2017 
Rayner JCW, 'Extended ANOVA', Journal of Statistical Theory and Practice, 11 208219 (2017)
Â© 2017 Crown copyright. Of interest here are analysis of variance (ANOVA) designs consistent with the general linear model. First, suppose that the levels of all independent vari... [more]
Â© 2017 Crown copyright. Of interest here are analysis of variance (ANOVA) designs consistent with the general linear model. First, suppose that the levels of all independent variables are not ordered or are treated as being unordered. Orthonormal polynomials up to a given order, typically three, on the responses are constructed and then analyses on the responses transformed by successive orthonormal polynomials are performed. These analyses assess moment effects and are uncorrelated. Next suppose that the levels of some of the independent variables are ordered. Orthonormal polynomials are constructed on the response variable and on each independent variable for which the levels are ordered. The responses are transformed by an orthonormal polynomial of a particular order, and each independent variable is also transformed by an orthonormal polynomial of a particular order. Then the product of the transformed variables is taken. A new design is formed from the original, without the independent variables for which the levels are ordered and with a new response, the product of orthonormal polynomials. ANOVAs of interest on the new design are then performed. These analyses assess generalized correlation effects and are uncorrelated. Of most interest are the usual order (1, 1) correlation that assesses linearÂ¿linear effects, and order (1, 2) correlations that assess umbrella effects. Models may be constructed for conditional moments.



2017 
Best DJ, Rayner JCW, 'Analysis of ranked data in randomized blocks when there are missing values', Journal of Applied Statistics, 44 1623 (2017)
Â© 2016 Informa UK Limited, trading as Taylor & Francis Group.Data consisting of ranks within blocks are considered for randomized block designs when there are missing values. Tie... [more]
Â© 2016 Informa UK Limited, trading as Taylor & Francis Group.Data consisting of ranks within blocks are considered for randomized block designs when there are missing values. Tied ranks are possible. Such data can be analysed using the SkillingsÂ¿Mack test. Here we suggest a new approach based on carrying out an ANOVA on the ranks using the general linear model platform available in many statistical packages. Such a platform allows an ANOVA to be calculated when there are missing values. Indicative sizes and powers show the ANOVA approach performs better than the SkillingsÂ¿Mack test.



2017 
Best DJ, Rayner JCW, 'A note on additional statistical analysis for JAR data', FOOD QUALITY AND PREFERENCE, 55 67 (2017) [C1]



2016 
Best DJ, Rayner JCW, Thas O, De Neve J, Allingham D, 'Comparing Nonparametric Tests of Equality of Means for Randomized Block Designs', Communications in Statistics: Simulation and Computation, 45 17181730 (2016) [C1]
Copyright Â© Taylor & Francis Group, LLC.A number of nonparametric tests are compared empirically for a randomized block layout. We assess tests appropriate for when the data are ... [more]
Copyright Â© Taylor & Francis Group, LLC.A number of nonparametric tests are compared empirically for a randomized block layout. We assess tests appropriate for when the data are not consistent with normality or when outliers invalidate traditional analysis of variance (ANOVA) tests. The objective is to assess, within this setting, tests that use ranks within blocks, the rank transform procedure that ranks the complete sample and continuous analogs of the CochranMantelHaenszel tests. The usual linear model is assumed, and our primary foci are tests of equality of means and component tests that assess linear and quadratic trends in the means. These tests include the traditional Page and Friedman tests. We conclude that the rank transform tests have competitive power and warrant greater use than is currently apparent.



2016 
Best DJ, Rayner JCW, Thas O, 'Corrigendum to Â¿Comparison of Some Tests of Fit for the Inverse Gaussian DistributionÂ¿', Advances in Decision Sciences, 2016 12 (2016)



2015 
Thas O, Rayner JCW, De Neve J, 'GENERALISED SMOOTH TESTS OF GOODNESS OF FIT UTILISING LMOMENTS', AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 57 481499 (2015) [C1]



2015 
Rayner JCW, Best DJ, Thas O, 'Extended Analysis of At Least Partially Ordered Multifactor ANOVA', Australian and New Zealand Journal of Statistics, 57 211224 (2015) [C1]
Â© 2015 Australian Statistical Publishing Association Inc.For multifactor experimental designs in which the levels of at least one of the factors are ordered we show how to constr... [more]
Â© 2015 Australian Statistical Publishing Association Inc.For multifactor experimental designs in which the levels of at least one of the factors are ordered we show how to construct components that provide a deep nonparametric scrutiny of the data. The components assess generalised correlations and the resulting tests include and extend the Page and umbrella tests. Application of the tests described is straightforward. Orthonormal polynomials on the ANOVA responses and the factors are required and the formulae needed are given subsequently. These depend on the moments of the responses and of each factor and are easily calculated. Products of at least two of these orthonormal polynomials are then used as inputs into standard ANOVA routines. For example, using the first order orthonormal polynomial on factor A and the second order orthonormal polynomial on the ANOVA response will assess if, with increasing levels of factor A there is an umbrella response with either an increase and then a decrease or a decrease and then an increase.



