Chi-squared test when observed near expected

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
project.org] On Behalf Of Troy S
Sent: Monday, December 03, 2012 3:41 PM
To: r-help at r-project.org
Subject: [R] Chi-squared test when observed near expected

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

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