2020 
Rayner JCW, Best DJ, 'Conditional and unconditional tests for the extended StuartMaxwell design', Communications in Statistics  Theory and Methods, (2020)
© 2020, © 2020 Taylor & Francis Group, LLC. A design is given that includes the designs for the StuartMaxwell and Cochran tests. Two models, called the conditional and unco... [more]
© 2020, © 2020 Taylor & Francis Group, LLC. A design is given that includes the designs for the StuartMaxwell and Cochran tests. Two models, called the conditional and unconditional, are given for this extended design and the corresponding Waldtype test statistics derived. These test statistics differ by a simple constant but purportedly have the same asymptotic ¿2 null distribution. Since the unconditional test statistic is always larger than the conditional, if inference is based on their asymptotic ¿2 null distributions, the unconditional test will always be more critical of the null hypothesis. The test of Stuart is based on a model that is neither conditional nor unconditional from this perspective, but coincides with the conditional test statistic. The discussion here addresses an apparent contradiction in the literature and indicates that for the unconditional tests inference should be based on resampling pvalues that reflect the model. The design for the extended StuartMaxwell tests is consistent with that for Cochran¿Mantel¿Haenszel general association test.



2018 
Rayner JCW, Best DJ, 'Extensions to the Cochran Mantel Haenszel Mean Scores and Correlation Tests', Journal of Statistical Theory and Practice, 12 561574 (2018) [C1]



2017 
Best DJ, Rayner JCW, 'A note on an unconditional alternative to Cochran's Q', Mathematical Scientist, 42 101103 (2017) [C1]



2017 
Best DJ, Rayner JCW, 'Analysis of ranked data in randomized blocks when there are missing values', JOURNAL OF APPLIED STATISTICS, 44 1623 (2017) [C1]



2017 
Rayner JCW, Best DJ, 'Unconditional analogues of Cochran Mantel Haenszel tests', Australian and New Zealand Journal of Statistics, 59 485494 (2017) [C1]



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 © Taylor & Francis Group, LLC. A number of nonparametric tests are compared empirically for a randomized block layout. We assess tests appropriate for when the dat... [more]
Copyright © 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.



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]
© 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]
© 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 
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]
© 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]
© 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]
© 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]
© 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 co... [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. © 2013 Elsevier Ltd.



2013 
Rayner JCW, Best DJ, 'Extended Anova And Rank Transform Procedures', Australian & New Zealand Journal Of Statistics, 55 305319 (2013) [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 
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 
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 applied tests of fit for the Rayleigh distribution', Sankhya B  Applied and Interdisciplinary Statistics, 72 254263 (2011) [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 für 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. © 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, 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]



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 
Szczerbanik MJ, Scott KJ, Paton JE, Best DJ, 'Susceptibility of Japanese pears to low concentrations of ethylene during storage', Australian Journal of Experimental Agriculture, 47 14801483 (2007) [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 
Szczerbanik MJ, Scott KJ, Paton CJE, Best DJ, 'The use of canola oil coatings to extend the storage life of Nashi pears', Australian Journal of Agricultural Research, 56 11151121 (2005)
Nashi cv. Nijisseiki was coated with canola oil before storage at 0°C over 3 consecutive seasons. This resulted in greater retention of green colour, even after only 8 weeks of st... [more]
Nashi cv. Nijisseiki was coated with canola oil before storage at 0°C over 3 consecutive seasons. This resulted in greater retention of green colour, even after only 8 weeks of storage. This effect continued throughout the 40week storage period and after 1 week at 20°C. Physiological disorders were generally low. The internal atmosphere was measured during storage at 0°C. The mean carbon dioxide levels for control and treated fruit were approximately 0.5 and 1.9%, and oxygen levels were 20 and 13%, respectively. The mean ethylene levels were approximately 5 and 30 µL/L, respectively. Thus, in oiled fruit, increased carbon dioxide levels may have overcome the effects of increased levels of ethylene. When fruit was transferred to 20°C, carbon dioxide and ethylene levels rose and oxygen levels fell but no damage was evident at the lower oil concentrations. Nonoiled fruit was then stored in polyethylene bags with or without a carbon dioxide absorbent (Calcium hydroxide) and an ethylene absorbent (Purafil). Fruit stored with the former became as yellow as the control fruit in air, whilst fruit with Purafil remained greener than fruit held in bags alone. When the absorbents were used together, much of the fruits' green colour was lost. Carbon dioxide levels therefore appear to be most important for the retention of green colour, and generally improve storage life. Ethylene removal further improves the retention of green colour in the Nijisseiki cultivar. A storage life of at least 40 weeks at 0°C was achieved with fruit from several sources in 3 seasons. Preliminary recommendations for smallscale hand applications are 1 or 2 drops per 240 g fruit. Commercial trials could involve dipping or spraying with 12% oil emulsified with Tween 80. © CSIRO 2005.