2015 
Rayner JCW, SUESSE TF, THAS O, 'Smooth tests of fit for Gaussian mixtures', Studies in Classification, Data Analysis and Knowledge Organisation, 133142 (2015) [C1]



2015 
Best DJ, Rayner JCW, 'An alternative to pages test permitting both tied and missing data', Journal of Statistical Theory and Practice, 9 524536 (2015) [C1]
Â© Grace Scientific Publishing, LLC.Data consisting of ranks within blocks are considered for randomized complete block layouts where treatment effects are expected to be ordered.... [more]
Â© Grace Scientific Publishing, LLC.Data consisting of ranks within blocks are considered for randomized complete block layouts where treatment effects are expected to be ordered. Ranks with and without ties are considered, as well as missing values. A small indicative test size study indicates both a new test and the Page test, modified by Thas et al. (2012) to easily permit ties, perform well. An advantage of the new test is that it can be easily applied to data with missing values. Three real examples are given. One of these illustrates a quadratic trend test. Comparisons between the new test and the Alvo and Cabilio (1995) extended Page test for missing values are given.



2014 
Best DJ, Rayner JCW, 'Conover's F test as an alternative to durbin's test', Journal of Modern Applied Statistical Methods, 13 7683 (2014) [C1]
Â© 2014 JMASM, Inc.Data consisting of ranks within blocks are considered for balanced incomplete block designs. An F test statistic from ANOVA is better approximated by an F distr... [more]
Â© 2014 JMASM, Inc.Data consisting of ranks within blocks are considered for balanced incomplete block designs. An F test statistic from ANOVA is better approximated by an F distribution than the Durbin statistic is approximated by a chisquared distribution. Indicative powers demonstrate that the F test is generally superior to Durbin's test.



2014 
Best DJ, Rayner JCW, Allingham D, 'A note on formulae for CMH statistics for JAR data', Food Quality and Preference, 31 1921 (2014) [C1]
CochranMantelHaenszel (CMH) test statistics can be used to compare products rated on JAR 'just about right' scales and for similar categorical data. In this note we consider the... [more]
CochranMantelHaenszel (CMH) test statistics can be used to compare products rated on JAR 'just about right' scales and for similar categorical data. In this note we consider the case of paired or related data. The simplified statistics we give allow 'by hand' calculation when the data set is small. We also give an R package for larger data sets or for when the user is not interested in 'by hand' calculation. Â© 2013 Elsevier Ltd.



2013 
Rayner JCW, Thas O, Pipelers P, Beh EJ, 'Calculating bivariate orthonormal polynomials by recurrence', AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 55 1524 (2013) [C1]



2013 
Rayner JCW, Best DJ, 'Extended Anova And Rank Transform Procedures', Australian & New Zealand Journal Of Statistics, 55 305319 (2013) [C1]



2012 
Thas O, Clement L, Rayner JC, Carvalho B, Van Criekinge W, 'An omnibus consistent adaptive percentile modified Wilcoxon rank sum test with applications in gene expression studies', Biometrics, 68 446454 (2012) [C1]



2012 
Thas O, Best DJ, Rayner JC, 'Using orthogonal trend contrasts for testing ranked data with ordered alternatives', Statistica Neerlandica, 66 452471 (2012) [C1]



2012 
Allingham D, Rayner JC, 'Testing equality of variances for multiple univariate normal populations', Journal of Statistical Theory and Practice, 6 524535 (2012) [C1]



2012 
Best DJ, Rayner JC, Thas O, 'Comparison of some tests of fit for the inverse Gaussian distribution', Advances in Decision Sciences, 2012 150303 (2012) [C1]



2011 
De Boeck B, Thas O, Rayner JC, Best DJ, 'Generalised smooth tests for the generalised Pareto distribution', Journal of Statistical Theory and Practice, 5 737750 (2011) [C1]



2011 
Rayner JC, Thas O, Best DJ, 'Smooth tests of goodness of fit', Wiley Interdisciplinary Reviews: Computational Statistics, 3 397406 (2011) [C1]



2011 
Allingham D, Rayner JC, 'A nonparametric twosample wald test of equality of variances', Advances in Decision Sciences, 2011 748580 (2011) [C1]



2011 
De Boeck B, Thas O, Rayner JC, Best DJ, 'Smooth tests for the gamma distribution', Journal of Statistical Computation and Simulation, 81 843855 (2011) [C1]



2011 
Best DJ, Rayner JC, Allingham D, 'A statistical test for ranking data from partially balanced incomplete block designs', Journal of Sensory Studies, 26 8184 (2011) [C1]



2011 
Best DJ, Rayner JC, Thas O, 'Easily appled tests of fit for the Rayleigh distribution', Sankhya B  Applied and Interdisciplinary Statistics, 72 254263 (2011) [C1]



2010 
Rippon PG, Rayner JC, 'Generalised score and Wald tests', Advances in Decision Sciences, 2010 Article ID 292013 (2010) [C1]



