page.trend.test {crank}

Page test for ordered alternatives

Description

calculates the Page test for ordered alternatives.

Usage

 page.trend.test(x,ranks=TRUE)

Arguments

x

a 2D matrix of ranks or observations.

ranks

Whether the values in x are ranks or observations.

Details

‘⁠page.trend.test⁠’ will accept a matrix of ranks where the rows represent methods (usually raters) and the columns represent related data objects. It apparently handles ties, but not missing values. For small values of k (methods) or N (data objects), ‘⁠page.trend.test⁠’ will try to look up the tabled values (as in Siegel & Castellan (1988) for significance. For ‘⁠k,N > 3,20⁠’ or ‘⁠k,N > 4-10,12⁠’, a normal approximation is returned. Only one of these values will be returned.

If ‘⁠ranks⁠’ is FALSE, the function ranks the values in ‘⁠x⁠’ and then calculates the test. If the values are already ranks, it usually makes no difference.

Value

ranks

matrix of ranks

mean.ranks

mean ranks of data objects

L

value of the L statistic

p.table

whether the obtained L exceeded the table value for small k,N

Z

The normal approximation for larger k,N

pZ

the probability of the obtained normal value for larger k,N

Note

The Page test for ordered alternatives is slightly more powerful than the Friedman analysis of variance by ranks.

Author(s)

Jim Lemon - thanks to Mikhail Trofimov and Michael Kirchhof for discovering major errors in the function and supplying the corrections

References

Siegel, S. & Castellan, N.J.Jr. (1988) Nonparametric statistics for the behavioral sciences. Boston, MA: McGraw-Hill.

Examples

 # 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)
 page.trend.test(soa.mat)