Analysis of singly ordered two-way contingency tables

Pearson's statistic is investigated for nominal-ordinal two-way contingency tables in which we wish to test for identical rows. The statistic is expressed as a sum, the rst summand of which is a statistic given by Yates (1948), and examines location eects for the nominal category. The second and subsequent summands reect the corresponding moments: for example, dispersion, skewness, kurtosis etc. The summands are shown to be weakly optimal in that they are score statistics.

[1]  John Bibby,et al.  The Analysis of Contingency Tables , 1978 .

[2]  S. K. Katti,et al.  Optimal scaling for ordered categories , 1962 .

[3]  John C. W. Rayner,et al.  Goodness-of-fit for grouped data using components of Pearson's X 2 , 1987 .

[4]  F. Yates.  The analysis of contingency tables with groupings based on quantitative characters. , 1948, Biometrika.

[5]  M. Kendall.  Theoretical Statistics , 1956, Nature.

[6]  Vijayan N. Nair,et al.  Testing in industrial experiments with ordered categorical data , 1986 .

[7]  W. J. Conover,et al.  Practical Nonparametric Statistics , 1972 .

[8]  Stephen Jones,et al.  [Testing in Industrial Experiments with Ordered Categorical Data]: Discussion , 1986 .

[9]  L Nyström,et al.  Statistical Analysis , 2008, Encyclopedia of Social Network Analysis and Mining.

[10]  Small-sample comparison of McCullagh and Nair analyses for nominal-ordinal categorical data , 1998 .

[11]  E. Korn,et al.  Choice of column scores for testing independence in ordered 2 X K contingency tables. , 1987, Biometrics.

[12]  Terry L King.  Smooth Tests of Goodness of Fit , 1991 .

[13]  Phillip L. Emerson,et al.  Numerical Construction of Orthogonal Polynomials from a General Recurrence Formula , 1968 .

[14]  E. Beh,et al.  Theory & Methods: Partitioning Pearson’s chi‐squared statistic for a partially ordered three‐way contingency table , 1999 .

[15]  Eric J. Beh,et al.  Theory & Methods: Partitioning Pearson’s Chi‐Squared Statistic for a Completely Ordered Three‐Way Contingency Table , 1998 .

[16]  A. W. Kemp,et al.  Kendall's Advanced Theory of Statistics. , 1994 .

[17]  C. F. Jeff Wu,et al.  A critical look at accumulation analysis and related methods , 1990 .

[18]  I. Bross.  How to use Ridit Analysis , 1958 .

[19]  M. F. Fuller,et al.  Practical Nonparametric Statistics; Nonparametric Statistical Inference , 1973 .

[20]  H. O. Lancaster.  The chi-squared distribution , 1971 .

[21]  P. Armitage.  Tests for Linear Trends in Proportions and Frequencies , 1955 .

[22]  P. McCullagh.  Regression Models for Ordinal Data , 1980 .

[23]  Gh. Brown.  The Statistical Comparison of Reproduction Rates for Groups of Sheep , 1988 .

[24]  V. LaRiccia,et al.  Test statistics derived as components of Pearson's phi-squared distance measure , 1987 .

[25]  A. Agresti,et al.  Analysis of Ordinal Categorical Data. , 1985 .