bda (version 1.2.7-31)

perm: To perform a permutation test to compare two samples/populations.

Description

To perform a permutation test to compare two samples/populations.

Usage

perm(x,y,fun,alternative = "two.sided", trials = 1000,...)

Arguments

x

Numerical or logical vector.

y

Numerical or logical vector.

fun

User-defined function to compare the difference of a function for two samples/data sets. If missing, compare the edf's.

alternative

Type of test. Either 'one-sided' or 'two-sided'.

trials

Iteration times, default: 10,000.

...

Controls.

Value

• Missing values are not allowed.

Details

To test a null hypothesis "H0: the two distributions are the same." against "H1: the two distributions are different". The test is performed by (1) computing the difference of the sample statistic; (2) pooling the two samples together to form a permutated population; (3) repeatedly bootstrapping/resampling from the permutated population without replacement, and computing the sample difference. (4) finding the p-value by check the percentage of times that the absoluted sample statistics differences are greater than the observed difference from (1).

References

R. A. Fisher, The Design of Experiment, New York: Hafner, 1935.

Pitman, E. J. G., "Significance tests which may be applied to samples from any population", Royal Statistical Society Supplement, 1937; 4: 119-130 and 225-32 (parts I and II).

Pitman, E. J. G., "Significance tests which may be applied to samples from any population. Part III. The analysis of variance test", Biometrika, 1938; 29: 322-335.

E. S. Edgington, Randomization tests, 3rd ed. New York: Marcel-Dekker, 1995. Phillip I. Good, Permutation, Parametric and Bootstrap Tests of Hypotheses, 3rd ed., Springer, 2005. ISBN 0-387-98898-X

Good, P. (2002) Extensions of the concept of exchangeability and their applications, J. Modern Appl. Statist. Methods, 1:243-247.

Lunneborg, Cliff. Data Analysis by Resampling, Duxbury Press, 1999. ISBN 0-534-22110-6.

Pesarin, F. 2001. Multivariate Permutation Tests, John Wiley & Sons.

Welch, W. J., Construction of permutation tests, Journal of American Statistical Association, 85:693-698, 1990.

Wang, B. and Wertelecki, W. (2012) Density Estimation for Data With Rounding Errors. Computational Statistics and Data Analysis, (in press), doi: 10.1016/j.csda.2012.02.016.

See Also

gof,mediation.test.

Examples

x1 = rnorm(100,34.5,1.5)
x2 = round(x1,0)
perm.test(x1,x2,trials=100)

## use user-defined function
foo = function(x,y) mean(x)-mean(y)
perm.test(x1,x2,fun=foo,trials=100)
## another user-defined function example
x3 = round(rnorm(10000,34.2,1.4),0)
foo = function(x,y){
 if(length(x)>length(y))
 cutoff = mean(x)-3*sd(x)
 else
 cutoff = mean(y)-3*sd(y)
 mean(x<cutoff)-mean(y<cutoff)
}
perm.test(x3,x2,fun=foo,trials=100)