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Conjoint Associate Professor John Best

Conjoint Associate Professor

School of Mathematical and Physical Sciences (Statistics)

Career Summary

Biography

Research Expertise
Goodness of Fit & Ranking Methods for Experimental Design

Qualifications

  • Doctor of Philosophy, University of Wollongong

Keywords

  • Goodness of Fit
  • Physical Science

Fields of Research

Code Description Percentage
010499 Statistics not elsewhere classified 70
080299 Computation Theory and Mathematics not elsewhere classified 20
019999 Mathematical Sciences not elsewhere classified 10
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Publications

For publications that are currently unpublished or in-press, details are shown in italics.


Book (2 outputs)

Year Citation Altmetrics Link
2009 Rayner JC, Thas O, Best DJ, Smooth Tests of Goodness of Fit: Using R, John Wiley & Sons (Asia), Singapore, 272 (2009) [A3]
Co-authors John Rayner
2008 Rayner JCW, Best DJ, Brockhoff PB, Rayner GD, Nonparametrics for Sensory Science: A More Informative Approach (2008) [A1]

Sensory evaluation is the perception science of the food industry. Sensory data can be costly to obtain and so gleaning the most information possible from the data is key. Increas... [more]

Sensory evaluation is the perception science of the food industry. Sensory data can be costly to obtain and so gleaning the most information possible from the data is key. Increasingly, value is added to sensory evaluation by the use of statistics, especially to improve the quality of product development and to make the most of market research. Nonparametrics for Sensory Science is written to complement existing parametric methodology. Nonparametric methods are appropriate when facts are only available in nominal or ordinal form, and when the model assumptions necessary for parametric procedures do not hold. Author Rayner and his colleagues consider problems including the most commonly occurring and important experimental designs: the one-sample, k-sample, blocked samples, samples with factorial structure and samples with correlation structure. Innovative new techniques are outlined and complemented with real examples. Techniques described may be applied to data where the traditional, most frequently applied nonparametric tests, such as the Kruskal-Wallis, the Friedman and the Spearman tests, are applied. Those familiar with traditional nonparametric testing will be able to update their knowledge, acquiring powerful new methods. Those without prior knowledge of nonparametric testing will be able to acquire that knowledge through this book. Aimed at sensory scientists and statisticians interested in nonparametrics, the techniques of Nonparametrics for Sensory Science are of broad general interest, but are of particular interest in sensory evaluation applications. © 2005 John Charles Rayner, John Best, Per Brunn Brockhoff, and Glen Rayner.

DOI 10.1002/9780470752586
Citations Scopus - 8
Co-authors John Rayner

Journal article (78 outputs)

Year Citation Altmetrics Link
2017 Best DJ, Rayner JCW, 'Analysis of ranked data in randomized blocks when there are missing values', Journal of Applied Statistics, 44 16-23 (2017)

© 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]

© 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 Skillings¿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 Skillings¿Mack test.

DOI 10.1080/02664763.2016.1158245
Co-authors John Rayner
2017 Best DJ, Rayner JCW, 'A note on additional statistical analysis for JAR data', FOOD QUALITY AND PREFERENCE, 55 6-7 (2017)
DOI 10.1016/j.foodqual.2016.08.005
Co-authors John Rayner
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 1718-1730 (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 data are ... [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 Cochran-Mantel-Haenszel 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.

DOI 10.1080/03610918.2013.861483
Co-authors John Rayner
2015 Rayner JCW, Best DJ, Thas O, 'Extended Analysis of At Least Partially Ordered Multi-factor ANOVA', Australian and New Zealand Journal of Statistics, 57 211-224 (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.

DOI 10.1111/anzs.12113
Citations Scopus - 1Web of Science - 1
Co-authors John Rayner
2015 Best DJ, Rayner JCW, 'An alternative to pages test permitting both tied and missing data', Journal of Statistical Theory and Practice, 9 524-536 (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.

DOI 10.1080/15598608.2014.940098
Co-authors John Rayner
2014 Best DJ, Rayner JCW, 'Conover's F test as an alternative to durbin's test', Journal of Modern Applied Statistical Methods, 13 76-83 (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 chi-squared distribution. Indicative powers demonstrate that the F test is generally superior to Durbin's test.

Citations Scopus - 1
Co-authors John Rayner
2014 Best DJ, Rayner JCW, Allingham D, 'A note on formulae for CMH statistics for JAR data', Food Quality and Preference, 31 19-21 (2014) [C1]

Cochran-Mantel-Haenszel (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]

Cochran-Mantel-Haenszel (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.

