diggingnumbers:tests_of_association

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:

- the
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.`p-value`

- there's a warning about a possible approximation of the
value`χ-squared`

Other 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

Start · Data description · Transforming variables · Tables · Pictorial displays · Measures of position and variability · Sampling · Tests of difference · Tests of distribution · Correlation · **Tests of association**

diggingnumbers/tests_of_association.txt · Last modified: 2012/11/30 09:58 (external edit)