page.test {cultevo}  R Documentation 
Page test for monotonicity of ranks.
Description
Given N
replications of k
different treatments/conditions,
tests whether the median ordinal ranks m_i
of the treatments
are identical
m_1 = m_2 = \ldots = m_k
against the alternative hypothesis
m_1 \leq m_2 \leq \ldots \leq m_k
where at least one of the inequalities is a strict inequality (Siegel and Castellan 1988, p.184). Given that even a single point change in the distribution of ranks across conditions represents evidence against the null hypothesis, the Page test is simply a test for some ordered differences in ranks, but not a 'trend test' in any meaningful way (see also the Page test tutorial).
Usage
page.test(data, verbose = TRUE)
page.L(data, verbose = TRUE, ties.method = "average")
page.compute.exact(k, N, L)
Arguments
data 
a matrix with the different conditions along its 
verbose 
whether to print the final rankings based on which the L statistic is computed 
ties.method 
how to resolve tied ranks. Passed on to

k 
number of conditions/generations 
N 
number of replications/chains 
L 
value of the Page L statistic 
Details
Tests the given matrix for monotonically increasing ranks across k
linearly ordered conditions (along columns) based on N
replications
(along rows). To test for monotonically decreasing ranks, either reverse
the order of columns, or simply invert the rank ordering by calling 
on
the entire dataset.
Exact pvalues are computed for k
up to 22, using the precomputed null
distributions from the
pspearman package. For
larger k
, pvalues are computed based on a Normal distribution
approximation (Siegel and Castellan, 1988).
Value
page.test
returns a list of class pagetest
(and
htest
) containing the following elements:
statistic
value of the L statistic for the data set
parameter
a named vector specifying the number of conditions (k) and replications (N) of the data (which is the number of columns and rows of the data set, respectively)
p.value
significance level
p.type
whether the computed pvalue is
"exact"
or"approximate"
Functions

page.test
: See above. 
page.L
: Calculate Page's L statistic for the given dataset. 
page.compute.exact
: Calculate exact significance levels of the Page L statistic. Returns a single numeric indicating the null probability of the Page statistic with the givenk
,N
being greater or equal than the givenL
.
References
Siegel, S., and N. J. Castellan, Jr. (1988). Nonparametric Statistics for the Behavioral Sciences. McGrawHill.
See Also
Examples
# exact p value computation for N=4, k=4
page.test(t(replicate(4, sample(4))))
# exact p value computation for N=4, k=10
page.test(t(replicate(4, sample(10))))
# approximate p value computation for N=4, k=23
result < page.test(t(replicate(4, sample(23))), verbose = FALSE)
print(result)
# raw calculation of the significance levels
page.compute.exact(6, 4, 322)