[R] Chi-squared test when observed near expected

[(Ted Harding)]

On 03-Dec-2012 21:40:35 Troy S wrote:
> Dear UseRs,
> I'm running a chi-squared test where the expected matrix is the same
> as the observed, after rounding. 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. 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

The reason is that (by default, see ?chisq.test ) the statistic
is caluclated using the "continuity correction" (1/2 is subtracted
from each abs(O-E) difference). The default setting in chisq.test()
is "correct = TRUE". Try it with "correct = FALSE":

  x0<-chisq.test(trial,correct=FALSE)
  x0
  #      Pearson's Chi-squared test
  # data:  trial 
  # X-squared = 0.0556, df = 1, p-value = 0.8136

which agrees with your calculation of

  sum((x$observed-x$expected)^2/x$expected)
  # [1] 0.05562457

Hoping this helps,
Ted.

-------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at wlandres.net>
Date: 03-Dec-2012  Time: 22:44:14
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