The Chi-squared test is a common test of association between nominal or ordinal data. More powerful tests exist (see below), but the X-squared is by far the most simple one.
The statistics value is calculated as: <m>chi^2 = sum{}{}{{(O - E)^2}/E}</m>
Where O means Observed values and E means Expected values. See the book for a detailed explanation.
Produce a contingency table of Mat
by Period
, a new variable made from Date
to have three categories, and calculate chi-squared.
Creating the Period
variable from Date
has already been covered in “Transforming variables”:
> Period <- Date > Period[(Date>650)&(Date<=1200)] <- 1 > Period[(Date>100)&(Date<=650)] <- 2 > Period[(Date<=100)] <- 3
You should probably tell R these values aren't numbers but categories. Notice the difference:
> summary(Period) Min. 1st Qu. Median Mean 3rd Qu. Max. 1.00 1.00 1.50 1.55 2.00 3.00 > Period <- factor(Period) > Mat <- factor(Mat) > summary(Period) 1 2 3 20 18 2
This hasn't really effect on the following operations, but it helps you keeping a clean working environment.
> table(Mat,Period) Period Mat 1 2 3 1 20 0 0 2 0 18 2
See http://finzi.psych.upenn.edu/R/Rhelp02a/archive/2847.html for another method using xtabs()
.
We are now ready to perform the Chi-squared test:
> crosstab <- table(Mat,Period) > xtabs() # similar to table, but different results > chisq.test(crosstab) Pearson`s Chi-squared test data: table(Mat, Period) X-squared = 40, df = 2, p-value = 2.061e-09 Warning message: In chisq.test(table(Mat, Period)) : Chi-squared approximation may be incorrect
This result is OK, but has some differences from the one you would get doing all the operations by hand:
p-value
is not a fixed one (because you're not using tables), but rather a floating point number, expressed in scientific notation. It is very low however.χ-squared
valueOther tests of association mentioned in Digging Numbers don't seem so widely used, and this is probably the reason why they are not part of the standard R distribution.
This test is included in the cramer
contributed package
This test is included in the contributed package Kendall
. See
Kendall's tau-c is not included in any package, but it can be defined as a custom function. See https://stat.ethz.ch/pipermail/r-help/2006-September/112806.html
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