DOI 10.1016/j.foodqual.2013.07.006
Citations Scopus - 3Web of Science - 3
Co-authors John Rayner
2013 Rayner JCW, Best DJ, 'Extended Anova And Rank Transform Procedures', Australian & New Zealand Journal Of Statistics, 55 305-319 (2013) [C1]
DOI 10.1111/anzs.12041
Citations Scopus - 4Web of Science - 4
Co-authors John Rayner
2012 Thas O, Best DJ, Rayner JC, 'Using orthogonal trend contrasts for testing ranked data with ordered alternatives', Statistica Neerlandica, 66 452-471 (2012) [C1]
DOI 10.1111/j.1467-9574.2012.00525.x
Citations Scopus - 2Web of Science - 1
Co-authors John Rayner
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]
Citations Scopus - 1
Co-authors John Rayner
2011 De Boeck B, Thas O, Rayner JC, Best DJ, 'Generalised smooth tests for the generalised Pareto distribution', Journal of Statistical Theory and Practice, 5 737-750 (2011) [C1]
DOI 10.1080/15598608.2011.10483742
Citations Scopus - 1
Co-authors John Rayner
2011 Rayner JC, Thas O, Best DJ, 'Smooth tests of goodness of fit', Wiley Interdisciplinary Reviews: Computational Statistics, 3 397-406 (2011) [C1]
Co-authors John Rayner
2011 De Boeck B, Thas O, Rayner JC, Best DJ, 'Smooth tests for the gamma distribution', Journal of Statistical Computation and Simulation, 81 843-855 (2011) [C1]
DOI 10.1080/00949650903520936
Citations Scopus - 3Web of Science - 2
Co-authors John Rayner
2011 Best DJ, Rayner JC, Allingham D, 'A statistical test for ranking data from partially balanced incomplete block designs', Journal of Sensory Studies, 26 81-84 (2011) [C1]
DOI 10.1111/j.1745-459X.2010.00324.x
Citations Scopus - 3Web of Science - 2
Co-authors John Rayner
2011 Best DJ, Rayner JC, Thas O, 'Easily appled tests of fit for the Rayleigh distribution', Sankhya B - Applied and Interdisciplinary Statistics, 72 254-263 (2011) [C1]
Citations Scopus - 4
Co-authors John Rayner
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 data-driven 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 data-driven 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 goodness-of-fit, statistical, and probabilistic model assessment courses. Practitioners wishing to make an informed choice of goodness-of-fit 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.

