nnspat (version 0.1.2)

exact.nnct: Exact version of Pearson's chi-square test on NNCTs

Description

An object of class "htest" performing exact version of Pearson's chi-square test on nearest neighbor contingency tables (NNCTs) for the RL or CSR independence for 2 classes. Pearson's \(\chi^2\) test is based on the test statistic \(\mathcal X^2=\sum_{j=1}^2\sum_{i=1}^2 (N_{ij}-\mu_{ij})^2/\mu_{ij}\), which has \(\chi^2_1\) distribution in the limit provided that the contingency table is constructed under the independence null hypothesis. The exact version of Pearson's test uses the exact distribution of \(\mathcal X^2\) rather than large sample \(\chi^2\) approximation. That is, for the one-sided alternative, we calculate the \(p\)-values as in the function exact.pval1s; and for the two-sided alternative, we calculate the \(p\)-values as in the function exact.pval2s with double argument determining the type of the correction.

This test would be equivalent to Fisher's exact test fisher.test if the odds ratio=1 (which can not be specified in the current version), and the odds ratio for the RL or CSR independence null hypothesis is \(\theta_0=(n_1-1)(n_2-1)/(n_1 n_2)\) which is used in the function and the \(p\)-value and confidence interval computations are are adapted from fisher.test.

See ceyhan:SWJ-spat-sym2014;textualnnspat for more details.

Usage

exact.nnct(
  ct,
  alternative = "two.sided",
  conf.level = 0.95,
  pval.type = "inc",
  double = FALSE
)

Value

A list with the elements

statistic

The test statistic, it is NULL for this function

p.value

The \(p\)-value for the hypothesis test for the corresponding alternative

conf.int

Confidence interval for the odds ratio 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 observed odds ratio the \(2 \times 2\) NNCT.

null.value

Hypothesized null value for the odds ratio in the \(2 \times 2\) NNCT, which is \(\theta_0=(n_1-1)(n_2-1)/(n_1 n_2)\) 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 contingency table, ct

Arguments

ct

A \(2 \times 2\) NNCT

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 odds ratio

pval.type

The type of the \(p\)-value correction for the exact test on the NNCT, default="inc". Takes on values "inc", "exc", "mid", "tocher" (or equivalently 1-4, respectively) for table inclusive, table-exclusive, mid-\(p\)-value, and Tocher corrected \(p\)-value, respectively.

double

A logical argument (default is FALSE) to determine whether type I or II correction should be applied to the two-sided \(p\)-value. Used only when alternative="two.sided". If TRUE type I correction (for doubling the minimum of the one-sided \(p\)-value) is applied, otherwise, type II correction (using the probabilities for the more extreme tables) is applied.

Author

Elvan Ceyhan

References

See Also

fisher.test, exact.pval1s, and exact.pval2s

Examples

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

exact.nnct(ct)
fisher.test(ct)

exact.nnct(ct,alt="g")
fisher.test(ct,alt="g")

exact.nnct(ct,alt="l",pval.type = "mid")

#############
ct<-matrix(sample(10:20,9),ncol=3)
fisher.test(ct) #here exact.nnct(ct) gives error message, since number of classes > 2