HelpersMG (version 6.2)

contingencyTable.compare: Contingency table comparison using Akaike weight

Description

This function is used as a replacement of chisq.test() to not use p-value.

Usage

contingencyTable.compare(
  table,
  criterion = c("AIC", "AICc", "BIC"),
  probs = NULL
)

Value

The probability that a single proportion model is sufficient to explain the data

Arguments

table

A matrix or a data.frame with series in rows and number of each category in column

criterion

Which criterion is used for model selection

probs

Series of probabilities used for conformity comparison

Author

Marc Girondot

Details

contingencyTable.compare compares contingency table using Akaike weight.

References

Girondot, M., Guillon, J.-M., 2018. The w-value: An alternative to t- and X2 tests. Journal of Biostatistics & Biometrics 1, 1-4.

See Also

Other w-value functions: compare(), series.compare()

Examples

if (FALSE) {
library("HelpersMG")

# Symmetry of Lepidochelys olivacea scutes
table <- t(data.frame(SriLanka=c(200, 157), AfricaAtl=c(19, 12), 
                      Guyana=c(8, 6), Suriname=c(162, 88), 
                      MexicoPac1984=c(42, 34), MexicoPac2014Dead=c(8, 9),
                      MexicoPac2014Alive=c(13, 12), 
                      row.names =c("Symmetric", "Asymmetric")))
table
contingencyTable.compare(table)

table <- t(data.frame(SriLanka=c(200, 157), AfricaAtl=c(19, 12), Guyana=c(8, 6),
                      Suriname=c(162, 88), MexicoPac1984=c(42, 34), 
                      MexicoPac2014Dead=c(8, 9),
                      MexicoPac2014Alive=c(13, 12), Lepidochelys.kempii=c(99, 1), 
                      row.names =c("Symmetric", "Asymmetric")))
table
contingencyTable.compare(table)

# Conformity to a model
table <- matrix(c(33, 12, 25, 75), ncol = 2, byrow = TRUE)
probs <- c(0.5, 0.5)
contingencyTable.compare(table, probs=probs)

# Conformity to a model
table <- matrix(c(33, 12), ncol = 2, byrow = TRUE)
probs <- c(0.5, 0.5)
contingencyTable.compare(table, probs=probs)

# Conformity to a model
table <- matrix(c(33, 12, 8, 25, 75, 9), ncol = 3, byrow = TRUE)
probs <- c(0.8, 0.1, 0.1)
contingencyTable.compare(table, probs=probs)

# Comparison of chisq.test() and this function
table <- matrix(c(NA, NA, 25, 75), ncol = 2, byrow = TRUE)

pv <- NULL
aw <- NULL
par(new=FALSE)
n <- 100

for (GroupA in 0:n) {
  table[1, 1] <- GroupA
  table[1, 2] <- n-GroupA
  pv <- c(pv, chisq.test(table)$p.value)
  aw <- c(aw, contingencyTable.compare(table, criterion="BIC")[1])
}

x <- 0:n
y <- pv
y2 <- aw
plot(x=x, y=y, type="l", bty="n", las=1, xlab="Number of type P in Group B", ylab="Probability", 
     main="", lwd=2)
lines(x=x, y=y2, type="l", col="red", lwd=2)

# w-value
(l1 <- x[which(aw>0.05)[1]])
(l2 <- rev(x)[which(rev(aw)>0.05)[1]])

aw[l1]
pv[l1]

aw[l2+2]
pv[l2+2]

# p-value
l1 <- which(pv>0.05)[1]
l2 <- max(which(pv>0.05))

aw[l1]
pv[l1]

aw[l2]
pv[l2]

y[which(y2>0.05)[1]]
y[which(rev(y2)>0.05)[1]]

par(xpd=TRUE)
text(x=25, y=1.15, labels="Group A: 25 type P / 100", pos=1)

segments(x0=25, y0=0, x1=25, y1=1, lty=3)

# plot(1, 1)

v1 <- c(expression(italic("p")*"-value"), expression("after "*chi^2*"-test"))
v2 <- c(expression(italic("w")*"-value for A"), expression("and B identical models"))
legend("topright", legend=c(v1, v2), 
       y.intersp = 1, 
       col=c("black", "black", "red", "red"), bty="n", lty=c(1, 0, 1, 0))

segments(x0=0, x1=n, y0=0.05, y1=0.05, lty=2)
text(x=101, y=0.05, labels = "0.05", pos=4)
}