2005 
Szczerbanik MJ, Scott KJ, Paton JE, Best DJ, 'Effects of polyethylene bags, ethylene absorbent and 1methylcyclopropene on the storage of Japanese pears', Journal of Horticultural Science and Biotechnology, 80 162166 (2005)
Storage of the 'Nijisseiki' cultivar of Japanese pears was studied over three seasons for periods up to 36 weeks at 0°C. Storage in 50 µm thick lowdensity polyethylene ... [more]
Storage of the 'Nijisseiki' cultivar of Japanese pears was studied over three seasons for periods up to 36 weeks at 0°C. Storage in 50 µm thick lowdensity polyethylene (LDPE) bags at 0°C considerably delayed yellowing in all experiments, even after fruit was removed to 20°C for 1 week at the end of storage. The addition of an ethylene absorbent made from potassium permanganate on aluminium oxide (Purafil II) further delayed yellowing. Carbon dioxide levels in both treatments varied, but were generally in the range 23%. Oxygen levels remained high, generally 1619%. In bags without Purafil, ethylene levels rose slightly during storage and were generally about 0.15 µl l 1. When Purafil was included in the bags, the ethylene level was reduced 10fold or more. A sensory test indicated that the use of LDPE bags and ethylene absorbent resulted in fruit with better eating quality than fruit stored in air. Disorders over the 3year investigation were low even after longterm storage. The use of polyethylene bags reduced the severity of flesh browning, and flesh spot decay was virtually absent. The use of bags increased the severity of core browning. Inclusion of an ethylene absorbent in bags reduced the severity of disorders, particularly core browning. Treatment of the fruit with 1methylcyclopropene (1MCP), before or during storage, resulted in higher ethylene levels in the polyethylene bags. At the concentrations used, 1MCP did not improve the storage of 'Nijisseiki' compared to the use of polyethylene bags with Purafil II.



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]



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 
Murray JM, Easton K, Best DJ, 'A study of ChineseOrigin and EuropeanOrigin Australian consumers' texture preferences using a novel extruded product', Journal of Sensory Studies, 16 485504 (2001)
Diverse food choices and preferences are commonly observed between consumers crossculturally, however, many aspects of these behavioral differences are not yet fully understood. ... [more]
Diverse food choices and preferences are commonly observed between consumers crossculturally, however, many aspects of these behavioral differences are not yet fully understood. In order to investigate crosscultural texture preferences, six extruded snack samples, manufactured under different processing conditions to represent a range of textural characteristics were characterized by a trained panel using descriptive sensory analysis. In parallel, thirtyeight naive EuropeanOrigin and thirtyseven naive ChineseOrigin Australian consumers (t = 75) rated their preference for the snacks. The snacks were not representative of any snacks on the market and thus represented a "novel" product in both cultures. Additionally, consumers answered a simple questionnaire and completed the food neophobia scale. Results of descriptive analysis indicated significant differences (p=0.01) between the samples for 13 out of 15 descriptive attributes but no significant differences in preference were found between Europeanorigin and Chineseorigin consumers. However, overall analysis of mean effects indicated that Chineseorigin consumers rated samples significantly higher than Europeanorigin consumers (p=0.05), suggesting a cultural bias in the use of line scales. Gender did not influence texture preference, however, age significantly influenced preference for three of the samples (p=0.05) and analysis of mean effects also indicated differences in consumers' ratings which were related to age. Food neophobia classification did not influence preference, although many more Chineseorigin consumers (28) were classified as neophobic than were Europeanorigin consumers (11).



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



2000 
Holt SHA, Cobiac L, BeaumontSmith NE, Easton K, Best DJ, 'Dietary habits and the perception and liking of sweetness among Australian and Malaysian students: A crosscultural study', Food Quality and Preference, 11 299312 (2000)
This study examined whether the perception of, and preference for, varying levels of sucrose in water, orange juice, custard and biscuit were related to dietary intakes of sugar a... [more]
This study examined whether the perception of, and preference for, varying levels of sucrose in water, orange juice, custard and biscuit were related to dietary intakes of sugar and sweet foods in 69 Caucasian Australian and 63 Malaysian university students living in Australia. The two ethnic groups were equally able to discriminate the relative differences in sucrose concentration among the test samples, and a similar percentage of each group were sweetness likers or dislikers. Some significant differences between the ethnic groups' sweetness intensity and preference ratings were observed, but the differences were foodspecific and were not always apparent for the same sucrose level in the different test foods. Within each ethnic group, more subjects had greater difficulty discriminating different sucrose levels in a solid, high fat biscuit. The Australian group had higher mean liking ratings than the Malaysian group for the orange juice and biscuit samples. However, both groups preferred similar levels of sucrose in the juice, custard and biscuit, which were similar to the amounts of sucrose present in current commercial products. The hedonic response pattern to the sucrose solution was not a good predictor of the hedonic responses to the other test stimuli, which indicates that preferred levels of sweetness are foodspecific. Sweetness intensity ratings were not significantly associated with any of the dietary intake variables or bitterness ratings to 6npropylthiouracil. However, subjects who preferred higher levels of sucrose in the test stimuli tended to have higher dietary intakes of sugar and sweet foods. © 2000 Published by Elsevier Science Ltd. All rights reserved.



