Exact Page Test for Ordered Alternatives
Performs a Page test for ordered alternatives using an exact algorithm by Stefan Wellek (1989) with unreplicated blocked data.
PageTest(y, ...) ## Default S3 method: PageTest(y, groups, blocks, ...) ## S3 method for class 'formula' PageTest(formula, data, subset, na.action, ...)
y |
either a numeric vector of data values, or a data matrix. |
groups |
a vector giving the group for the corresponding
elements of |
blocks |
a vector giving the block for the corresponding
elements of |
formula |
a formula of the form |
data |
an optional matrix or data frame (or similar: see
|
subset |
an optional vector specifying a subset of observations to be used. |
na.action |
a function which indicates what should happen when
the data contain |
... |
further arguments to be passed to or from methods. |
PageTest can be used for analyzing unreplicated complete
block designs (i.e., there is exactly one observation in y
for each combination of levels of groups and blocks)
where the normality assumption may be violated.
The null hypothesis is that apart from an effect of blocks,
the location parameter of y is the same in each of the
groups.
The implemented alternative is, that the location parameter will be monotonly greater along the groups,
H_{A}: θ_{1} ≤ θ_{2} ≤ θ_{3} ... (where at least one inequality is strict).
If the other direction is required, the order of the groups has to be reversed.
The Page test for ordered alternatives is slightly more powerful than
the Friedman analysis of variance by ranks.
If y is a matrix, groups and blocks are
obtained from the column and row indices, respectively. NA's
are not allowed in groups or blocks; if y
contains NA's, corresponding blocks are removed.
For small values of k (methods) or N (data objects), PageTest will calculate the exact p-values. For k, N > 15, Inf, a normal approximation is returned. Only one of these values will be returned.
A list with class "htest" containing the following components:
statistic |
the L-statistic with names attribute “L”. |
p.value |
the p-value of the test. |
method |
the character string |
data.name |
a character string giving the names of the data. |
Special thanks to Prof. S. Wellek for porting old GAUSS code to R.
Stefan Wellek <stefan.wellek@zi-mannheim.de> (exact p-values), Andri Signorell <andri@signorell.net> (interface) (strongly based on R-Core code)
Page, E. (1963): Ordered hypotheses for multiple treatments: A significance test for linear ranks. Journal of the American Statistical Association, 58, 216-230.
Siegel, S. & Castellan, N. J. Jr. (1988): Nonparametric statistics for the behavioral sciences. Boston, MA: McGraw-Hill.
Wellek, S. (1989): Computing exact p-values in Page's nonparametric test against trend. Biometrie und Informatik in Medizin und Biologie 20, 163-170
# Craig's data from Siegel & Castellan, p 186
soa.mat <- matrix(c(.797,.873,.888,.923,.942,.956,
.794,.772,.908,.982,.946,.913,
.838,.801,.853,.951,.883,.837,
.815,.801,.747,.859,.887,.902), nrow=4, byrow=TRUE)
PageTest(soa.mat)
# Duller, pg. 236
pers <- matrix(c(
1, 72, 72, 71.5, 69, 70, 69.5, 68, 68, 67, 68,
2, 83, 81, 81, 82, 82.5, 81, 79, 80.5, 80, 81,
3, 95, 92, 91.5, 89, 89, 90.5, 89, 89, 88, 88,
4, 71, 72, 71, 70.5, 70, 71, 71, 70, 69.5, 69,
5, 79, 79, 78.5, 77, 77.5, 78, 77.5, 76, 76.5, 76,
6, 80, 78.5, 78, 77, 77.5, 77, 76, 76, 75.5, 75.5
), nrow=6, byrow=TRUE)
colnames(pers) <- c("person", paste("week",1:10))
# Alternative: week10 < week9 < week8 ...
PageTest(pers[, 11:2])
# Sachs, pg. 464
pers <- matrix(c(
3,2,1,4,
4,2,3,1,
4,1,2,3,
4,2,3,1,
3,2,1,4,
4,1,2,3,
4,3,2,1,
3,1,2,4,
3,1,4,2),
nrow=9, byrow=TRUE, dimnames=list(1:9, LETTERS[1:4]))
# Alternative: B < C < D < A
PageTest(pers[, c("B","C","D","A")])
# long shape and formula interface
plng <- data.frame(expand.grid(1:9, c("B","C","D","A")),
as.vector(pers[, c("B","C","D","A")]))
colnames(plng) <- c("block","group","x")
PageTest(plng$x, plng$group, plng$block)
PageTest(x ~ group | block, data = plng)
score <- matrix(c(
3,4,6,9,
4,3,7,8,
3,4,4,6,
5,6,8,9,
4,4,9,9,
6,7,11,10
), nrow=6, byrow=TRUE)
PageTest(score)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.