R devel - Oct 2005 - Yates' correction for continuity in chisq.test (PR#8265)

Full_Name: foo ba baz
Version: R2.2.0
OS: Mac OS X (10.4)
Submission from: (NULL) (219.66.32.183)


chisq.test(matrix(c(9,10,9,11),2,2))

Chi-square value must be 0, and, P value must be 0
R does over correction

when | a d - b c | < n / 2 &#65292;chi-sq must be 0

dih69530 at syd.odn.ne.jp wrote:
> Full_Name: foo ba baz
> Version: R2.2.0
> OS: Mac OS X (10.4)
> Submission from: (NULL) (219.66.32.183)
> 
> 
> chisq.test(matrix(c(9,10,9,11),2,2))
> 
> Chi-square value must be 0, and, P value must be 0
> R does over correction
> 
> when | a d - b c | < n / 2 &#65292;chi-sq must be 0
> 
(Presumably, you mean P-value = 1.)
If you don't want the correction, set correct=FALSE. (The
results won't differ much.)

A better example is

  chisq.test(matrix(c(9,10,9,10),2,2))

for which R probably should return X-squared = 0.

Peter Ehlers

On Sun, 30 Oct 2005, P Ehlers wrote:
> dih69530 at syd.odn.ne.jp wrote:
>> Full_Name: foo ba baz
>> Version: R2.2.0
>> OS: Mac OS X (10.4)
>> Submission from: (NULL) (219.66.32.183)
>>
>>
>> chisq.test(matrix(c(9,10,9,11),2,2))
>>
>> Chi-square value must be 0, and, P value must be 0
>> R does over correction
>>
>> when | a d - b c | < n / 2 &#65292;chi-sq must be 0
>
> (Presumably, you mean P-value = 1.)
> If you don't want the correction, set correct=FALSE. (The
> results won't differ much.)
>
> A better example is
>
>  chisq.test(matrix(c(9,10,9,10),2,2))
>
> for which R probably should return X-squared = 0.
R is using the correction that almost all the sources I looked at suggest. 
You can't go around adjusting X^2 for just some values of the data: the 
claim is that the adjusted statistic has a more accurate chisq 
distribution under the null.

I think at this remove it does not matter what Yates' suggested (although 
if I were writing a textbook I would find out), especially as the R 
documentation does not mention Yates.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

Prof Brian Ripley wrote:
> On Sun, 30 Oct 2005, P Ehlers wrote:
> 
>> dih69530 at syd.odn.ne.jp wrote:
>>
>>> Full_Name: foo ba baz
>>> Version: R2.2.0
>>> OS: Mac OS X (10.4)
>>> Submission from: (NULL) (219.66.32.183)
>>>
>>>
>>> chisq.test(matrix(c(9,10,9,11),2,2))
>>>
>>> Chi-square value must be 0, and, P value must be 0
>>> R does over correction
>>>
>>> when | a d - b c | < n / 2 &#65292;chi-sq must be 0
>>
>>
>> (Presumably, you mean P-value = 1.)
>> If you don't want the correction, set correct=FALSE. (The
>> results won't differ much.)
>>
>> A better example is
>>
>>  chisq.test(matrix(c(9,10,9,10),2,2))
>>
>> for which R probably should return X-squared = 0.
> 
> 
> R is using the correction that almost all the sources I looked at 
> suggest. You can't go around adjusting X^2 for just some values of the 
> data: the claim is that the adjusted statistic has a more accurate chisq 
> distribution under the null.
> 
> I think at this remove it does not matter what Yates' suggested 
> (although if I were writing a textbook I would find out), especially as 
> the R documentation does not mention Yates.
> 
You're quite right that, for consistency, the correction should be
applied even in the silly example I gave. And, of course, one
should not be doing a chisquare test on silly examples.

Peter Ehlers

On Mon, 31 Oct 2005, Prof Brian Ripley wrote:
> On Sun, 30 Oct 2005, P Ehlers wrote:
>
>> dih69530 at syd.odn.ne.jp wrote:
>>> Full_Name: foo ba baz
>>> Version: R2.2.0
>>> OS: Mac OS X (10.4)
>>> Submission from: (NULL) (219.66.32.183)
>>> 
>>> 
>>> chisq.test(matrix(c(9,10,9,11),2,2))
>>> 
>>> Chi-square value must be 0, and, P value must be 0
>>> R does over correction
>>> 
>>> when | a d - b c | < n / 2 &#65292;chi-sq must be 0
>> 
>> (Presumably, you mean P-value = 1.)
>> If you don't want the correction, set correct=FALSE. (The
>> results won't differ much.)
>> 
>> A better example is
>> 
>>  chisq.test(matrix(c(9,10,9,10),2,2))
>> 
>> for which R probably should return X-squared = 0.
>
> R is using the correction that almost all the sources I looked at suggest. 
> You can't go around adjusting X^2 for just some values of the data: the
claim
> is that the adjusted statistic has a more accurate chisq distribution under
> the null.
>
> I think at this remove it does not matter what Yates' suggested
(although if
> I were writing a textbook I would find out), especially as the R 
> documentation does not mention Yates.
I have now checked Yates (1934), Fisher's 'Statistical Methods for 
Research Workers' and the Encyclopedia of Statistical Sciences.  The first 
two are vague (and could perhaps be read as not correcting O-E = 0), but 
the latter agrees with R in giving a formula which always subtracts 1/2. 
Also, it mentions that Pearson stated that the formula for the continuity 
correction long preceded Yates' publication, so it is perhaps reasonable 
not to mention Yates.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595