Chi-squared test when observed near expected
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
[[alternative HTML version deleted]]
______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
David Winsemius, MD Alameda, CA, USA