotted the difference
between the matched z-scores against the third variable.

I think it worked as I can see a pattern as expected from the below:
a) The first test appears to be dependent on the third variable
linearly (lower results, I think artifactual, with higher levels of
the third variable).

b) The second test values appear flat when plotted against the third
varilable  (i.e the results from this test do not appear to be
affected by this variable).

c) The difference in z-scores between the two tests does have a
significant slope (p<0.005) when plotted against the third variable.
I take this to suggest that there is a significant difference in the
way the two tests interact with the variable (else their z-scores
should cancel out and produce a horizontal plot along the 0 line).  I
guess this is effectively showing that there is a significant
difference in their respective regression line coefficients against
the third variable but in a graphical way.

Does this make sense?  I appreciate this is not directly a Stata
question but I'm a clinician with limited statistics experience and
have never come across a similar plot and neither have I found it
mentioned anywhere. I think that (if valid) it should be helpful...
(maybe this could be the start of a new Stata command :)

Many thanks again,

Nikos

On Thu, Apr 11, 2013 at 10:55 AM, Nick Cox <njcoxstata@gmail.com> wrote:
> Plotting difference against mean is a standard plot for many people.
>
> It is a relative of  the principle that it is helpful to plot residual
> against fitted.
>
> Plotting some difference against a third variable might similarly be
> useful. It is a bit like the standard practice of plotting residuals
> from some model against a predictor not in the model.
>
> The question is does it work, that is, can you see a pattern?
>
> There are some general references in
>
> SJ-4-3  gr0005  . . . . .  Speaking Stata: Graphing agreement and disagreement
>         . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  N. J. Cox
>         Q3/04   SJ 4(3):329--349                                 (no commands)
>         how to select the right graph to portray comparison or
>         assessment of agreement or disagreement between data
>         measured on identical scales
>
> .pdf accessible via http://www.stata-journal.com/article.html?article=gr0005
>
> Nick
> njcoxstata@gmail.com
>
>
> On 11 April 2013 15:24, Nikos Kakouros <nkakouros@gmail.com> wrote:
>> Thanks, Joseph.
>> I was hoping to have a single graph demonstrating the interaction
>> between the three variables.
>> I wonder what anyone thought of the proposed idea of plotting the
>> z-score difference between the two tests against the interacting
>> variable...
>> KR
>> Nikos
>>
>> On Wed, Apr 10, 2013 at 10:40 PM, Joseph Coveney <stajc2@gmail.com> wrote:
>>> Nikos Kakouros wrote:
>>>
>>> I'd like to first apologize upfront for the lack of specificity in my
>>> question - please be sensitive to my lack of experience with Stata. :)
>>>
>>> I have two tests that are meant to measure the same thing (blood
>>> thickness) but with totally different units. On the whole they
>>> correlate well (patients with thick blood have higher values on both
>>> measurements), but the first test is affected (on univariate analysis)
>>> by another blood parameter but the second test is not. Their
>>> correlation is, therefore, dependent on the third parameter.
>>>
>>> I would appreciate on comments/advice on how to best visually show
>>> this relationship in Stata. I was thinking the following: convert all
>>> measurements to z-scores and depict the difference in z-score for the
>>> two measurements at different values (y axis) vs the value of the
>>> third variable that affects one of the tests more than the other
>>> (x-axis).
>>>
>>> Is anyone familiar with such a visualization?
>>>
>>> --------------------------------------------------------------------------------
>>>
>>> I'm not familiar with it.  Would a scatterplot matrix (SPLOM) help?
>>> (See -help graph matrix-.)
>>>
>>> Joseph Coveney
>>>
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```