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, 'Nonparametric tests for data in randomised blocks with ordered alternatives', Journal of Applied Mathematics and Decision Sciences, 3 143153 (2000)
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. © Journal of Applied Mathematics & Decision Sciences.



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... [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. © Journal of Applied Mathematics & Decision Sciences.



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



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)



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



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



1995 
Best DJ, 'Consumer dataStatistical tests for differences in dispersion', Food Quality and Preference, 6 221225 (1995)
Three types of category or rank data, commonly obtained in consumer taste tests will be analysed via a ranks transformation followed by a partition of Pearson's X2. These thr... [more]
Three types of category or rank data, commonly obtained in consumer taste tests will be analysed via a ranks transformation followed by a partition of Pearson's X2. These three types of data are: independent samples data with ties, related samples data without ties, and related samples data with ties. The data are summarized as twoway tables of counts, where some of the counts are zero or small. Thus Monte Carlo P values are appropriate. The partition of X2 method places a number of common nonparametric statistics in the same family. All the examples relate to actual taste tests done at the CSIRO Food Research Laboratory. © 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 hypothes... [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 © 1995, Wiley Blackwell. All rights reserved



1994 
Best DJ, 'Nonparametric comparison of two histograms', Biometrics, 50 538541 (1994)
Scholz and Stephens (1987, Journal of the American Statistical Association 82, 918924) proposed a nonparametric ksample AndersonDarling statistic for grouped data. This note de... [more]
Scholz and Stephens (1987, Journal of the American Statistical Association 82, 918924) proposed a nonparametric ksample AndersonDarling statistic for grouped data. This note demonstrates that a partitionof¿2 method may give a more powerful nonparametric test, particularly when alternatives other than location shift are important. A tastetest example provides motivation.



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



1993 
Laing DG, Prescott J, Bell GA, Gillmore R, James C, Best DJ, et al., 'A crosscultural study of taste discrimination with Australians and Japanese', Chemical Senses, 18 161168 (1993)
As part of a larger crosscultural study of the chemoreceptive abilities and preferences of Australians and Japanese, this study investigated the differential taste sensitivity of... [more]
As part of a larger crosscultural study of the chemoreceptive abilities and preferences of Australians and Japanese, this study investigated the differential taste sensitivity of subjects from both cultures. The results indicate that there are no significant differences between the abilities of subjects from the two cultures to discriminate small increments (just noticeable differences) in the intensities of the four common tastants: sucrose, sodium chloride, citric acid and caffeine. Furthermore, the Weber ratios found with each tastant were within the range of those reported in the literature. These findings represent further evidence for the view that differences in responses of subjects from different cultures to chemosensory stimuli are restricted to preference behaviour arising from experience rather than from geneticallybased influences. © 1993 Oxford University Press.



1992 
Shorter AJ, Scott KJ, Ward G, Best DJ, 'Effect of ethylene absorption on the storage of Granny Smith apples held in polyethylene bags', Postharvest Biology and Technology, 1 189194 (1992)
Granny Smith apples grown in Western Australia are highly susceptible to the physiological disorders bitter pit and superficial scald, after short periods of storage. Granny Smith... [more]
Granny Smith apples grown in Western Australia are highly susceptible to the physiological disorders bitter pit and superficial scald, after short periods of storage. Granny Smith apples were held in sealed polyethylene bags with and without an ethylene absorbent Purafil (potassium permanganate on aluminium oxide). In two seasons the ethylene levels were markedly reduced with the use of potassium permanganate while the severity of bitter pit and superficial scald were also reduced. These effects of ethylene removal may be due to the delaying of fruit senescence. © 1992.



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



1992 
BEST DJ, RAYNER JCW, 'DISEASE CLUSTERING IN TIME  REPLY', BIOMETRICS, 48 327327 (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 © 1991, Wiley Bla... [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 © 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, 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)



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)



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 
Best DJ, Rayner JCW, 'Welch s approximate solution for the behrens fisher problem', Technometrics, 29 205210 (1987)
The Wald, likelihood ratio, and score statistics have been calculated for the Behrens¿Fisher problem. These statistics provide asymptotically equivalent and weakly optimal tests. ... [more]
The Wald, likelihood ratio, and score statistics have been calculated for the Behrens¿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. © 1987 Taylor and Francis Group, LLC.



