two.sample.test: Two sample test for psi

In PEkit: Partition Exchangeability Toolkit

Description

Likelihood ratio test for the hypotheses H_0: \: ψ_1=ψ_2 and H_1: \: ψ_1 \neq ψ_2, where ψ_1 and ψ_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{ψ})/L(\hat{ψ}_1, \hat{ψ}_2)),

where L is the likelihood function of observing the two input samples given a single ψ in the numerator and two different parameters ψ_1 and ψ_2 for each sample respectively in the denominator. According to the theory of Likelihood Ratio Tests, this statistic converges in distribution to a χ_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 ψ_1,\: ψ_2 of H_1 and the shared ψ 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. <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)

PEkit documentation built on Nov. 22, 2021, 9:08 a.m.