Znnsym2cl {nnspat}

NN Symmetry Test with Normal Approximation for Two Classes

Description

An object of class "htest" performing hypothesis test of equality of the expected value of the off-diagonal cell counts (i.e., entries) under RL or CSR in the NNCT for k=2 classes. That is, the test performs Dixon's or Pielou's (first type of) NN symmetry test which is appropriate (i.e., have the appropriate asymptotic sampling distribution) for completely mapped data and for sparsely sample data, respectively. (See Ceyhan (2014) for more detail).

The symmetry test is based on the normal approximation of the difference of the off-diagonal entries in the NNCT and are due to Pielou (1961); Dixon (1994).

The type="dixon" refers to Dixon's NN symmetry test and type="pielou" refers to Pielou's first type of NN symmetry test.

The function yields the test statistic, p-value for the corresponding alternative, the confidence interval, estimate and null value for the parameter of interest (which is the difference of the off-diagonal entries in the NNCT), and method and name of the data set used.

The null hypothesis is that all E(N_{12})=E(N_{21}) in the 2 \times 2 NNCT (i.e., symmetry in the mixed NN structure).

See also (Pielou (1961); Dixon (1994); Ceyhan (2014)) and the references therein.

Usage

Znnsym2cl(
  dat,
  lab,
  type = "dixon",
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95
)

Arguments

dat

The data set in one or higher dimensions, each row corresponds to a data point.

lab

The vector of class labels (numerical or categorical)

type

The type of the NN symmetry test with default="dixon". Takes on values "dixon" and "pielou" for Dixon's and Pielou's (first type) NN symmetry test

alternative

Type of the alternative hypothesis in the test, one of "two.sided", "less" or "greater".

conf.level

Level of the upper and lower confidence limits, default is 0.95, for the difference of the off-diagonal entries, N_{12}-N_{21}

Value

A list with the elements

statistic

The Z test statistic for Pielou's first type of NN symmetry test

p.value

The p-value for the hypothesis test for the corresponding alternative

conf.int

Confidence interval for the difference of the off-diagonal entries, N_{12}-N_{21} in the 2 \times 2 NNCT at the given confidence level conf.level and depends on the type of alternative.

estimate

Estimate, i.e., the difference of the off-diagonal entries of the 2 \times 2 NNCT, N_{12}-N_{21}.

null.value

Hypothesized null value for the expected difference between the off-diagonal entries, E(N_{12})-E(N_{21}) in the 2 \times 2 NNCT, which is 0 for this function.

alternative

Type of the alternative hypothesis in the test, one of "two.sided", "less", "greater"

method

Description of the hypothesis test

data.name

Name of the data set, dat, or name of the contingency table, ct

Author(s)

Elvan Ceyhan

References

Ceyhan E (2014). “Testing Spatial Symmetry Using Contingency Tables Based on Nearest Neighbor Relations.” The Scientific World Journal, Volume 2014, Article ID 698296.

Dixon PM (1994). “Testing spatial segregation using a nearest-neighbor contingency table.” Ecology, 75(7), 1940-1948.

Pielou EC (1961). “Segregation and symmetry in two-species populations as studied by nearest-neighbor relationships.” Journal of Ecology, 49(2), 255-269.

See Also

Znnsym2cl.ss.ct, Znnsym2cl.ss, Znnsym2cl.dx.ct, Znnsym2cl.dx, Znnsym.ss.ct, Znnsym.ss, Znnsym.dx.ct, Znnsym.dx, Znnsym.dx.ct, Znnsym.dx and Znnsym

Examples

n<-20  #or try sample(1:20,1)
Y<-matrix(runif(3*n),ncol=3)
cls<-sample(1:2,n,replace = TRUE)  #or try cls<-rep(1:2,c(10,10))

Znnsym2cl(Y,cls)
Znnsym2cl(Y,cls,type="pielou")

Znnsym2cl(Y,cls,alt="g")
Znnsym2cl(Y,cls,type="pielou",alt="g")