DOI 10.1002/9780470824443
Co-authors John Rayner
2010 Best DJ, Rayner JC, Thas O, 'Four tests of fit for the beta-binomial distribution', Journal of Applied Statistics, 37 1547-1554 (2010) [C1]
DOI 10.1080/02664760903089664
Co-authors John Rayner
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 1-15 (2010) [C1]
Co-authors John Rayner
2009 Best DJ, Rayner JC, Thas O, 'Anscombe's Tests of fit for the negative binomial distribution', Journal of Statistical Theory and Practice, 3 555-565 (2009) [C1]
DOI 10.1080/15598608.2009.10411946
Citations Scopus - 1
Co-authors John Rayner
2009 Rayner JC, Best DJ, Thas O, 'Generalised smooth tests of goodness of fit', Journal of Statistical Theory and Practice, 3 665-679 (2009) [C1]
DOI 10.1080/15598608.2009.10411953
Citations Scopus - 2
Co-authors John Rayner
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, 3 705-733 (2009) [C1]
DOI 10.1080/15598608.2009.10411955
Citations Scopus - 1
Co-authors John Rayner
2009 Rayner JC, Best DJ, Thas O, 'Guest editors', Journal of Statistical Theory and Practice, 3 (2009) [C2]
Co-authors John Rayner
2009 Rayner JC, Thas O, Best DJ, 'Introduction to modern goodness of fit methods', Journal of Statistical Theory and Practice, 3 537-541 (2009) [C3]
DOI 10.1080/15598608.2009.10411944
Co-authors John Rayner
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]
DOI 10.1155/2008/463781
Citations Scopus - 1
Co-authors John Rayner
2008 Best DJ, Rayner JC, Thas O, 'Comparison of some tests of fit for the Laplace distribution', Computational Statistics and Data Analysis, 52 5338-5343 (2008) [C1]
DOI 10.1016/j.csda.2008.05.023
Citations Scopus - 4Web of Science - 2
Co-authors John Rayner
2008 Best DJ, Rayner JC, Thas O, 'X-2 and its components as tests of normality for grouped data', Journal of Applied Statistics, 35 481-492 (2008) [C1]
DOI 10.1080/02664760701835219
Citations Scopus - 2Web of Science - 1
Co-authors John Rayner
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 1480-1483 (2007) [C1]
DOI 10.1071/ea06186
Citations Scopus - 2Web of Science - 2
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 89-99 (2007) [C1]
Co-authors John Rayner
2007 Best DJ, Rayner JC, Thas O, 'Goodness of fit for the zero-truncated Poisson distribution', Journal of Statistical Computation and Simulation, 77 585-591 (2007) [C1]
DOI 10.1080/10629360600569329
Citations Scopus - 4Web of Science - 2
Co-authors John Rayner
2007 Best DJ, Rayner JC, 'Chi-squared components for tests of fit and improved models for the grouped exponential distribution', Computational Statistics and Data Analysis, 51 3946-3954 (2007) [C1]
DOI 10.1016/j.csda.2006.03.014
Citations Scopus - 6Web of Science - 4
Co-authors John Rayner
2006 Best DJ, Brockhoff PB, Rayner JCW, 'Tests for balanced incomplete block ranked data with ties', STATISTICA NEERLANDICA, 60 3-11 (2006) [C1]
DOI 10.1111/j.1467-9574.2006.00305.x
Citations Scopus - 2Web of Science - 2
Co-authors John Rayner
2006 Best DJ, Rayner JCW, 'Improved testing for the binomial distribution using chi-squared components with data-dependent cells', JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 76 75-81 (2006) [C1]
DOI 10.1080/00949650412331320891
Citations Scopus - 4Web of Science - 2
Co-authors John Rayner
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]
DOI 10.1155/JAMDS/2006/31089
Co-authors John Rayner
2005 Best DJ, Rayner JCW, 'Improved testing for the Poisson distribution using chisquared components with data dependent cells', COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 34 85-96 (2005) [C1]
DOI 10.1081/SAC-200053153
Citations Scopus - 3Web of Science - 2
Co-authors John Rayner
2005 Thas O, Rayner JCW, Best DJ, 'Tests for symmetry based on the one-sample Wilcoxon signed rank statistic', COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 34 957-973 (2005) [C1]
DOI 10.1080/03610910500308354
Citations Scopus - 10Web of Science - 9
Co-authors John Rayner
2004 Brockhoff PB, Best DJ, Rayner JCW, 'Partitioning Anderson's statistic for tied data', JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 121 93-111 (2004) [C1]
DOI 10.1016/S0378-3758(02)00508-6
Citations Scopus - 8Web of Science - 4
Co-authors John Rayner
2004 Brockhoff PB, Best DJ, Rayner JCW, 'An application of extended analysis for ranked data with ties', AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 46 197-204 (2004) [C1]
DOI 10.1111/j.1467-842X.2004.00324.x
Citations Scopus - 1
Co-authors John Rayner
2003 Best DJ, Rayner JCW, 'Tests of fit for the geometric distribution', COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 32 1065-1078 (2003) [C1]
DOI 10.1081/SAC-120023878
Citations Scopus - 10Web of Science - 7
Co-authors John Rayner
2003 Brockhoff PB, Best DJ, Rayner JCW, 'Using Anderson's statistic to compare distributions of consumer preference rankings', JOURNAL OF SENSORY STUDIES, 18 77-82 (2003)
DOI 10.1111/j.1745-459X.2003.tb00374.x
Citations Scopus - 3Web of Science - 2
Co-authors John Rayner
2001 Best DJ, Rayner JCW, 'Nonparametric analysis for trinary sensory data', JOURNAL OF SENSORY STUDIES, 16 249-260 (2001)
DOI 10.1111/j.1745-459X.2001.tb00299.x
Citations Scopus - 1Web of Science - 1
Co-authors John Rayner
2000 Holt SHA, Cobiac L, Beaumont-Smith NE, Easton K, Best DJ, 'Dietary habits and the perception and liking of sweetness among Australian and Malaysian students: A cross-cultural study', Food Quality and Preference, 11 299-312 (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 food-specific 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 food-specific. Sweetness intensity ratings were not significantly associated with any of the dietary intake variables or bitterness ratings to 6-n-propylthiouracil. 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.

