cuzick.test: Rank-sum test for trend of ordered groups
In raredd/rawr: rawr miscellaneous

cuzick.test

R Documentation

Rank-sum test for trend of ordered groups

Description

An implementation of Cuzick's extension of the Wilcoxon rank-sum test to assess trend in data with three or more ordinal groups.

Usage

cuzick.test(x, ...)

## Default S3 method:
cuzick.test(
  x,
  g,
  details = wilcox.test,
  correct = TRUE,
  ...,
  simulate.p.value = FALSE,
  B = 2000L
)

## S3 method for class 'formula'
cuzick.test(formula, data, ...)

Arguments

`x`	a numeric vector of data values or a list of numeric data vectors; non-numeric elements of a list will be coerced with a warning; if `x` is a list, the list elements are assumed to be groups ordered as `x[[1]], x[[2]], ..., x[[n]]`
`...`	additional arguments passed to the function given by `details`
`g`	a vector or factor object giving the group for the corresponding elements of `x`, ignored with a warning if `x` is a list; if `g` is not a factor, it will be coerced, and groups will be ordered as `sort(unique(g))`; see `factor`
`details`	`FALSE` or a function to compute comparisons between pairs of groups; see details
`correct`	logical; if `TRUE`, a correction is applied to the standard error of the test statistic (default)
`simulate.p.value`	logical; if `TRUE`, p-value is computed using by Monte Carlo simulation
`B`	an integer specifying the number of replicates used in the Monte Carlo test
`formula`	a formula of the form `response ~ group` where `response` is a numeric variable and `group` is a factor-like variable with three or more unique values (groups)
`data`	an optional matrix or data frame (or similar: see `model.frame`) containing the variables in `formula`; by default, the variables are taken from `environment(formula)`

Details

Data are assumed to be from independent groups with a natural or meaningful order. If x and g are given as vectors and g is a factor, the order of levels(g) will be respected; however, if g is not a factor, it will be coerced, and the levels will be the same as levels(factor(g)).

For example, if g is (a character string of) c("5mg", "10mg", "15mg"), then the groups will be ordered as "10mg" "15mg" "5mg" which may not be desired.

Pairwise comparisons between each pair of groups is performed using the function given by details (default is wilcox.test); the overall will be compared by kruskal.test. Other functions may be used (e.g., in cases with ties), but these need a formula method similar to cuzick.test, wilcox.test, etc. Common methods such as wilcox_test or kruskal_test from the coin package will work; see examples.

Value

A list with class "htest" containing the following elements:

`statistic`	the value of the test statistic with a name describing it
`p.value`	the p-value for the test (two-sided, (un)corrected for ties)
`estimate`	the medians by group
`method`	a character string describing the test used
`data.name`	a character string giving the names of the data
`details`	a list of pairwise (`details`) and overall (`kruskal.test`) comparisons
`conf.int`	optionally, (if `simulate.p.value = TRUE`) the 99% confidence interval of the Monte Carlo p-value
`summary`	optionally (if `simulate.p.value = TRUE`), a summary of the simulated test statistics

References

Altman, D. G. 1991. Practical Statistics for Medical Research. London: Chapman & Hall/CRC.

Cuzick, J. 1985. A Wilcoxon-type test for trend. Statistics in Medicine 4: 87-90.

Examples

## Altman (1991), 217
## ocular exposure to ultraviolet radiation for 32 pairs of sunglasses
## classified into three groups according to the amount of visible light
## transmitted

x <- list(c(1.4, 1.4, 1.4, 1.6, 2.3, 2.5),
          c(0.9, 1.0, 1.1, 1.1, 1.2, 1.2,
            1.5, 1.9, 2.2, 2.6, 2.6, 2.6,
            2.8, 2.8, 3.2, 3.5, 4.3, 5.1),
          c(0.8, 1.7, 1.7, 1.7, 3.4, 7.1, 8.9, 13.5))
cuzick.test(x, correct = FALSE)


## equivalent ways to call cuzick.test
cuzick.test(x)
cuzick.test(unlist(x), rep(seq_along(x), lengths(x)))
cuzick.test(x ~ g, data.frame(x = unlist(x), g = rep(1:3, lengths(x))))


## all pairwise comparisons are returned by default in $details
cuzick.test(x)$details
cuzick.test(x, alternative = 'less', correct = FALSE)$details
cuzick.test(x, details = kruskal.test)$details
cuzick.test(x, details = t.test)$details
# cuzick.test(x, details = coin::wilcox_test)$details


## Cuzick (1985), 87-90
## mice inoculated with five cell lines which had been selected for their
## increasing metastatic potential; number of lung metastases found in each
## mouse after inoculation

x <- list(
  'CMT 64'  = c(0, 0, 1, 1, 2, 2, 4, 9),
  'CMT 167' = c(0, 0, 5, 7, 8, 11, 13, 23, 25, 97),
  'CMT 170' = c(2, 3, 6, 9, 10, 11, 11, 12, 21),
  'CMT 175' = c(0, 3, 5, 6, 10, 19, 56, 100, 132),
  'CMT 181' = c(2, 4, 6, 6, 6, 7, 18, 39, 60)
)
cuzick.test(x)$p.value / 2 ## one-sided (corrected for ties)


## coercing character group vector g to factor may have undesired order
set.seed(1)
x  <- sort(rnorm(20))
g1 <- sample(paste0(c(5, 10, 15), 'mg'), 20, replace = TRUE)
g2 <- factor(g1, levels = paste0(c(5, 10, 15), 'mg'))

## wrong order
tplot(x ~ g1, data.frame(x, g1), type = 'db', test = cuzick.test)

## correct order
tplot(x ~ g2, data.frame(x, g2), type = 'db', test = cuzick.test)


## groups need not be equally-spaced but will affect statistic/p-value
set.seed(1)
x  <- sort(rnorm(20))
g1 <- sample(1:3, 20, replace = TRUE)
g2 <- g1 + (g1 == 3)

tplot(x, g1, test = cuzick.test)
tplot(x, g2, test = cuzick.test)
## compare
tplot(x, factor(g2), test = cuzick.test)

raredd/rawr documentation built on May 9, 2024, 6:14 p.m.