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.
Value
Gives a vector with the Likelihood Ratio Test -statistic Lambda, as well as the
p-value of the test p.
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.
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. <10.1098/rsta.1933.0009>.
# NOT RUN {##Create samples with different n and psi:set.seed(111)
x<-rPD(500, 15)
y<-rPD(1000, 20)
z<-rPD(800, 30)
##Run teststwo.sample.test(x,y)
two.sample.test(x,z)
two.sample.test(y,z)
# }