Citations Scopus - 36
2000 Best DJ, Rayner JCW, 'Extended statistical analysis of ranked data from balanced incomplete block and paired comparison designs', JOURNAL OF SENSORY STUDIES, 15 383-392 (2000)
DOI 10.1111/j.1745-459X.2000.tb00277.x
Citations Scopus - 2Web of Science - 2
Co-authors John Rayner
2000 Rayner JCW, Best DJ, 'Analysis of singly ordered two-way contingency tables', Journal of Applied Mathematics and Decision Sciences, 4 83-98 (2000)

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 first summ... [more]

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 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.

Citations Scopus - 9
Co-authors John Rayner
1999 Rayner JCW, 'Modelling ties in the sign test', BIOMETRICS, 55 663-665 (1999)
DOI 10.1111/j.0006-341X.1999.00663.x
Citations Scopus - 13Web of Science - 12
Co-authors John Rayner
1999 Rayner JCW, Best DJ, 'Nonparametric tests for data in randomised blocks with ordered alternatives', Journal of Applied Mathematics and Decision Sciences, 3 143-153 (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. © Journal of Applied Mathematics & Decision Sciences.

Citations Scopus - 1
Co-authors John Rayner
1999 Best DJ, Rayner JCW, 'Goodness of fit for the Poisson distribution', STATISTICS & PROBABILITY LETTERS, 44 259-265 (1999)
DOI 10.1016/S0167-7152(99)00017-6
Citations Scopus - 6Web of Science - 8
Co-authors John Rayner
1998 Best DJ, Rayner JCW, 'Nonparametric analysis of ordinal categorical response data with factorial structure', JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS, 47 439-446 (1998)
Citations Web of Science - 7
Co-authors John Rayner
1998 Best DJ, Rayner JCW, Stephens LG, 'Small-sample comparison of McCullagh and Nair analyses for nominal-ordinal categorical data', COMPUTATIONAL STATISTICS & DATA ANALYSIS, 28 217-223 (1998)
DOI 10.1016/S0167-9473(98)00031-0
Citations Scopus - 5Web of Science - 4
Co-authors John Rayner
1997 Best DJ, Rayner JCW, 'Goodness of fit for the binomial distribution', AUSTRALIAN JOURNAL OF STATISTICS, 39 355-364 (1997)
Citations Web of Science - 3
Co-authors John Rayner
1997 Best DJ, Rayner JCW, 'Product maps for ranked preference data', STATISTICIAN, 46 347-354 (1997)
Citations Scopus - 4Web of Science - 2
Co-authors John Rayner
1997 Rayner JCW, Best DJ, 'How order affects the sign test', BIOMETRICS, 53 1416-1421 (1997)
DOI 10.2307/2533507
Co-authors John Rayner
1997 Rayner JCW, Best DJ, 'Extensions to the Kruskal-Wallis test and a generalised median test with extensions', Journal of Applied Mathematics and Decision Sciences, 1 13-25 (1997)

The data for the tests considered here may be presented in two-way 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 two-way 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 Kruskal-Wallis-type data when there are no ties, the location component is the Kruskal-Wallis 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 well-known median test. In this situation the location-detecting 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.

Citations Scopus - 3
Co-authors John Rayner
1997 Best DJ, Rayner JCW, 'Crockett's test of fit for the bivariate Poisson', BIOMETRICAL JOURNAL, 39 423-430 (1997)
DOI 10.1002/bimj.4710390404
Citations Scopus - 1
Co-authors John Rayner
1997 Best DJ, Rayner JCW, 'Goodness of fit for the ordered categories discrete uniform distribution', COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 26 899-909 (1997)
DOI 10.1080/03610929708831957
Citations Scopus - 2Web of Science - 2
Co-authors John Rayner
1996 Best DJ, Rayner JCW, 'Nonparametric analysis for doubly ordered two-way contingency tables', BIOMETRICS, 52 1153-1156 (1996)
DOI 10.2307/2533077
Citations Scopus - 26Web of Science - 22
Co-authors John Rayner
1996 Rayner JCW, Best DJ, 'Smooth extensions of Pearsons's product moment correlation and Spearman's rho', STATISTICS & PROBABILITY LETTERS, 30 171-177 (1996)
DOI 10.1016/0167-7152(95)00216-2
Citations Scopus - 20Web of Science - 16
Co-authors John Rayner
1995 RAYNER JCW, BEST DJ, MATHEWS KL, 'INTERPRETING THE SKEWNESS COEFFICIENT', COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 24 593-600 (1995)
DOI 10.1080/03610929508831509
Citations Scopus - 31Web of Science - 22
Co-authors John Rayner
1995 Rayner JCW, Best DJ, 'SMOOTH TESTS FOR THE BIVARIATE POISSON DISTRIBUTION', Australian Journal of Statistics, 37 233-245 (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 © 1995, Wiley Blackwell. All rights reserved

