[R] Chi-squared test when observed near expected

[David Winsemius]

On Dec 3, 2012, at 1:40 PM, Troy S wrote:

> Dear UseRs,
>
> I'm running a chi-squared test where the expected matrix is the same  
> as the
> observed, after rounding.

   ... after rounding you say?

>  R reports a X-squared of zero with a p value of
> one.  I can justify this because any other result will deviate at  
> least as
> much from the expected because what we observe is the expected, after
> rounding.  But the formula for X-squared, sum (O-E)^2/E gives a  
> positive
> value.

  If  O==E that sum would be identically 0 if the conditions stated  
held ...  which they do NOT for the case below.


>  What is the reason for X-Squared being zero in this case?
>
> Troy
>
>> trial<-as.table(matrix(c(26,16,13,7),ncol=2))
>> x<-chisq.test(trial)
>> x
>
>
>
> data:  trial
> X-squared = 0, df = 1, p-value = 1
>
>> x$expected
>         A         B
> A 26.41935 12.580645
> B 15.58065  7.419355
>>
>> x$statistic
>   X-squared
> 5.596653e-31
>> (x$observed-x$expected)^2/x$expected
>            A           B
> A 0.006656426 0.013978495
> B 0.011286983 0.023702665
>> sum((x$observed-x$expected)^2/x$expected)
> [1] 0.05562457
>>
>
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>
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David Winsemius, MD
Alameda, CA, USA