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RE: st: Line of equality in scatter plot


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Line of equality in scatter plot
Date   Thu, 9 Oct 2008 15:43:30 +0100

-concord- is a user-written program whose latest public version was
released through the Stata Journal in 2007. A even later version with
tweaked dialog will be released with Stata Journal 8(4) later this year.
See the help for -concord- for many further details, including
references. 

Please note also that -concord- has been written up and revised
intermittently over a period of 10 years now by Thomas Steichen and
myself. Almost all the publications on -concord- are visible to all
under the 3-year moving window policy of the Stata Journal (here
including the Stata Technical Bulletin). 

Also in this domain note -pairplot- from SSC. This includes a variety of
graphical handles. For example, as Ronan rightly says it is a good idea
to plot difference versus mean. On the other hand, if it's a better
approximation that two (strictly positive) variables vary
multiplicatively then the more natural plot is the logarithmic
equivalent, i.e. log of ratio vs geometric mean. See the help for
-pairplot- for more details. 

Nick
n.j.cox@durham.ac.uk 

Ronan Conroy

On 8 Oct 2008, at 15:59, LL Miller, Avon Longitudinal Study Parents  
and Children wrote:

> I'm trying to assess the reliability of a continuous variable with  
> the same
> variable assessed by a second person. I have used alpha var1 var2 to  
> get
> Cronbachs alpha but wanted to see what it is doing visually. I  
> created a
> scatter plot but can't find any option that will allow me to draw a  
> line on
> the plot through the diagonal i.e. where the points should fall if  
> there is
> no difference in the two assessments.

Now that you have been told how to do it, I wonder if you would  
consider why you are doing it!

A Limits of Agreement plot is a better way of expressing the agreement  
between two raters, neither of whom is the gold standard. It shows the  
average of the two raters for each observation (the best estimate of  
the observation's true value) against the difference between the  
raters. Your method does not display the differences but instead  
leaves it to the person to judge them by using an angled line -  
something that most people find hard.

It allows you to detect situations in which there is more agreement in  
some scale regions than others (for example, examiners may agree  
pretty well on a really bad and a really good student but may disagree  
more about mid-range student performance).

This is available by installing -concord- which will also give you a  
concordance coefficient between the raters.

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