DOI 10.1111/j.1467-842X.1995.tb00656.x
Co-authors John Rayner
1994 BEST DJ, GRAHAM D, RAYNER JCW, 'ESTIMATING CORRELATION FROM CATEGORIZED BIVARIATE NORMAL DATA', JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 49 141-149 (1994)
DOI 10.1080/00949659408811567
Co-authors John Rayner
1992 Best DJ, Rayner JC, 'Response', Technometrics, 34 250 (1992)
DOI 10.1080/00401706.1992.10484948
Co-authors John Rayner
1992 BEST DJ, RAYNER JCW, 'DISEASE CLUSTERING IN TIME - REPLY', BIOMETRICS, 48 327-327 (1992)
Co-authors John Rayner
1991 Rayner JCW, Best DJ, 'What Divisor for the Sample Variance?', Teaching Statistics, 13 85-87 (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 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 © 1991, Wiley Blackwell. All rights reserved

DOI 10.1111/j.1467-9639.1991.tb00184.x
Co-authors John Rayner
1991 RAYNER JCW, BEST DJ, LIDDELL GF, 'OPTIMAL TESTING IN A 3 WAY ANOVA MODEL', COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 20 411-425 (1991)
DOI 10.1080/03610919108812962
Citations Web of Science - 2
Co-authors John Rayner
1990 RAYNER JCW, BEST DJ, 'SMOOTH TESTS OF GOODNESS OF FIT - AN OVERVIEW', INTERNATIONAL STATISTICAL REVIEW, 58 9-17 (1990)
DOI 10.2307/1403470
Citations Web of Science - 36
Co-authors John Rayner
1989 BEST DJ, RAYNER JCW, 'GOODNESS OF FIT FOR THE GEOMETRIC DISTRIBUTION', BIOMETRICAL JOURNAL, 31 307-311 (1989)
DOI 10.1002/bimj.4710310307
Citations Web of Science - 5
Co-authors John Rayner
1988 BEST DJ, RAYNER JCW, 'A TEST FOR BIVARIATE NORMALITY', STATISTICS & PROBABILITY LETTERS, 6 407-412 (1988)
DOI 10.1016/0167-7152(88)90100-9
Citations Scopus - 7Web of Science - 4
Co-authors John Rayner
1988 RAYNER JCW, BEST DJ, 'SMOOTH TESTS OF GOODNESS OF FIT FOR REGULAR DISTRIBUTIONS', COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 17 3235-3267 (1988)
DOI 10.1080/03610928808829801
Citations Scopus - 6Web of Science - 5
Co-authors John Rayner
1987 BEST DJ, RAYNER JCW, 'WELCH APPROXIMATE SOLUTION FOR THE BEHRENS-FISHER PROBLEM', TECHNOMETRICS, 29 205-210 (1987)
DOI 10.2307/1269775
Citations Web of Science - 58
Co-authors John Rayner
1987 BEST DJ, RAYNER JCW, 'GOODNESS-OF-FIT FOR GROUPED DATA USING COMPONENTS OF PEARSON-X2', COMPUTATIONAL STATISTICS & DATA ANALYSIS, 5 53-57 (1987)
DOI 10.1016/0167-9473(87)90007-7
Citations Scopus - 6Web of Science - 9
Co-authors John Rayner
1987 Best DJ, Rayner JCW, 'Welch¿s approximate solution for the behrens¿fisher problem', Technometrics, 29 205-210 (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.

