A Trinomial Test for Paired Data When There are Many Ties

This paper develops a new test, the trinomial test, for pairwise ordinal data samples to improve the power of the sign test by modifying its treatment of zero diRerences between observations, thereby increasing the use of sample information. Simulations demonstrate the power superiority of the proposed trinomial test statis- tic over the sign test in small samples in the presence of tie observations. We also show that the proposed trinomial test has substantially higher power than the sign test in large samples and also in the presence of tie observations, as the sign test ignores information from observations resulting in ties.

[1]  Wilfrid J. Dixon,et al.  An Introduction to Statistical Analysis , 1951 .

[2]  A. Huitson,et al.  Bibliography on Non-Parametric Statistics. , 1963 .

[3]  Bruce E. Hansen,et al.  Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis , 1996 .

[4]  F. Massey,et al.  Introduction to Statistical Analysis , 1970 .

[5]  A. Mood,et al.  The statistical sign test. , 1946, Journal of the American Statistical Association.

[6]  D. Andrews,et al.  Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative , 1992 .

[7]  W. J. Dixon,et al.  Introduction to Statistical Analysis , 1951 .

[8]  Albrecht Irle,et al.  Note on the Sign Test in the Presence of Ties , 1980 .

[9]  Knut M. Wittkowski,et al.  An asymptotic UMP sign test for discretised data , 1989 .

[10]  W. J. Dixon,et al.  Power Functions of the Sign Test and Power Efficiency for Normal Alternatives , 1953 .

[11]  J. Putter.  The Treatment of Ties in Some Nonparametric Tests , 1955 .

[12]  R. Davies.  Hypothesis testing when a nuisance parameter is present only under the alternative , 1977 .

[13]  C. W. Coakley,et al.  Versions of the Sign Test in the Presence of Ties , 1996 .

[14]  W. W. Daniel.  Applied Nonparametric Statistics , 1979 .

[15]  F. Wilcoxon.  Individual Comparisons by Ranking Methods , 1945 .

[16]  S. Shott,et al.  Nonparametric Statistics , 2018, The Encyclopedia of Archaeological Sciences.

[17]  J. Hemelrijk,et al.  A theorem on the sign test when ties are present , 1952 .

[18]  William J. Mackinnon,et al.  Table for Both the Sign Test and Distribution-Free Confidence Intervals of the Median for Sample Sizes to 1,000 , 1964 .

[19]  Paul S. Dwyer,et al.  Basic Instructions in Statistical Computations , 1957 .

[20]  William G. Cochran,et al.  An Introduction to Statistical Analysis. , 1952 .

[21]  John E. Walsh,et al.  On the Power Function of the Sign Test for Slippage of Means , 1946 .