2010 
Rayner JCW, Thas O, Best DJ, 'Smooth Tests of Goodness of Fit: Using R: Second Edition', Smooth Tests of Goodness of Fit: Using R: Second Edition, (2010)
In this fully revised and expanded edition of Smooth Tests of Goodness of Fit, the latest powerful techniques for assessing statistical and probabilistic models using this proven ... [more]
In this fully revised and expanded edition of Smooth Tests of Goodness of Fit, the latest powerful techniques for assessing statistical and probabilistic models using this proven class of procedures are presented in a practical and easily accessible manner. Emphasis is placed on modern developments such as datadriven tests, diagnostic properties, and model selection techniques. Applicable to most statistical distributions, the methodology described in this book is optimal for deriving tests of fit for new distributions and complex probabilistic models, and is a standard against which new procedures should be compared. New features of the second edition include: Expansion of the methodology to cover virtually any statistical distribution, including exponential families. Discussion and application of datadriven smooth tests. Techniques for the selection of the best model for the data, with a guide to acceptable alternatives. Numerous new, revised, and expanded examples, generated using R code. Smooth Tests of Goodness of Fit is an invaluable resource for all methodological researchers as well as graduate students undertaking goodnessoffit, statistical, and probabilistic model assessment courses. Practitioners wishing to make an informed choice of goodnessoffit test will also find this book an indispensible guide. Reviews of the first edition: "This book gives a very readable account of the smooth tests of goodness of fit. The book can be read by scientists having only an introductory knowledge of statistics. It contains a fairly extensive list of references; research will find it helpful for the further development of smooth tests." T.K. Chandra, Zentralblatt fÃ¼r Mathematik und ihre Grenzgebiete, Band 73, 1/92' "An excellent job of showing how smooth tests (a class of goodness of fit tests) are generally and easily applicable in assessing the validity of models involving statistical distributions....Highly recommended for undergraduate and graduate libraries." Choice. "The book can be read by scientists having only an introductory knowledge of statistics. It contains a fairly extensive list of references; researchers will find it helpful for the further development of smooth tests."Mathematical Reviews. "Very rich in examples . . . Should find its way to the desks of many statisticians." Technometrics. Â© 2009 John Wiley & Sons (Asia) Pte Ltd.



2010 
Best DJ, Rayner JC, Thas O, 'Four tests of fit for the betabinomial distribution', Journal of Applied Statistics, 37 15471554 (2010) [C1]



2010 
Best DJ, Rayner JC, Thas O, 'Moment tests of fit for some discrete distributions with ecological applications', International Journal of Ecological Economics and Statistics, 17 115 (2010) [C1]



2009 
Best DJ, Rayner JC, Thas O, 'Anscombe's Tests of fit for the negative binomial distribution', Journal of Statistical Theory and Practice, 3 555565 (2009) [C1]



2009 
Rayner JC, Carolan AM, 'Partially parametric testing', Journal of Statistical Theory and Practice, 3 735750 (2009) [C1]



2009 
Rayner JC, Best DJ, Thas O, 'Generalised smooth tests of goodness of fit', Journal of Statistical Theory and Practice, 3 665679 (2009) [C1]



2009 
Thas O, Rayner JC, Best DJ, De Boeck D, 'Informative statistical analyses using smooth goodness of fit tests', Journal of Statistical Theory and Practice, 3 705733 (2009) [C1]



2009 
Rayner JC, Best DJ, Thas O, 'Guest editors', Journal of Statistical Theory and Practice, 3 (2009) [C2]



2009 
Rayner JC, Thas O, Best DJ, 'Introduction to modern goodness of fit methods', Journal of Statistical Theory and Practice, 3 537541 (2009) [C3]



2009 
Rayner JC, Beh EJ, 'Towards a better understanding of correlation', Statistica Neerlandica, 63 324333 (2009) [C1]



2009 
Rayner JC, Beh EJ, 'Components of Pearson's statistic for at least partially ordered mway contingency tables', Journal of Applied Mathematics and Decision Sciences, 2009 19 (2009) [C1]



2008 
Rayner JC, Thas O, De Boeck B, 'A generalised Emerson recurrence relation', Australian and New Zealand Journal of Statistics, 50 235240 (2008) [C1]



2008 
Best DJ, Rayner JC, Thas O, 'Tests of fit for the logarithmic distribution', Journal of Applied Mathematics and Decision Sciences, 2008 463781 (2008) [C1]



2008 
Best DJ, Rayner JC, Thas O, 'Comparison of some tests of fit for the Laplace distribution', Computational Statistics and Data Analysis, 52 53385343 (2008) [C1]



2008 
Best DJ, Rayner JC, Thas O, 'X2 and its components as tests of normality for grouped data', Journal of Applied Statistics, 35 481492 (2008) [C1]



2007 
Best DJ, Rayner JC, Thas O, 'Comparison of five tests of fit for the extreme value distribution', Journal of Statistical Theory and Practice, 1 8999 (2007) [C1]



