two.sample.test: Two sample test for psi

In AmiryousefiLab/PEkit: Partition Exchangeability Toolkit

Two sample test for \psi

Description

Likelihood ratio test for the hypotheses H_0: \: \psi_1=\psi_2 and H_1: \: \psi_1 \neq \psi_2, where \psi_1 and \psi_2 are the dispersal parameters of two input samples s1 and s2.

Usage

two.sample.test(s1, s2)

Arguments

s1, s2

The two data vectors to be tested.

Details

Calculates the Likelihood Ratio Test statistic

-2log(L(\hat{\psi})/L(\hat{\psi}_1, \hat{\psi}_2)),

where L is the likelihood function of observing the two input samples given a single \psi in the numerator and two different parameters \psi_1 and \psi_2 for each sample respectively in the denominator. According to the theory of Likelihood Ratio Tests, this statistic converges in distribution to a \chi_d^2-distribution under the null-hypothesis, where d is the difference in the amount of parameters between the considered models, which is 1 here. To calculate the statistic, the Maximum Likelihood Estimate for \psi_1,\: \psi_2 of H_1 and the shared \psi of H_0 are calculated.

Value

Gives a vector with the Likelihood Ratio Test -statistic Lambda, as well as the p-value of the test p.

References

Neyman, J., & Pearson, E. S. (1933). On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical Or Physical Character, 231(694-706), 289-337. <\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1098/rsta.1933.0009")}>.

Examples

##Create samples with different n and psi:
set.seed(111)
x<-rPD(500, 15)
y<-rPD(1000, 20)
z<-rPD(800, 30)
##Run tests
two.sample.test(x,y)
two.sample.test(x,z)
two.sample.test(y,z)

AmiryousefiLab/PEkit documentation built on May 14, 2023, 3:20 a.m.