DOI 10.1080/00401706.1987.10488211
Citations Scopus - 58
Co-authors John Rayner
1986 RAYNER JCW, BEST DJ, 'NEYMAN-TYPE SMOOTH TESTS FOR LOCATION-SCALE FAMILIES', BIOMETRIKA, 73 437-446 (1986)
Citations Scopus - 19Web of Science - 21
Co-authors John Rayner
1985 BEST DJ, RAYNER JCW, 'A COMPARISON OF THE MPN AND FISHER-YATES ESTIMATORS FOR THE DENSITY OF ORGANISMS', BIOMETRICAL JOURNAL, 27 167-172 (1985)
DOI 10.1002/bimj.4710270208
Citations Web of Science - 7
Co-authors John Rayner
1985 RAYNER JCW, BEST DJ, 'THE EFFECT OF CATEGORIZATION ON TESTING FOR AN EXPONENTIAL SCALE SHIFT', JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 11 197-206 (1985)
DOI 10.1016/0378-3758(85)90006-0
Citations Scopus - 3Web of Science - 1
Co-authors John Rayner
1985 BEST DJ, RAYNER JCW, 'LANCASTERS TEST OF NORMALITY', JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 12 395-400 (1985)
DOI 10.1016/0378-3758(85)90088-6
Citations Scopus - 6Web of Science - 6
Co-authors John Rayner
1985 BEST DJ, RAYNER JCW, 'UNIFORMITY TESTING WHEN ALTERNATIVES HAVE LOW ORDER', SANKHYA-THE INDIAN JOURNAL OF STATISTICS SERIES A, 47 25-35 (1985)
Citations Web of Science - 5
Co-authors John Rayner
1985 Rayner JCW, Best DJ, Dodds KG, 'THE CONSTRUCTION OF THE SIMPLE X2 AND NEYMAN SMOOTH GOODNESS OF FIT TESTS', Statistica Neerlandica, 39 35-50 (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 © 1985, Wiley Blackwell. All rights reserved

DOI 10.1111/j.1467-9574.1985.tb01123.x
Citations Scopus - 7
Co-authors John Rayner
1981 BEST DJ, RAYNER JCW, 'A NOTE ON MINEO GROUPING METHOD FOR THE CHI-SQUARE TEST OF GOODNESS OF FIT', SCANDINAVIAN JOURNAL OF STATISTICS, 8 185-186 (1981)
Co-authors John Rayner
1981 Best DJ, Rayner JCW, 'Are Two Classes Enough for the X2Goodness of Fit Test?', Statistica Neerlandica, 35 157-163 (1981)

The chi-squared 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 chi-squared 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

DOI 10.1111/j.1467-9574.1981.tb00724.x
Citations Scopus - 3
Co-authors John Rayner
Show 75 more journal articles

Review (1 outputs)

Year Citation Altmetrics Link
2015 Rayner JCW, Thas O, Best DJ, 'Statistical Distribution Models: Goodness of Fit Tests (2015)
Co-authors John Rayner

Conference (6 outputs)

Year Citation Altmetrics Link
2011 Rayner JC, Best DJ, 'Nonparametric tests for two factor designs with an application to latin squares', Proceedings of the 4th Applied Statistics Education and Research Collaboration (ASEARC) Conference (2011) [E1]
Co-authors John Rayner
2011 Best DJ, Rayner JC, Thas O, 'Smooth tests of fit for a mixture of two Poisson distributions', Proceedings of the 4th Applied Statistics Education and Research Collaboration (ASEARC) Conference (2011) [E1]
Co-authors John Rayner
2009 Best DJ, Rayner JC, Thas O, 'Nonparametric tests for randomized block data with ties and ordered alternatives', ASEARC: Proceedings of the Third Annual ASEARC Research Conference (2009) [E1]
Co-authors John Rayner
2008 Best DJ, Rayner JC, Thas O, 'Tests of fit for the beta binomial distribution', JSM 2008 Abstract Book (2008) [E3]
Co-authors John Rayner
2001 Best DJ, Rayner JCW, 'Application of the Stuart test to sensory evaluation data', FOOD QUALITY AND PREFERENCE (2001)
DOI 10.1016/S0950-3293(01)00024-6
Citations Scopus - 6Web of Science - 6
Co-authors John Rayner
2000 Best DJ, Rayner JCW, O'Sullivan MG, 'Product maps for consumer categorical data', FOOD QUALITY AND PREFERENCE (2000)
DOI 10.1016/S0950-3293(99)00044-0
Citations Scopus - 5Web of Science - 5
Co-authors John Rayner
Show 3 more conferences
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Conjoint Associate Professor John Best

Position

Conjoint Associate Professor
School of Mathematical and Physical Sciences
Faculty of Science

Focus area

Statistics

Contact Details

Email john.best@newcastle.edu.au
Phone (02) 4921 5515
Fax (02) 4921 6898

Office

Room E.1.12
Building Science Offices
Location Ourimbah
10 Chittaway Road
Ourimbah, NSW 2258
Australia
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