Abstract
This paper develops a new design that relies on subjective judgment ranking to compare subsets of experimental units. This judgment ranking is used along with restricted randomization to improve statistical inference for the contrast between two levels of a treatment. The new design assigns the judgment ranked units in a subset to different treatments. Such an assignment translates the positive dependence among units within each subset into negative dependence for the estimators of treatment means, and hence leads to a reduction in variance for the contrast. For the proposed design, a test for the difference in means of two treatment levels is developed along with an associated confidence interval. It is shown that the null distribution of the proposed test is approximated reasonably well with the Student’s t-distribution for sample sizes as small as 6. A simulation study indicates that the proposed design is advantageous compared to its competitors in the literature for both high and low quality rankings. The new design’s advantage increases with the quality of rankings.
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References
Barnett V (1999). Ranked set sample design for environmental investigation. Environ Ecol Stat 6: 59–74
Bohn LL and Wolfe DA (1992). Nonparametric two-sample procedures for ranked-set samples data. J Am Stat Assoc 87: 552–62
Bohn LL and Wolfe DA (1994). The effect of imperfect judgment rankings on properties of procedures based on the ranked-set samples analog of the Mann-Whitney-Wilcoxon statistics. J Am Stat Assoc 89: 168–176
Chen Z (2001). The optimal ranked-set sampling scheme for inference on population quantiles. Stat Sinica 11: 23–27
Dell TR and Clutter JL (1977). Ranked-set sampling theory with order statistics background. Biometrics 28: 545–555
Hammer SM, Squires KE, HughesMD, Grimes JM, Demeter LM, Currier JS, Eron JJ Jr, Feinberg JE, Balfour HH Jr, Deyton LR, Chodakewitz JA, Fisch MA (1997). A controlled trial of two nucleosides analogues plus indinavir in persons with human immunodeficiency virus infection and CD4 cell counts of 200 per cubic millimiter or less. New Eng J Med 337: 725–733
Kaur A, Patil GP and Taillie C (1997). Unequal allocation models for ranked-set sampling with skew distributions. Biometrics 53: 123–130
MacEachern SN, Ozturk O, Stark G and Wolfe DA (2002). A new ranked set sample estimator of variance. J Roy Stat Soc B 64: 177–188
McIntyre GA (1952). A method of unbiased selective sampling using ranked-set sampling. Aust J Agric Res 3: 385–390
McIntyre GA (2005). A method of unbiased selective sampling using ranked sets. Am Stat 3: 230–232
Muttlak HA (1996). Estimation of parameters for one-way layout with rank set sampling. Biom J 38: 405–515
Nahhas RW, Wolfe DA and Chen HY (2002). Ranked set sampling: cost and optimal set size. Biometrics 58: 964–971
Ozturk O (2002). Rank regression in ranked-set samples. J Am Stat Assoc 97: 1180–1191
Ozturk O (2007). Two sample median test for order restricted randomized designs. Stat Probabl Lett 17: 131–141
Ozturk O and MacEachern SN (2004). Order restricted randomized design for control versus treatment comparison. Ann Inst Stat Math 56: 701–720
Ozturk O and Wolfe DA (2000a). Optimal allocation procedure in ranked set two-sample median test. J Nonparamet Stat 13: 57–76
Ozturk O and Wolfe DA (2000b). An improved ranked-set two-sample Mann-Whitney-Wilcoxon test. Can J Stat 28: 123–135
Ozturk O and Wolfe DA (2000c). Optimal allocation procedure in ranked-set sampling for unimodal and multi-modal distributions. Environ Ecol Stat 7: 343–356
Perron F and Sinha BK (2004). Estimation of variance based on a ranked set sample. J Stat Plan Infer 120: 21–28
Sinha BK, Sinha BK and Purkayastha S (1996). On some aspects of ranked set sampling for estimation of normal and exponential parameters. Stat Decsns 14: 223–240
Stokes SL (1977). Ranked set sampling with concomitant variables. Commun Stat Theor Meth 12: 1207–1211
Stokes SL (1980). Estimation of variance using ‘judgment ordered ranked set samples. Biometrics 36: 35–42
Stokes SL (1995). Parametric ranked set sampling.. Ann Inst Stat Math 83: 35–42
Takahasi K and Wakimoto K (1968). On unbiased estimates of the population mean based on the sample stratified by means of ordering. Ann Inst Stat Math 20: 1–31
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Ozturk, O., MacEachern, S.N. Order restricted randomized designs and two sample inference. Environ Ecol Stat 14, 365–381 (2007). https://doi.org/10.1007/s10651-007-0023-2
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DOI: https://doi.org/10.1007/s10651-007-0023-2