From: http://statland.org/R/Rchisq.htm
1. Chi-square with R
R can do all the usual chi-square tests, with either raw data or tables of counts. We start with the heart attack
data and the Goodness-of-Fit test.
> names(heartatk)
[1] "Patient"
"DIAGNOSIS" "SEX"
[7] "LOS"
"AGE"
"DRG"
"DIED"
"CHARGES"
> attach(heartatk)
> table(SEX)
SEX
F
M
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> chisq.test(table(SEX))
Chi-squared test for given probabilities
data: table(SEX)
X-squared = 573.4815, df = 1, p-value < 2.2e-16
The command chisq.test(table(SEX)) does a chi-square goodness of fit test on the table for the SEX
variable. The default is to test for equal expected counts in every cell. That is hardly the case here. 2.2e-16
means 2.2X10-16 = 0.00000000000000022, which is small.
If you do not want equal proportions, you need to give a set of proportions for each cell. For example, genetic
theory predicts that certain fruit flies will fall into four categories in proportions 9:3:3:1. Data showed counts of
59, 20, 11 and 10.
> chisq.test(c(59,20,11,10),p=c(9/16,3/16,3/16,1/16))
Chi-squared test for given probabilities
data: c(59, 20, 11, 10)
X-squared = 5.6711, df = 3, p-value = 0.1288
We would not reject the theoretical hypothesis with these data.
You can make a cross-tabulation of two categorical variables with table and do a test of independence or
homogeneity with chisq.test. (We return to the heart attack data.)
> table(SEX,DIED)
DIED
SEX
0
1
F 4298 767
M 7136 643
> chisq.test(table(SEX,DIED))
Pearson's Chi-squared test with Yates' continuity correction
data: table(SEX, DIED)
X-squared = 147.7612, df = 1, p-value < 2.2e-16
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We have seen this p-value before! It is probably the smallest non-zero number R can handle and hence not
very accurate. However, p is definitely small! Hence we reject the hypothesis that the mortality rate is the
same for men and women. Looking at the data, it is higher for men.
With 12,844 observations, getting the table is a lot more work than computing chi-square, and it is best to let
the computer do it. If you have an existing table, R will analyze it -- but not without putting up a fight. You need
to enter the table one row at a time and use rbind to combine the rows into a table. Here is some data on
hepatitis C incidence (yes,no) and tattoo "status": from a parlor, elsewhere, and no tattoo.
> hep=rbind(c(17,35),c(8,53),c(22,491))
> hep
[,1] [,2]
[1,]
17
35
[2,]
8
53
[3,]
22 491
> chisq.test(hep)
Pearson's Chi-squared test
data: hep
X-squared = 57.9122, df = 2, p-value = 2.658e-13
Warning message:
Chi-squared approximation may be incorrect in: chisq.test(hep)
The warning message probably refers to the small expected count the cell where the 8 appears. You could
overcome that by pooling the two tattoo sources together. Either way, getting tattoos seems to greatly
increase the risk of hepatitis C.
http://statland.org/R/
2. Reading Tables into R
In school, we work mainly with tiny datasets we can type into our technology if all else fails. In practice, we
generally start with raw data in a computer file. Often, getting the data into a form our technology can work
with is a major undertaking. We will go through that once right now.
R can read data from a text file. The text file has to be in the form of a table with columns representing
variables. All columns must be the same length. Missing data must be signified by "NA". Optionally, the first
row of the file may contain names for the variables. You can access such a file named heartatk4R.txt. Download
and save this file in the directory where the R program lives. The file looks like this.
Patient
1
2
3
4
5
6
7
8
9
10
11
12
DIAGNOSIS
41041
F
41041
F
41091
F
41081
F
41091
M
41091
M
41091
F
41091
F
41041
M
41041
F
41041
F
41091
M
SEX
122
122
122
122
122
121
121
121
121
123
121
121
DRG
0
0
0
0
0
0
0
0
0
1
0
0
DIED
CHARGES
4752
0010
3941
0006
3657
0005
1481
0002
1681
0001
6378.6400
10958.520
16583.930
4015.3300
1989.4400
7471.6300
3930.6300
LOS
079
034
076
080
055
0009
0015
0015
0002
0001
0006
0005
AGE
084
084
070
076
065
052
072
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13
14
15
16
17
41091
41091
41041
41041
41041
F
F
M
M
M
122
122
122
122
121
0
0
0
0
0
¥
0009
4433.9300
3318.2100
4863.8300
5000.6400
083
0004
0002
0005
0003
061
053
077
053
Above are only the first 17 cases (of 12,844). To use this in R you must define a variable to be equal to the
contents of this file.
> heartatk = read.table("heartatk4R.txt",header=TRUE)
The argument header=TRUE tells R that the first row of the file should be interpreted as variable names.
(These should not include spaces.) You can now get a table of contents for what you have created in R with
> objects()
This should return heartatk along with any other variables you may have created. You will not see on this list
any of the variables that are inside of heartatk because they are hiding. To see them, type
> names(heartatk)
[1] "Patient"
"DIAGNOSIS" "SEX"
[7] "LOS"
"AGE"
"DRG"
"DIED"
"CHARGES"
To bring them out of hiding, you must "attach" them to your R workspace. (This avoids conflicts if several
tables include variables with the same name. Attach just one at a time.)
> attach(heartatk)
These data came from an ActivStats CD which provided this background information:
Heart Attack Patients
This set of data is all of the hospital discharges in New York State with an
admitting diagnosis
of an Acute Myocardial Infarction (AMI), also called a heart attack, who did not
have surgery,
in the year 1993. There are 12,844 cases.
AGE gives age in years
SEX is coded M for males F for females
DIAGNOSIS is in the form of an International Classification of Diseases, 9th
Edition, Clinical
Modification code. These tell which part of the heart was affected.
DRG is the Diagnosis Related Group. It groups together patients with similar
management.
In this data set there are just three different drgs.
121 for AMIs with cardiovascular complications who did not die.
122 for AMIs without cardiovascular complications who did not die.
123 for AMIs where the patient died.
LOS gives the hospital length of stay in days.
DIED has a 1 for patients who died in hospital and a 0 otherwise.
CHARGES gives the total hospital charges in dollars.
Data
provided by Health Process Management of Doylestown, PA.
After you attach the data table you can work with the internal variables providing you remember that R is casesensitive.
> table(sex)
Error in table(sex) : object "sex" not found
> table(SEX)
SEX
F
M
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© 2006 Robert W. Hayden. Data Desk is a registered trademark of Data Description.
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