2007 
Best DJ, Rayner JC, Thas O, 'Goodness of fit for the zerotruncated Poisson distribution', Journal of Statistical Computation and Simulation, 77 585591 (2007) [C1]



2007 
Best DJ, Rayner JC, 'Chisquared components for tests of fit and improved models for the grouped exponential distribution', Computational Statistics and Data Analysis, 51 39463954 (2007) [C1]



2006 
Best DJ, Brockhoff PB, Rayner JCW, 'Tests for balanced incomplete block ranked data with ties', STATISTICA NEERLANDICA, 60 311 (2006) [C1]



2006 
Best DJ, Rayner JCW, 'Improved testing for the binomial distribution using chisquared components with datadependent cells', JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 76 7581 (2006) [C1]



2006 
Thas O, Best DJ, Rayner JC, 'Nonparametric analysis of blocked ordered categories data: some examples revisited', Journal of Applied Mathematics and Decision Sciences, 2006  (2006) [C1]



2005 
Thas O, Rayner JCW, 'Smooth tests for the zeroinflated poisson distribution', BIOMETRICS, 61 808815 (2005) [C1]



2005 
Best DJ, Rayner JCW, 'Improved testing for the Poisson distribution using chisquared components with data dependent cells', COMMUNICATIONS IN STATISTICSSIMULATION AND COMPUTATION, 34 8596 (2005) [C1]



2005 
Thas O, Rayner JCW, Best DJ, 'Tests for symmetry based on the onesample Wilcoxon signed rank statistic', COMMUNICATIONS IN STATISTICSSIMULATION AND COMPUTATION, 34 957973 (2005) [C1]



2005 
Rayner JCW, Thas O, 'More informative testing for bivariate symmetry', AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 47 211217 (2005) [C1]



2004 
Brockhoff PB, Best DJ, Rayner JCW, 'Partitioning Anderson's statistic for tied data', JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 121 93111 (2004) [C1]



2004 
Brockhoff PB, Best DJ, Rayner JCW, 'An application of extended analysis for ranked data with ties', AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 46 197204 (2004) [C1]



2003 
Best DJ, Rayner JCW, 'Tests of fit for the geometric distribution', COMMUNICATIONS IN STATISTICSSIMULATION AND COMPUTATION, 32 10651078 (2003) [C1]



2003 
Brockhoff PB, Best DJ, Rayner JCW, 'Using Anderson's statistic to compare distributions of consumer preference rankings', JOURNAL OF SENSORY STUDIES, 18 7782 (2003)



2001 
Rayner GD, Rayner JCW, 'Power of the Neyman smooth tests for the uniform distribution', Journal of Applied Mathematics and Decision Sciences, 5 181191 (2001) [C1]
This paper compares and investigates the generalised Neyman smooth test, its components, and the classical chisquared test with a variety of equiprobable classes. Each test is ev... [more]
This paper compares and investigates the generalised Neyman smooth test, its components, and the classical chisquared test with a variety of equiprobable classes. Each test is evaluated in terms of its power to reject a wavelike alternative to the uniform distribution, chosen to quantify the complexity of the alternative. Results indicate that if broadly focused tests (rather than strongly directional or weakly omnibus) are sought, then smooth tests of order about four, or the chisquared test with between five and ten classes, will perform well. CopyrightÂ© 2001, Lawrence Erlbaum Associates, Inc.



2001 
Carolan AM, Rayner JCW, 'One sample tests for the location of modes of nonnormal data', Journal of Applied Mathematics and Decision Sciences, 5 119 (2001) [C1]
There are few techniques available for testing if modes take specified values. We show that standard tests of location such as the ttest and the Wilcoxon test, which test for the... [more]
There are few techniques available for testing if modes take specified values. We show that standard tests of location such as the ttest and the Wilcoxon test, which test for the mean and median respectively, can perform poorly as tests for modes when the data is other than unimodal and symmetric. Carolan and Rayner [1] proposed a score test of location for symmetric nonnormal data. We consider a family of distributions similar to those considered by Carolan and Rayner [1] and propose a test for the mode or modes of data from multimodal or skewed distributions and demonstrate by way of simulations that it is reasonably effective. CopyrightÂ© 2001, Lawrence Erlbaum Associates, Inc.



