Description Usage Arguments Details Value References Examples
View source: R/Parameter_estimation_and_hypothesis_testing.R
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
.
1 | two.sample.test(s1, s2)
|
s1, s2 |
The two data vectors to be tested. |
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.
Gives a vector with the Likelihood Ratio Test -statistic Lambda
, as well as the
p-value of the test p
.
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>.
1 2 3 4 5 6 7 8 9 | ##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)
|
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