Ranked Set Two-Sample Permutation Test

Authors

  • Monjed H. Samuh Palestine Polytechnic University

DOI:

https://doi.org/10.6092/issn.1973-2201/6742

Keywords:

Permutation test, Ranked set sampling, Statistical power, Type I error

Abstract

In this paper, ranked set two-sample permutation test of comparing two-independent groups in terms of some measure of location is presented. Three test statistics are proposed. The statistical power of these new test statistics are evaluated numerically. The results are compared with the statistical power of the usual two-sample permutation test under simple random sampling and with the classical independent two-sample t-test.

References

L. AMRO, M. H. SAMUH (2017). More powerful permutation test based on multistage ranked set sampling. Communications in Statistics-Simulation and Computation, 46, no. 7, pp. 5271–5284.

V. BARNETT, K. MOORE (1997). Best linear unbiased estimates in ranked-set sampling with particular reference to imperfect ordering. Journal of Applied Statistics, 24, no. 6, pp. 697–710.

L. L. BOHN, D. A. WOLFE (1992). Nonparametric two-sample procedures for ranked-set samples data. Journal of the American Statistical Association, 87, no. 418, pp. 552–561.

L. L. BOHN, D. A. WOLFE (1994). The effect of imperfect judgment rankings on properties of procedures based on the ranked-set samples analog of the Mann-Whitney-Wilcoxon statistic. Journal of the American Statistical Association, 89, no. 425, pp. 168–176.

Z. CHEN, Z. BAI, B. K. SINHA (2004). Ranked set sampling: theory and applications, vol.176. Springer Verlag, New York.

T. R. DELL, J. L. CLUTTER (1972). Ranked set sampling theory with order statistics background. Biometrics, 28, no. 2, pp. 545–555.

R. A. FISHER (1934). Statistical Methods for Research Workers. Oliver and Boyd, Edinburgh.

K. M. KOTI, G. JOGESH BABU (1996). Sign test for ranked-set sampling. Communications in Statistics-Theory and Methods, 25, no. 7, pp. 1617–1630.

Z. LIANGYONG, D. XIAOFANG (2010). Optimal ranked set sampling design for the sign test. Chinese Journal of Applied Probability and Statistics, 26, no. 3, pp. 225–233.

T. LIPTAK (1958). On the combination of independent tests. Magyar Tud Akad Mat Kutato Int Kozl, 3, pp. 171–197.

S. N.MACEACHERN, Ö. ÖZTÜRK, D. A.WOLFE, G. V. STARK (2002). A new ranked set sample estimator of variance. Journal of the Royal Statistical Society: Series B, 64, no. 2, pp. 177–188.

G. MCINTYRE (1952). A method for unbiased selective sampling, using ranked sets. Australian Journal of Agricultural Research, 3, no. 4, pp. 385–390.

G. MCINTYRE (2005). A method for unbiased selective sampling, using ranked sets. The American Statistician, 59, no. 3, pp. 230–232.

G. S.MUDHOLKAR, E. O.GEORGE (1979). The logit statistic for combining probabilities - an overview. In J. S.RUSTAGI (ed.), Optimizing Methods in Statistics,Academic Press, New York, pp. 345–365.

E. J. T. MURFF, T. W. SAGER (2006). The relative efficiency of ranked set sampling in ordinary least squares regression. Environmental and Ecological Statistics, 13, no. 1, pp. 41–51.

R. A. MURRAY, M. S. RIDOUT, J. V. CROSS (2000). The use of ranked set sampling in spray deposit assessment. Aspects of Applied Biology, 57, pp. 141–146.

Ö. ÖZTÜRK (1999). Two-sample inference based on one-sample ranked set sample sign statistics. Journal of Nonparametric Statistics, 10, no. 2, pp. 197–212.

Ö. ÖZTÜRK, D. A. WOLFE (2000). Optimal allocation procedure in ranked set two sample median test. Journal of Nonparametric Statistics, 13, no. 1, pp. 57–76.

G. P. PATIL (1995). Editorial: Ranked set sampling. Environmental and Ecological Statistics, 2, no. 4, pp. 271–285.

F. PESARIN, L. SALMASO (2010). Permutation Tests for Complex Data: Theory, Application and Software. JohnWiley & Sons, Ltd., Chichester.

L. H. PHILIP, K. LAM (1997). Regression estimator in ranked set sampling. Biometrics, 53, no. 3, pp. 1070–1080.

D. S. REY (2004). The Informational Order in Ranked Set Sampling Experiments. Ph.D. thesis, Mathematisches Institut der Universität Göttingen.

M. H. SAMUH (2012). Some Advances in Permutation Testing. Ph.D. thesis, Department of Statistical Science, Padua University, Italy.

G. R. SHORACK, J. A.WELLNER (1986). Empirical Processes with Applications to Statistics. Wiley Series in Probability & Mathematical Statistics, New York.

L. STOKES (1995). Parametric ranked set sampling. Annals of the Institute of Statistical Mathematics, 47, no. 3, pp. 465–482.

S. L. STOKES, T.W. SAGER (1988). Characterization of a ranked-set sample with application to estimating distribution functions. Journal of the American Statistical Association, 83, no. 402, pp. 374–381.

K. TAKAHASI, K. WAKIMOTO (1968). On unbiased estimates of the population mean based on the sample stratified by means of ordering. Annals of the Institute of Statistical Mathematics, 20, no. 1, pp. 1–31.

Downloads

Published

2018-01-11

How to Cite

Samuh, M. H. (2017). Ranked Set Two-Sample Permutation Test. Statistica, 77(3), 237–249. https://doi.org/10.6092/issn.1973-2201/6742

Issue

Section

Articles