# [R] chisq.test, basic question

Jan_Svatos@eurotel.cz Jan_Svatos at eurotel.cz
Wed Jul 31 08:52:54 CEST 2002

```Hi,

your first use of chisq.test is correct.
But by multiplying by 100 and dividing by sum(m) (210), you analyze
different experiment
(with fewer "observations") and, in general, this is a _gross_ mistake.
In general, our example is (very basic, though) a well-known problem with
statistical vs. practical "significance".
Just try to chisq.test(2*m), chisq.test(3*m), etc.
With sufficiently large sample it is almost sure (in practical, not
mathematical meaning) that you get
statistically significant difference even when practical, "real-life"
difference is negligible.

An trivial example:
m<-matrix(c(100,101,110,115),2,2) #rows and cols are "practically"
independent
chisq.test(m)  #X-squared = 0.0065, df = 1, p-value = 0.9357
chisq.test(10*m)  #X-squared = 0.2823, df = 1, p-value = 0.5952
chisq.test(100*m)  #X-squared = 3.1241, df = 1, p-value = 0.07714
chisq.test(1000*m)  #X-squared = 31.551, df = 1, p-value = 1.943e-08

math-statistical principles behind chisq.test.

HTH,
Jan

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/- Jan Svatos,  PhD         Sokolovska 855/225 -/
/- Data Analyst             Prague 9           -/
/- Eurotel Praha            190 00             -/
/- jan_svatos at eurotel.cz    Czechia            -/
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- - - Original message: - - -
From: owner-r-help at stat.math.ethz.ch
Send: 30.7.2002 18:47:51
To: r-help <r-help at stat.math.ethz.ch>
Subject: [R] chisq.test, basic question

Dear R-users,
I have a question, which I?m not sure if it is related to my
misunderstanding of basic statistics, or my misunderstanding of R, or
both.
I?ve got the counts of a 2 x 2 contingency table, and I'd like to test
the association:

m <-  matrix(c(15,28,32,135), 2, 2)
colnames(m) <- c("R-", "R+"); rownames(m) <- c("P-", "P+")
m
#    R-  R+
# P- 15  32
# P+ 28 135

chisq.test(m)  # X-squared = 4.0027, df = 1, p-value = 0.04543

Is this the correct way to test association between P and R? (I haven?t
got the original data).
My problem is that if I use percentage, then I get different results:

m2 <- 100*m/sum(m) #
chisq.test(round(m2)) # X-squared = 1.5318, df = 1, p-value = 0.2158

Should this give about the same (a part from the rounding)? Should the
degree of association between P and R be he same?  Or, am I using
chisq.test() wrongly?

Juli

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```