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There are a few different options for performing G-tests of independence in R. One is the G.test function in the package RVAideMemoire. Another is the GTest function in the package DescTools.
When to use it
G-test example with functions in DescTools and RVAideMemoire
###
--------------------------------------------------------------
### Vaccination example, G-test of independence, pp. 68–69
### --------------------------------------------------------------
Input =("
Injection.area No.severe Severe
Thigh 4788 30
Arm 8916 76
")
Matriz = as.matrix(read.table(textConnection(Input),
header=TRUE,
row.names=1))
Matriz
library(DescTools)
GTest(Matriz,
correct="none") #
"none" "williams" "yates"
Log likelihood ratio (G-test) test of independence without correction
G = 2.1087, X-squared df = 1, p-value = 0.1465
library(RVAideMemoire)
G.test(Matriz)
G = 2.1087, df = 1, p-value = 0.1465 # Note values differ from
# the Handbook
# for this example
# # #
See the Handbook for information on these topics.
Post-hoc tests
For the following example of post-hoc pairwise testing, we’ll use the pairwise.G.test function from the package RVAideMemoire to make the task easier. Then we’ll use pairwise.table in the native stats package as an alternative.
Post-hoc pairwise G-tests with RVAideMemoire
###
--------------------------------------------------------------
### Post-hoc example, G-test of independence, pp. 69–70
### --------------------------------------------------------------
Input =("
Supplement No.cancer Cancer
'Selenium' 8177 575
'Vitamin E' 8117 620
'Selenium+E' 8147 555
'Placebo' 8167 529
")
Matriz = as.matrix(read.table(textConnection(Input),
header=TRUE,
row.names=1))
Matriz
library(RVAideMemoire)
G.test(Matriz)
G = 7.7325, df = 3, p-value = 0.05188
library(RVAideMemoire)
pairwise.G.test(Matriz,
p.method = "none") #
Can adjust p-values;
# see ?p.adjust for options
Selenium Vitamin E Selenium+E
Vitamin E 0.168 - -
Selenium+E 0.606 0.058 -
Placebo 0.187 0.007 0.422
Post-hoc pairwise G-tests with pairwise.table
As is, this function works on a matrix with two columns, and compares rows.
###
--------------------------------------------------------------
### Post-hoc example, G-test of independence, pp. 69–70
### --------------------------------------------------------------
Input =("
Supplement No.cancer Cancer
'Selenium' 8177 575
'Vitamin E' 8117 620
'Selenium+E' 8147 555
'Placebo' 8167 529
")
Matriz = as.matrix(read.table(textConnection(Input),
header=TRUE,
row.names=1))
Matriz
library(DescTools)
GTest(Matriz,
correct="none")
Log likelihood ratio (G-test) test of independence without correction
G = 7.7325, X-squared df = 3, p-value = 0.05188
FUN = function(i,j){
GTest(matrix(c(Matriz[i,1], Matriz[i,2],
Matriz[j,1], Matriz[j,2]),
nrow=2,
byrow=TRUE),
correct="none")$ p.value #
"none" "williams" "yates"
}
pairwise.table(FUN,
rownames(Matriz),
p.adjust.method="none") #
Can adjust p-values
# See
?p.adjust for options
Selenium Vitamin E Selenium+E
Vitamin E 0.1677388 NA NA
Selenium+E 0.6060951 0.058385135 NA
Placebo 0.1866826 0.007004601 0.4215013
# # #
See the Handbook for information on this topic.
Examples
G-tests with DescTools and RVAideMemoire
### --------------------------------------------------------------
### Helmet example, G-test of independence, p. 72
### --------------------------------------------------------------
Input =("
PSE Head.injury Other.injury
Helemt 372 4715
No.helmet 267 1391
")
Matriz = as.matrix(read.table(textConnection(Input),
header=TRUE,
row.names=1))
Matriz
library(DescTools)
GTest(Matriz,
correct="none") #
"none" "williams" "yates"
Log likelihood ratio (G-test) test of independence without correction
G = 101.54, X-squared df = 1, p-value < 2.2e-16
library(RVAideMemoire)
G.test(Matriz)
G = 101.5437, df = 1, p-value < 2.2e-16
# # #
### --------------------------------------------------------------
### Gardemann apolipoprotein example, G-test of independence,
### p. 72
### --------------------------------------------------------------
Input =("
Genotype No.disease Coronary.disease
ins.ins 268 807
ins.del 199 759
del.del 42 184
")
Matriz = as.matrix(read.table(textConnection(Input),
header=TRUE,
row.names=1))
Matriz
library(DescTools)
GTest(Matriz,
correct="none") #
"none" "williams" "yates"
Log likelihood ratio (G-test) test of independence without correction
G = 7.3008, X-squared df = 2, p-value = 0.02598
library(RVAideMemoire)
G.test(Matriz)
G = 7.3008, df = 2, p-value = 0.02598
# # #
Graphing is discussed above in the “Chi-square Test of Independence” section.
See the Handbook for information on these topics. Fisher’s exact test, chi-square test, and McNemar’s test are discussed elsewhere in this book.
How to do the test
G-test of independence with data as a data frame
In the following example, the data is read in as a data frame, and the xtabs function is used to tabulate the data and convert them to a contingency table.
###
--------------------------------------------------------------
### Gardemann apolipoprotein example, G-test of independence,
### SAS example, pp. 74–75
### Example using cross-tabulation
### --------------------------------------------------------------
Input =("
Genotype Health Count
ins-ins no_disease 268
ins-ins disease 807
ins-del no_disease 199
ins-del disease 759
del-del no_disease 42
del-del disease 184
")
Data.frame = read.table(textConnection(Input),header=TRUE)
### Cross-tabulate the data
Data.xtabs = xtabs(Count ~ Genotype + Health,
data=Data.frame)
Data.xtabs
Health
Genotype disease no_disease
del-del 184 42
ins-del 759 199
ins-ins 807 268
summary(Data.xtabs) # includes N and factors
Number of cases in table: 2259
Number of factors: 2
### G-tests
library(DescTools)
GTest(Data.xtabs,
correct="none") #
"none" "williams" "yates"
Log likelihood ratio (G-test) test of independence without correction
G = 7.3008, X-squared df = 2, p-value = 0.02598
library(RVAideMemoire)
G.test(Data.xtabs)
G = 7.3008, df = 2, p-value = 0.02598
# # #
To calculate power or required samples, follow examples in the “Chi-square Test of Independence” section.