2001 
Best DJ, Rayner JCW, 'Nonparametric analysis for trinary sensory data', JOURNAL OF SENSORY STUDIES, 16 249260 (2001)



2001 
Best DJ, Rayner J, 'Application of the Stuart test to sensory evaluation data', Food Quality and Preference, 12 353357 (2001) [C1] 


2000 
Carolan AM, Rayner JCW, 'Wald tests of location for symmetric nonnormal data', BIOMETRICAL JOURNAL, 42 777792 (2000)



2000 
Carolan AM, Rayner JCW, 'One sample tests of location for nonnormal symmetric data', COMMUNICATIONS IN STATISTICSTHEORY AND METHODS, 29 15691581 (2000)



2000 
Jones G, Lai CD, Rayner JCW, 'A bivariate gamma mixture distribution', COMMUNICATIONS IN STATISTICSTHEORY AND METHODS, 29 27752790 (2000)



2000 
Best DJ, Rayner JCW, 'Extended statistical analysis of ranked data from balanced incomplete block and paired comparison designs', JOURNAL OF SENSORY STUDIES, 15 383392 (2000)



2000 
Rayner JCW, Best DJ, 'Analysis of singly ordered twoway contingency tables', Journal of Applied Mathematics and Decision Sciences, 4 8398 (2000)
Pearson's statistic is investigated for nominalordinal twoway contingency tables in which we wish to test for identical rows. The statistic is expressed as a sum, the first summ... [more]
Pearson's statistic is investigated for nominalordinal twoway contingency tables in which we wish to test for identical rows. The statistic is expressed as a sum, the first summand of which is a statistic given by Yates (1948), and examines location effects for the nominal category. The second and subsequent summands reflect the corresponding moments: for example, dispersion, skewness, kurtosis etc. The summands are shown to be weakly optimal in that they are score statistics. Â© Journal of Applied Mathematics & Decision Sciences.



1999 
Rayner JCW, 'Modelling ties in the sign test', BIOMETRICS, 55 663665 (1999)



1999 
Lai CD, Rayner JCW, Hutchinson TP, 'Robustness of the sample correlation  The bivariate lognormal case', Journal of Applied Mathematics and Decision Sciences, 3 719 (1999)
The sample correlation coefficient R is almost universally used to estimate the population correlation coefficient p. If the pair (X, Y) has a bivariate normal distribution, this ... [more]
The sample correlation coefficient R is almost universally used to estimate the population correlation coefficient p. If the pair (X, Y) has a bivariate normal distribution, this would not cause any trouble. However, if the marginals are nonnormal, particularly if they have high skewness and kurtosis, the estimated value from a sample may be quite different from the population correlation coefficient Â¿. The bivariate lognormal is chosen as our case study for this robustness study. Two approaches are used: (i) by simulation and (ii) numerical computations. Our simulation analysis indicates that for the bivariate lognormal, the bias in estimating pÂ¿ can be very large if Â¿ Â¿0, and it can be substantially reduced only after a large number (three to four million) of observations. This phenomenon, though unexpected at first, was found to be consistent to our findings by our numerical analysis. Â© Journal of Applied Mathematics & Decision Sciences.



1999 
Rayner JCW, Best DJ, 'Nonparametric tests for data in randomised blocks with ordered alternatives', Journal of Applied Mathematics and Decision Sciences, 3 143153 (1999)
For randomized block designs, nonparametric treatment comparisons are usually made using the Friedman test for complete designs, and the Durbin test for incomplete designs; see, f... [more]
For randomized block designs, nonparametric treatment comparisons are usually made using the Friedman test for complete designs, and the Durbin test for incomplete designs; see, for example, Conover (1998). This permits assessment of only the mean rankings. Such comparisons are here extended to permit assessments of bivariate effects such as the linear by linear effect and the quadratic by linear, or umbrella effect. Â© Journal of Applied Mathematics & Decision Sciences.



1999 
Best DJ, Rayner JCW, 'Goodness of fit for the Poisson distribution', STATISTICS & PROBABILITY LETTERS, 44 259265 (1999)



1998 
Best DJ, Rayner JCW, 'Nonparametric analysis of ordinal categorical response data with factorial structure', JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES CAPPLIED STATISTICS, 47 439446 (1998)



1998 
Best DJ, Rayner JCW, Stephens LG, 'Smallsample comparison of McCullagh and Nair analyses for nominalordinal categorical data', COMPUTATIONAL STATISTICS & DATA ANALYSIS, 28 217223 (1998)



1998 
Rayner JCW, Rayner GD, 'Ssample smooth goodness of fit testing: Rederivation and Monte Carlo assessment', BIOMETRICAL JOURNAL, 40 651663 (1998) 


1997 
Best DJ, Rayner JCW, 'Goodness of fit for the binomial distribution', AUSTRALIAN JOURNAL OF STATISTICS, 39 355364 (1997)



1997 
Rayner JCW, 'The asymptotically optimal tests', STATISTICIAN, 46 337346 (1997)



1997 
Best DJ, Rayner JCW, 'Product maps for ranked preference data', STATISTICIAN, 46 347354 (1997)



1997 
Rayner JCW, Best DJ, 'How order affects the sign test', BIOMETRICS, 53 14161421 (1997)



1997 
Rayner JCW, Best DJ, 'Extensions to the KruskalWallis test and a generalised median test with extensions', Journal of Applied Mathematics and Decision Sciences, 1 1325 (1997)
The data for the tests considered here may be presented in twoway contingency tables with all marginal totals fixed. We show that Pearson's test statistic XP2 (P for Pearson) may... [more]
The data for the tests considered here may be presented in twoway contingency tables with all marginal totals fixed. We show that Pearson's test statistic XP2 (P for Pearson) may be partitioned into useful and informative components. The first detects location differences between the treatments, and the subsequent components detect dispersion and higher order moment differences. For KruskalWallistype data when there are no ties, the location component is the KruskalWallis test. The subsequent components are the extensions. Our approach enables us to generalise to when there are ties, and to when there is a fixed number of categories and a large number of observations. We also propose a generalisation of the wellknown median test. In this situation the locationdetecting first component of X P2 reduces to the usual median test statistic when there are only two categories. Subsequent components detect higher moment departures from the null hypothesis of equal treatment effects. Â© Journal of Applied Mathematics & Decision Sciences.



