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.hard...@wlandres.net> Date: 03-Dec-2012 Time: 22:44:14 This message was sent by XFMail ______________________________________________ R-help@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.
