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These examples use the G.test function in the RVAideMemoire package, but the GTest function in the DescTools package could be used in the same manner.
See the Handbook for information on these topics.
How to do the test
Repeated G–tests of goodness-of-fit example
###
--------------------------------------------------------------
### Arm crossing example, Repeated G–tests of goodness-of-fit,
### pp. 91–93
### --------------------------------------------------------------
Input =("
Ethnic.group R L
Yemen 168 174
Djerba 132 195
Kurdistan 167 204
Libya 162 212
Berber 143 194
Cochin 153 174
")
Data = read.table(textConnection(Input),header=TRUE)
Individual G-tests
library(RVAideMemoire)
Fun.G = function (Q){ # Functions
G.test(x=c(Q["R"], Q["L"]), # to calculate
p=c(0.5, 0.5) #
individual G’s,
)$statistic #
df’s, and p-values
}
Fun.df = function (Q){
G.test(x=c(Q["R"], Q["L"]),
p=c(0.5, 0.5)
)$parameter
}
Fun.p = function (Q){
G.test(x=c(Q["R"], Q["L"]),
p=c(0.5, 0.5)
)$p.value
}
library(dplyr)
Data=
mutate(Data,
Prop.R = R / (R + L), #
Calculate proportion
#
of right arms
G = apply(Data[c("R", "L")], 1, Fun.G),
df = apply(Data[c("R", "L")], 1, Fun.df),
p.Value = apply(Data[c("R", "L")], 1, Fun.p)
)
Data
Ethnic.group R L Prop.R G df p.Value
1 Yemen 168 174 0.4912281 0.1052686 1 0.745596489
2 Djerba 132 195 0.4036697 12.2138397 1 0.000474363
3 Kurdistan 167 204 0.4501348 3.6961684 1 0.054537574
4 Libya 162 212 0.4331551 6.7045477 1 0.009616732
5 Berber 143 194 0.4243323 7.7478346 1 0.005377698
6 Cochin 153 174 0.4678899 1.3495524 1 0.245356383
Heterogeneity G-test
Data.matrix = as.matrix(Data[c("R", "L")]) # We need a data matrix
#
to run G-test
Data.matrix #
for heterogeneity
R L
[1,] 168 174
[2,] 132 195
[3,] 167 204
[4,] 162 212
[5,] 143 194
[6,] 153 174
G.test(Data.matrix) # Heterogeneity
G-test
G = 6.7504, df = 5, p-value = 0.2399
Pooled G-test
Total.R = sum(Data$R) # Set up data for pooled
Total.L = sum(Data$L) #
G-test
observed = c(Total.R, Total.L)
expected = c(0.5, 0.5)
G.test(x=observed,
p=expected)
G-test for given probabilities
G = 25.0668, df = 1, p-value = 5.538e-07
Total G-test
Total.G = sum(Data$G) # Set up data for total
#
G-test
Total.df = sum(Data$df)
Total.G #
Total
[1] 31.81721
Total.df
[1] 6
pchisq(Total.G,
df= Total.df,
lower.tail=FALSE)
[1] 1.768815e-05
# # #
Example
Repeated G–tests of goodness-of-fit example
###
--------------------------------------------------------------
### Drosophila example, Repeated G–tests of goodness-of-fit,
### p. 93
### --------------------------------------------------------------
Input =("
Trial D S
'Trial 1' 296 366
'Trial 2' 78 72
'Trial 3' 417 467
")
Data = read.table(textConnection(Input),header=TRUE)
Individual G-tests
library(RVAideMemoire)
Fun.G = function (Q){ # Functions
G.test(x=c(Q["D"], Q["S"]), # to calculate
p=c(0.5, 0.5) #
individual G’s and
)$statistic #
p-values
}
Fun.df = function (Q){
G.test(x=c(Q["D"], Q["S"]),
p=c(0.5, 0.5)
)$parameter
}
Fun.p = function (Q){
G.test(x=c(Q["D"], Q["S"]),
p=c(0.5, 0.5)
)$p.value
}
library(dplyr)
Data =
mutate(Data,
G = apply(Data[c("D", "S")], 1, Fun.G),
df = apply(Data[c("D", "S")], 1, Fun.df),
p.Value = apply(Data[c("D", "S")], 1, Fun.p))
Data
Trial D S G df p.Value
1 Trial 1 296 366 7.415668 1 0.00646583
2 Trial 2 78 72 0.240064 1 0.62415986
3 Trial 3 417 467 2.829564 1 0.09254347
Heterogeneity G-test
Data.matrix = as.matrix(Data[c("D", "S")]) # We need a data matrix
#
to run G-test
Data.matrix #
for heterogeneity
D S
[1,] 296 366
[2,] 78 72
[3,] 417 467
G.test(Data.matrix) # Heterogeneity
G-test
G = 2.8168, df = 2, p-value = 0.2445
Pooled G-test
Total.D = sum(Data$D) # Set up data for pooled
Total.S = sum(Data$S) #
G-test
observed = c(Total.D, Total.S)
expected = c(0.5, 0.5)
G.test(x=observed, #
Pooled
p=expected)
G-test for given probabilities
G = 7.6685, df = 1, p-value = 0.005619
Total G-test
Total.G = sum(Data$G) # Set up data for total
#
G-test
degrees = 3
Total.G = sum(Data$G) #
Set up data for total
#
G-test
Total.df = sum(Data$df)
Total.G #
Total
[1] 10.4853
Total.df
[1] 3
pchisq(Total.G,
df=Total.df,
lower.tail=FALSE)
[1] 0.01486097
# # #
See the Handbook for information on these topics.