1997 
Best DJ, Rayner JCW, 'Crockett's test of fit for the bivariate Poisson', BIOMETRICAL JOURNAL, 39 423430 (1997)



1997 
Best DJ, Rayner JCW, 'Goodness of fit for the ordered categories discrete uniform distribution', COMMUNICATIONS IN STATISTICSTHEORY AND METHODS, 26 899909 (1997)



1996 
Best DJ, Rayner JCW, 'Nonparametric analysis for doubly ordered twoway contingency tables', BIOMETRICS, 52 11531156 (1996)



1996 
Rayner JCW, Best DJ, 'Smooth extensions of Pearsons's product moment correlation and Spearman's rho', STATISTICS & PROBABILITY LETTERS, 30 171177 (1996)



1996 
Davy PJ, Rayner JCW, 'Multivariate geometric distributions', COMMUNICATIONS IN STATISTICSTHEORY AND METHODS, 25 29712987 (1996)



1995 
RAYNER JCW, BEST DJ, MATHEWS KL, 'INTERPRETING THE SKEWNESS COEFFICIENT', COMMUNICATIONS IN STATISTICSTHEORY AND METHODS, 24 593600 (1995)



1995 
Rayner JCW, Best DJ, 'SMOOTH TESTS FOR THE BIVARIATE POISSON DISTRIBUTION', Australian Journal of Statistics, 37 233245 (1995)
A theorem of Rayner & Best (1989) is generalised to permit the construction of smooth tests of goodness of fit without requiring a set of orthonormal functions on the hypothesised... [more]
A theorem of Rayner & Best (1989) is generalised to permit the construction of smooth tests of goodness of fit without requiring a set of orthonormal functions on the hypothesised distribution. This result is used to construct smooth tests for the bivariate Poisson distribution. The test due to Crockett (1979) is similar to a smooth test that assesses the variance structure under the bivariate Poisson model; the test due to Loukas & Kemp (1986) is related to a smooth test that seeks to detect a particular linear relationship between the variances and covariance under the bivariate Poisson model. Using focused smooth tests may be more informative than using previously suggested tests. The distribution of the Loukas & Kemp (1986) statistic is not well approximated by the x2distribution for larger correlations, and a revised statistic is suggested. Copyright Â© 1995, Wiley Blackwell. All rights reserved



1994 
BEST DJ, GRAHAM D, RAYNER JCW, 'ESTIMATING CORRELATION FROM CATEGORIZED BIVARIATE NORMAL DATA', JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 49 141149 (1994)



1993 
Rayner JCW, 'Assumptions are Important: the Paired and Pooled t tests', Teaching Statistics, 15 1517 (1993)
The relationship between the test statistics for the paired and pooled t tests, when applied to the same data set, is obtained. This assists us to understand why each is preferred... [more]
The relationship between the test statistics for the paired and pooled t tests, when applied to the same data set, is obtained. This assists us to understand why each is preferred over the other in appropriate circumstances. Copyright Â© 1993, Wiley Blackwell. All rights reserved



1992 
Best DJ, Rayner JC, 'Response', Technometrics, 34 250 (1992)



1992 
BEST DJ, RAYNER JCW, 'DISEASE CLUSTERING IN TIME  REPLY', BIOMETRICS, 48 327327 (1992)



1992 
RAYNER JCW, LIDDELL GF, SEYB AJ, 'THE EFFECT OF CATEGORIZATION ON BALANCED INCOMPLETE BLOCKS AND LATIN SQUARES', BIOMETRICAL JOURNAL, 34 3755 (1992)



1991 
BEST DJ, RAYNER JCW, 'DISEASE CLUSTERING IN TIME', BIOMETRICS, 47 589593 (1991)



1991 
Rayner JCW, Best DJ, 'What Divisor for the Sample Variance?', Teaching Statistics, 13 8587 (1991)
Simulation is used to show why the divisor in the sample variance is n,  1. Choice of the divisor for the sample standard deviation is also discussed. Copyright Â© 1991, Wiley Bl... [more]
Simulation is used to show why the divisor in the sample variance is n,  1. Choice of the divisor for the sample standard deviation is also discussed. Copyright Â© 1991, Wiley Blackwell. All rights reserved



1991 
RAYNER JCW, BEST DJ, LIDDELL GF, 'OPTIMAL TESTING IN A 3 WAY ANOVA MODEL', COMMUNICATIONS IN STATISTICSSIMULATION AND COMPUTATION, 20 411425 (1991)



