Exact testing for heteroscedasticity in a two‐way layout in variety frost trials when incorporating a covariate

Angelika A. Pilkington; Brenton R. Clarke; Dean A. Diepeveen

doi:10.1111/anzs.12404

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Exact testing for heteroscedasticity in a two‐way layout in variety frost trials when incorporating a covariate

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Exact testing for heteroscedasticity in a two‐way layout in variety frost trials when incorporating a covariate

Angelika A. Pilkington, Brenton R. Clarke and Dean A. Diepeveen

Australian & New Zealand journal of statistics, Vol.65(4), pp.309-326

2024

DOI: https://doi.org/10.1111/anzs.12404

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Abstract

Two‐way layouts are common in grain industry research where it is often the case that there are one or more covariates. It is widely recognised that when estimating fixed effect parameters, one should also examine for possible extra error variance structure. An exact test for heteroscedasticity, when there is a covariate, is illustrated for a data set from frost trials in Western Australia. While the general algebra for the test is known, albeit in past literature, there are computational aspects of implementing the test for the two way when there are covariates. In this scenario the test is shown to have greater power than the industry standard, and because of its exact size, is preferable to use of the restricted maximum likelihood ratio test (REMLRT) based on the approximate asymptotic distribution in this instance. Formulation of the exact test considered here involves creation of appropriate contrasts in the experimental design. This is illustrated using specific choices of observations corresponding to an index set in the linear model for the two‐way layout. Also an algorithm supplied complements the test. Comparisons of size and power then ensue. The test has natural extensions when there are unbalanced data, and more than one covariate may be present. Results can be extended to Balanced Incomplete Block Designs.

Details

Title: Exact testing for heteroscedasticity in a two‐way layout in variety frost trials when incorporating a covariate
Authors/Creators: Angelika A. Pilkington - Murdoch University
Brenton R. Clarke - Murdoch University, School of Mathematics, Statistics, Chemistry and Physics
Dean A. Diepeveen - Centre for Crop and Food Innovation, Food Futures Institute Murdoch University Murdoch WA 6150 Australia, Department of Primary Industries and Regional Development Western Australia South Perth WA 6151 Australia
Publication Details: Australian & New Zealand journal of statistics, Vol.65(4), pp.309-326
Publisher: John Wiley & Sons Australia, Ltd on behalf of Statistical Society of Australia.
Identifiers: 991005624668607891
Murdoch Affiliation: School of Mathematics, Statistics, Chemistry and Physics; School of Information Technology
Language: English
Resource Type: Journal article

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Collaboration types: Domestic collaboration
Citation topics: 9 Mathematics; 9.92 Statistical Methods; 9.92.220 Robust Estimation
Web Of Science research areas: Statistics & Probability
ESI research areas: Mathematics