Re: Standardized vs. Adjusted Standardized Residuals for Statistically Significant Chi-Square

Posted by Rich Ulrich on May 28, 2014; 4:51am
URL: http://spssx-discussion.165.s1.nabble.com/Standardized-vs-Adjusted-Standardized-Residuals-for-Statistically-Significant-Chi-Square-tp5717593p5726234.html

Nice summary formulas.

When you recognize that the "expected" is the variance of a Poisson
count, then you see that the Standardized Residual is *exactly* a z-score,
to the extent that you can assume that the count is Poisson (mainly, being
a small part of the total).  In any case, the formula reveals that the SR reflects
the contribution of the cell to the total chi-squared for the contingency table,
when you write that as  Sum ( ((O-E)**2 )/E ) .

I occasionally glanced as these to find the oddest cell in a table, but I can't
say that I ever recommended either of them in publishing results.

--
Rich Ulrich

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Date: Tue, 27 May 2014 17:17:57 -0700
From: [hidden email]
Subject: Re: Standardized vs. Adjusted Standardized Residuals for Statistically Significant Chi-Square
To: [hidden email]

The names are misleading. 

Standardized residuals aren't standardized in the same sense that zscores are.

For a zscore , the deviation (residual) is divided by the standard deviation, i.e.  (x-xbar) / sd(x)

For a "standardized residual", the deviation is divided by the square root of the expectation

For an adjusted standardized residual, the deviation is adjusted by a quantity equivalent to the std dev

I would always recommend the adjusted variant.

Quoting from  http://www.geneseo.edu/~bearden/socl211/chisquareweb/chisquare.html

Standardized Residuals

Standardized residuals indicate the importance of the cell to the ultimate chi-square value. The standardized residuals are a kind of z-score indicating how many standard deviations above or below the expected count a particular observed count is. By comparing these standardized residuals you can easily identify the particular cells that contribute most to chi-square and will help you understand the association in the table.

<img src="http&#58;//www.geneseo.edu/&#126;bearden/socl211/chisquareweb/stdresid.png" alt="observed minus expected divided by the square root of the expected" style="" height="58" width="356">

Adjusted Residuals

Adjusted residuals are a related and more useful way to do the same thing.  Unlike the standardized residual, the adjusted residual takes into account the overall size of the sample and gives a fairer indication of how far off the observed count is from the expected count.

<img src="http&#58;//www.geneseo.edu/&#126;bearden/socl211/chisquareweb/adjresid.png" alt="observed minus expected divided by the square root of the expected" style="" height="52" width="543">

... Mark Miller

On Sun, May 25, 2014 at 10:15 PM, marc <[hidden email]> wrote:

Hi,

I don't think there were any responses to this query and so hoping my post
will at least make it to the author.  I'm afraid I'm not able to answer your
question well just yet (perhaps you've already found the answers!?), but
would like to get other's understanding of 'adjusted standardised residuals'
and how these differ to standardised residuals, which i've also seen
adjusted residuals.  I've been asked to provide ASRs but basic google
searches yield little clear on these specifically, compared to many hits on
ARs and SRs...

any thoughts and guidance on this would be great!

cheers!