1990 
RAYNER JCW, MCALEVEY LG, 'SMOOTH GOODNESS OF FIT TESTS FOR CATEGORIZED COMPOSITE NULL HYPOTHESES', STATISTICS & PROBABILITY LETTERS, 9 423429 (1990)



1990 
RAYNER JCW, BEST DJ, 'A COMPARISON OF SOME RANKTESTS USED IN TASTETESTING', JOURNAL OF THE ROYAL SOCIETY OF NEW ZEALAND, 20 269272 (1990)



1990 
RAYNER JCW, BEST DJ, 'SMOOTH TESTS OF GOODNESS OF FIT  AN OVERVIEW', INTERNATIONAL STATISTICAL REVIEW, 58 917 (1990)



1989 
BEST DJ, RAYNER JCW, 'GOODNESS OF FIT FOR THE GEOMETRIC DISTRIBUTION', BIOMETRICAL JOURNAL, 31 307311 (1989)



1989 
MANLY BFJ, RAYNER JCW, 'CONSIDERATIONS FOR EFFECTIVE SIMULATION STUDY ANALYSIS  COMMENTS', COMMUNICATIONS IN STATISTICSSIMULATION AND COMPUTATION, 18 12411244 (1989)



1988 
RAYNER JCW, 'CONSTRUCTING A USABLE OVERLAPPING CELLS X2 GOODNESS OF FIT TEST', STATISTICS & PROBABILITY LETTERS, 6 257261 (1988)



1988 
BEST DJ, RAYNER JCW, 'A TEST FOR BIVARIATE NORMALITY', STATISTICS & PROBABILITY LETTERS, 6 407412 (1988)



1988 
RAYNER JCW, BEST DJ, 'SMOOTH TESTS OF GOODNESS OF FIT FOR REGULAR DISTRIBUTIONS', COMMUNICATIONS IN STATISTICSTHEORY AND METHODS, 17 32353267 (1988)



1988 
Rayner JCW, Seyb AJ, 'ANOVA Under Categorisation', Journal of Statistical Computation and Simulation, 29 181193 (1988)
A basic assumption in the analysis of variance is that the observations are realisations of a univariate normal distribution. However, if the observations are rounded, the questio... [more]
A basic assumption in the analysis of variance is that the observations are realisations of a univariate normal distribution. However, if the observations are rounded, the question arises of how this affects the usual tests. Rayner, Dodds and Best (1986) considered a one factor fixed effects model with regard to simulated sizes and approximate asymptotic relative efficiencies. Here asymptotic relative efficiencies are considered for a three factor mixed effects model. The method generalises readily to other ANOVA models. Â© 1988 Taylor & Francis Group, LLC. All rights reserved.



1987 
MANLY BFJ, RAYNER JCW, 'THE COMPARISON OF SAMPLE COVARIANCE MATRICES USING LIKELIHOOD RATIO TESTS', BIOMETRIKA, 74 841847 (1987)



1987 
BEST DJ, RAYNER JCW, 'WELCH APPROXIMATE SOLUTION FOR THE BEHRENSFISHER PROBLEM', TECHNOMETRICS, 29 205210 (1987)



1987 
BEST DJ, RAYNER JCW, 'GOODNESSOFFIT FOR GROUPED DATA USING COMPONENTS OF PEARSONX2', COMPUTATIONAL STATISTICS & DATA ANALYSIS, 5 5357 (1987)



1987 
Rayner JCW, Shanks JA, 'The redundant hypergeometric distribution', International Journal of Mathematical Education in Science and Technology, 18 287295 (1987)
The redundant hypergeometric distribution results from a model similar to that for the ordinary hypergeometric, but where selections are made Â¿redundantlyÂ¿. The distribution has... [more]
The redundant hypergeometric distribution results from a model similar to that for the ordinary hypergeometric, but where selections are made Â¿redundantlyÂ¿. The distribution has applications in the area of statistical physics. However, the probability function is elementary and standard properties may be derived by familiar techniques. We anticipate therefore that the main use of the distribution may be as a source of novel but tractable exercises. Â© 1987 Taylor and Francis Group, LLC.



1987 
Best DJ, Rayner JCW, 'WelchÂ¿s approximate solution for the behrensÂ¿fisher problem', Technometrics, 29 205210 (1987)
The Wald, likelihood ratio, and score statistics have been calculated for the BehrensÂ¿Fisher problem. These statistics provide asymptotically equivalent and weakly optimal tests.... [more]
The Wald, likelihood ratio, and score statistics have been calculated for the BehrensÂ¿Fisher problem. These statistics provide asymptotically equivalent and weakly optimal tests. The test based on the Wald statistic was found to be very similar to the V test discussed by Welch (1937); hence the V test was compared with the likelihood ratio and score tests in a power study. Since the powers were very similar and the V test was more convenient to use from several points of view, we recommend this test. Sizes of the V test, as well as a power comparison with the usual pooled t test, were also obtained. Â© 1987 Taylor and Francis Group, LLC.



