chi square vs proportions

[Maguin, Eugene]

Can anyone offer evaluations (or references to such) of a chi square test with yates correction versus a test of proportions for 2x2 crosstab tables with a cell (or two) having expected frequencies in the yates correction range.

Thanks, Gene Maguin

 

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[Bruce Weaver]

Hi Gene.  Assuming you don't have the (rare) situation where all marginal totals are fixed in advance, the N-1 Chi-square is a far better choice (IMO) than either Fisher's exact test (aka., the Fisher-Irwin test) or Pearson's Chi-square with Yates' correction.  Ian Campbell published a very nice simulation study a few years ago demonstrating the superiority of the N-1 Chi-square.  You can read a summary of it (and find an online calculator) on his website:

  http://www.iancampbell.co.uk/twobytwo/twobytwo.htm  -- Campbell's website
  http://onlinelibrary.wiley.com/doi/10.1002/sim.2832/full -- the article

And as it happens, when you have a 2x2 table, the N-1 Chi-square is equivalent to the test of "linear-by-linear association" that you see in the CROSSTABS output from SPSS.  If you have institutional access to Statistics in Medicine, you can find a short article supporting that claim here:

  http://onlinelibrary.wiley.com/doi/10.1002/sim.6808/full

I know one of the authors quite well.  ;-)  

HTH.

Maguin, Eugene wrote

Can anyone offer evaluations (or references to such) of a chi square test with yates correction versus a test of proportions for 2x2 crosstab tables with a cell (or two) having expected frequencies in the yates correction range.
Thanks, Gene Maguin


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[Anthony Babinec]

Gene, In addition to what Bruce has said, I believe the current wisdom
frowns on Yates correction. See Wikipedia.

https://en.wikipedia.org/wiki/Yates%27s_correction_for_continuity


Tony Babinec
[hidden email]

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[Rich Ulrich]

The rare situation where all marginals are fixed is achieved by,
for instance, having a fixed sample where the criterion is assessed
by a forced-choice to create a pre-set number of each of two outcomes;
or by a median-split (where, by the way, you would probably be better
off analyzing the actual numbers).

What the Yates correction achieves is a very good match to Fisher's
Exact Test for 2x2 tables, which also formally assumes that both sets
of marginal totals are fixed. 

A decade or so ago, I had a Stats-FAQ for questions posted to several
Usenet groups.  Here is a comment from that (by me) from 2001 about
a published dialogue from the 1980s:

  The company of other statisticians: Yates argued in the JRSS
  (Journal of the Royal Statistical Society, Series B, about 1982 or 3)
  that marginal totals should be treated as fixed, and almost all
  testing (but not quite *all*, I think) should use either Fisher's test,
  or the the Yates' correction which he (Yates) had devised 50 years
  earlier. He was fairly adamant about treating the marginals as fixed,
  almost always.

One of the co-participants in that published dialogue who opposed
Fisher's view during that discussion publicly changed his mind, a couple
of years later.  Those arguments partly pivot on whether you accept an
"average p" level or demand a "minimum p"; for the latter, Fisher and
Yates must be right.  But I still agree with Bruce's preference.

--
Rich Ulrich

> Date: Mon, 25 Jan 2016 13:42:23 -0700

> From: [hidden email]
> Subject: Re: chi square vs proportions
> To: [hidden email]
>
> Hi Gene. Assuming you don't have the (rare) situation where all marginal
> totals are fixed in advance, the N-1 Chi-square is a far better choice (IMO)
> than either Fisher's exact test (aka., the Fisher-Irwin test) or Pearson's
> Chi-square with Yates' correction. Ian Campbell published a very nice
> simulation study a few years ago demonstrating the superiority of the N-1
> Chi-square. You can read a summary of it (and find an online calculator) on
> his website:
>
> http://www.iancampbell.co.uk/twobytwo/twobytwo.htm -- Campbell's website
> http://onlinelibrary.wiley.com/doi/10.1002/sim.2832/full -- the article
>
> And as it happens, when you have a 2x2 table, the N-1 Chi-square is
> equivalent to the test of "linear-by-linear association" that you see in the
> CROSSTABS output from SPSS. If you have institutional access to Statistics
> in Medicine, you can find a short article supporting that claim here:
>
> http://onlinelibrary.wiley.com/doi/10.1002/sim.6808/full
>
> I know one of the authors quite well. ;-)
>
> HTH.
>
>
>
>
> Maguin, Eugene wrote
> > Can anyone offer evaluations (or references to such) of a chi square test
> > with yates correction versus a test of proportions for 2x2 crosstab tables
> > with a cell (or two) having expected frequencies in the yates correction
> > range.
> > Thanks, Gene Maguin
> >

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