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Chi-squared test when observed near expected
5 messages · Troy S, William Dunlap, (Ted Harding) +2 more
sum((x$observed-x$expected)^2/x$expected)
[1] 0.05562457
Read about Yate's continuity correction - your formula does not use it
and chisq.test does unless you suppress it:
> chisq.test(trial)
Pearson's Chi-squared test with Yates' continuity correction
data: trial
X-squared = 0, df = 1, p-value = 1
> chisq.test(trial, correct=FALSE)
Pearson's Chi-squared test
data: trial
X-squared = 0.0556, df = 1, p-value = 0.8136
Bill Dunlap
Spotfire, TIBCO Software
wdunlap tibco.com
-----Original Message----- From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Troy S Sent: Monday, December 03, 2012 1:41 PM To: r-help at r-project.org Subject: [R] Chi-squared test when observed near expected Dear UseRs, I'm running a chi-squared test where the expected matrix is the same as the observed, after rounding. R reports a X-squared of zero with a p value of one. I can justify this because any other result will deviate at least as much from the expected because what we observe is the expected, after rounding. But the formula for X-squared, sum (O-E)^2/E gives a positive value. What is the reason for X-Squared being zero in this case? Troy
trial<-as.table(matrix(c(26,16,13,7),ncol=2)) x<-chisq.test(trial) x
data: trial X-squared = 0, df = 1, p-value = 1
x$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$expected)
[1] 0.05562457
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______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
On 03-Dec-2012 21:40:35 Troy S wrote:
Dear UseRs, I'm running a chi-squared test where the expected matrix is the same as the observed, after rounding. R reports a X-squared of zero with a p value of one. I can justify this because any other result will deviate at least as much from the expected because what we observe is the expected, after rounding. But the formula for X-squared, sum (O-E)^2/E gives a positive value. What is the reason for X-Squared
being zero in this case?
Troy
trial<-as.table(matrix(c(26,16,13,7),ncol=2)) x<-chisq.test(trial) x
data: trial X-squared = 0, df = 1, p-value = 1
x$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 This message was sent by XFMail
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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______________________________________________ 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
When you typed x as a command, R runs the command print(x). That function produces a summary of the results which may include round off numbers to a few decimal places to make them more readable. When you typed x$statistic, you got the unrounded version of the result 5.6e-31 which I think you will agree is pretty close to 0. ---------------------------------------------- David L Carlson Associate Professor of Anthropology Texas A&M University College Station, TX 77843-4352
-----Original Message----- From: r-help-bounces at r-project.org [mailto:r-help-bounces at r- project.org] On Behalf Of Troy S Sent: Monday, December 03, 2012 3:41 PM To: r-help at r-project.org Subject: [R] Chi-squared test when observed near expected Dear UseRs, I'm running a chi-squared test where the expected matrix is the same as the observed, after rounding. R reports a X-squared of zero with a p value of one. I can justify this because any other result will deviate at least as much from the expected because what we observe is the expected, after rounding. But the formula for X-squared, sum (O-E)^2/E gives a positive value. What is the reason for X-Squared being zero in this case? Troy
trial<-as.table(matrix(c(26,16,13,7),ncol=2)) x<-chisq.test(trial) x
data: trial X-squared = 0, df = 1, p-value = 1
x$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
[[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.