1986 
RAYNER JCW, BEST DJ, 'NEYMANTYPE SMOOTH TESTS FOR LOCATIONSCALE FAMILIES', BIOMETRIKA, 73 437446 (1986)



1986 
RAYNER JCW, DODDS KG, BEST DJ, 'THE EFFECT OF CATEGORIZATION ON A SIMPLE ANALYSIS OF VARIANCE MODEL', BIOMETRICAL JOURNAL, 28 159170 (1986)



1985 
RAYNER JCW, 'MAXIMUMLIKELIHOOD ESTIMATION OF MU AND SIGMA FROM A MULTIVARIATE NORMALDISTRIBUTION', AMERICAN STATISTICIAN, 39 123124 (1985)



1985 
RAYNER JCW, 'BIAS OF THE PEARSON CHISQUARED TEST', JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 21 329331 (1985)



1985 
RAYNER JCW, MCINTYRE RI, 'USE OF THE SCORE STATISTIC FOR TESTING GOODNESSOFFIT OF SOME GENERALIZED DISTRIBUTIONS', BIOMETRICAL JOURNAL, 27 159166 (1985)



1985 
BEST DJ, RAYNER JCW, 'A COMPARISON OF THE MPN AND FISHERYATES ESTIMATORS FOR THE DENSITY OF ORGANISMS', BIOMETRICAL JOURNAL, 27 167172 (1985)



1985 
RAYNER JCW, BEST DJ, 'THE EFFECT OF CATEGORIZATION ON TESTING FOR AN EXPONENTIAL SCALE SHIFT', JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 11 197206 (1985)



1985 
BEST DJ, RAYNER JCW, 'LANCASTERS TEST OF NORMALITY', JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 12 395400 (1985)



1985 
BEST DJ, RAYNER JCW, 'UNIFORMITY TESTING WHEN ALTERNATIVES HAVE LOW ORDER', SANKHYATHE INDIAN JOURNAL OF STATISTICS SERIES A, 47 2535 (1985)



1985 
Rayner JCW, Best DJ, Dodds KG, 'THE CONSTRUCTION OF THE SIMPLE X^{2} AND NEYMAN SMOOTH GOODNESS OF FIT TESTS', Statistica Neerlandica, 39 3550 (1985)
Suppose we wish to test whether data are consistent with a completely specified continuous distribution against a general alternative. Familiar omnibus tests are PEARSON'S X2 test... [more]
Suppose we wish to test whether data are consistent with a completely specified continuous distribution against a general alternative. Familiar omnibus tests are PEARSON'S X2 test and NEYMAN'S smooth test. Fundamental problems in the application of these tests are the construction and number of classes to use for X2, and the choice of the order of the NEYMAN smooth test. This paper examines these questions. Copyright Â© 1985, Wiley Blackwell. All rights reserved



1985 
Rayner JCW, 'Maximum likelihood estimation of Âµ and Sfrom a multivariate normal distribution', American Statistician, 39 123124 (1985)
In finding the maximum likelihood estimators of the parameters of a multivariate normal distribution, the following derivation first diagonalizes the covariance matrix and then ma... [more]
In finding the maximum likelihood estimators of the parameters of a multivariate normal distribution, the following derivation first diagonalizes the covariance matrix and then maximizes the likelihood by the choice of the elements of the transformed mean and the latent roots of the covariance matrix. Multivariate calculus is used to verify quickly and simply that the likelihood is indeed maximized. Â© 1985 Taylor & Francis Group, LLC.



1982 
RAYNER JCW, 'CONSTRUCTING OPTIMAL UNIVARIATE TESTS', COMMUNICATIONS IN STATISTICS PART ATHEORY AND METHODS, 11 19031917 (1982)



1981 
BEST DJ, RAYNER JCW, 'A NOTE ON MINEO GROUPING METHOD FOR THE CHISQUARE TEST OF GOODNESS OF FIT', SCANDINAVIAN JOURNAL OF STATISTICS, 8 185186 (1981)



1981 
Best DJ, Rayner JCW, 'Are Two Classes Enough for the X^{2}Goodness of Fit Test?', Statistica Neerlandica, 35 157163 (1981)
The chisquared goodness of fit test (also known as the PearsonX2test) is often used to test whether data are consistent with a specified continuous distribution. The value of X2(... [more]
The chisquared goodness of fit test (also known as the PearsonX2test) is often used to test whether data are consistent with a specified continuous distribution. The value of X2(and hence its associated probability level) can be altered by the choice of (i) the number of classes and (ii) the class probabilities. The effect on the power of the X2test of varying the number of classes when class probabilities are chosen to be equal is investigated. Copyright Â© 1981, Wiley Blackwell. All rights reserved



1975 
RAYNER JCW, 'VARIANCE BOUNDS', SANKHYATHE INDIAN JOURNAL OF STATISTICS SERIES B, 37 135138 (1975)