1986 
Best DJ, Fisher NI, 'GOODNESSOFFIT AND DISCORDANCY TESTS FOR SAMPLES FROM THE WATSON DISTRIBUTION ON THE SPHERE', Australian Journal of Statistics, 28 1331 (1986)
The only parametric model in current use for axial data from a rotationally symmetric bipolar or girdle distribution on the sphere is the Watson distribution. This paper develops ... [more]
The only parametric model in current use for axial data from a rotationally symmetric bipolar or girdle distribution on the sphere is the Watson distribution. This paper develops methods for evaluating the model as a fit to data using graphical and formal goodnessoffit tests, and tests of discordancy. Copyright © 1986, Wiley Blackwell. All rights reserved



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 
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
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... [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 © 1985, Wiley Blackwell. All rights reserved



1984 
Best DJ, Cameron MA, Eagleson GK, Shaw DE, Speed TP, 'Downwind and longterm effects of cloud seeding in southeastern Australia.', Search, 15 154157 (1984)
Records of cloudseeding in the period from 1947 to 1974 have been used to assess which meteorological districts may have been affected if there were downwind and longterm effect... [more]
Records of cloudseeding in the period from 1947 to 1974 have been used to assess which meteorological districts may have been affected if there were downwind and longterm effects of seeding. Examination of monthly rainfall figures for the Central Tablelands (South) District indicates that, although the figures show an apparent effect of seeding, the same apparent effect occurs in a District which could not have been affected by seeding.from Authors



1984 
Fisher NI, Best DJ, 'GOODNESSOFFIT TESTS FOR FISHER'S DISTRIBUTION ON THE SPHERE', Australian Journal of Statistics, 26 142150 (1984)
A set of three goodnessoffit procedures is proposed to investigate the adequacy of fit of Fisher's distribution on the sphere as a model for a given sample of spherical dat... [more]
A set of three goodnessoffit procedures is proposed to investigate the adequacy of fit of Fisher's distribution on the sphere as a model for a given sample of spherical data. The procedures are all based on standard tests using the empirical distribution function. Copyright © 1984, Wiley Blackwell. All rights reserved



1983 
Best DJ, Cameron MA, Csiro GKE, 'A test for comparing large sets of tau values', Biometrika, 70 447453 (1983)
A test for the maximum of a large number of values of Kendall's t is obtained by an application of a Poisson limit theorem for symmetric statistics proved by Silverman & ... [more]
A test for the maximum of a large number of values of Kendall's t is obtained by an application of a Poisson limit theorem for symmetric statistics proved by Silverman & Brown (1978). The test depends on the number of comparisons rather than the sample size being large. It is shown that the asymptotics are always practically useful. A table of critical values for the test statistic is given, together with an illustrative application. © 1983 Biometrika Trust.



1981 
Best DJ, Fisher NI, 'The bias of the maximum likelihood estimators of the von misesfisher concentration parameters', Communications in Statistics  Simulation and Computation, 10 493502 (1981)
It is shown that the bias of the maximum likelihood estimators of the concentration parameters of the von Mises and Fisher distributions is considerable. New estimators which are ... [more]
It is shown that the bias of the maximum likelihood estimators of the concentration parameters of the von Mises and Fisher distributions is considerable. New estimators which are either nearly unbiased or nearly median unbiased are proposed. © 1981, Taylor & Francis Group, LLC. All rights reserved.



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
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 © 1981, Wiley Blackwell. All rights reserved



1981 
Rayner JCW, Best DJ, 'On HÜHN's Notion of Optimal Sample Size in the
Hühn's notion of optimal sample size for the ¿2 goodness of fit test is discussed. It involves minimising the achievable level of the test subject to a given nominal level. T... [more]
Hühn's notion of optimal sample size for the ¿2 goodness of fit test is discussed. It involves minimising the achievable level of the test subject to a given nominal level. This ignores the power of the competing tests and can lead to an ¿optimal¿ test that is uniformly less powerful than all the competing tests considered. Copyright © 1981 WILEYVCH Verlag GmbH & Co. KGaA



1975 
Best DJ, 'THE DIFFERENCE BETWEEN TWO POISSON EXPECTATIONS', Australian Journal of Statistics, 17 2933 (1975)
A number of statistics have been suggested for testing the difference between two Poisson expectations. On the basis of size and power calculations a new statistic, v= (2x+ 3/4)1/... [more]
A number of statistics have been suggested for testing the difference between two Poisson expectations. On the basis of size and power calculations a new statistic, v= (2x+ 3/4)1/2  (2y + 3/4)1/2, where x and y are the two observed Poisson values, is recommended for testing such differences. This statistic is shown to be similar in performance to the familiar u=(xy)f(x+y)1/2, except in the tails of the distribution where it is superior. Copyright © 1975, Wiley Blackwell. All rights reserved


