A method for testing interaction in unreplicated two-way tables: using all pairwise interaction contrasts

Kharrati-Kopaei, Mahmood; Miller, Arden

doi:10.1080/00949655.2015.1057821

Cited by 3 publications

(13 citation statements)

References 16 publications

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“…In this section, we review briefly some additivity tests that we later combine. We actually review the tests proposed by Boik (), Piepho (), Kharrati‐Kopaei & Sadooghi‐Alvandi (), Franck et al (), Malik et al () and Kharrati‐Kopaei & Miller (). We use abbreviations B93, P94, KS07, F13, M16 and KM16 for these tests, respectively.…”

Section: A Review Of the Utilized Interaction Testsmentioning

confidence: 99%

“…KM16. Kharrati‐Kopaei & Miller () provided a test statistic based on inspecting all pairwise interaction contrasts (PICs); that is,

μ_{i j} - μ_{i^{'} j} - μ_{i j^{'}} + μ_{i^{'} j^{'}}, i \neq i^{'}

and j ≠ j ′ where the μ i j s denote the cell means. The main idea in this procedure is that if a significant interaction presents, its corresponding interaction contrast shall be active (significant).…”

Section: A Review Of the Utilized Interaction Testsmentioning

confidence: 99%

“…Note that n = a b ( a −1)( b −1)/4. Let

S_{0} = m e d i a n ({}, (||, Z_{k}); k = 1, \dots, n) / c_{0}

, where c 0 is an unbiasing constant given by Kharrati‐Kopaei & Miller (), and Z k is the k ‐th element of Z . Let

P S E = m e d i a n ({}, (||, Z_{k}); (||, Z_{k}) \leq 5 S_{0})

and

T_{K M 16} = m a x ({}, (||, Z_{k}); k = 1, \dots, n) / P S E

.…”

Section: A Review Of the Utilized Interaction Testsmentioning

confidence: 99%

“…The latter group (i.e. non‐functional‐form‐based methods) includes methods proposed by Milliken & Rasmuson (), Tusell (), Boik (), Piepho (), Kharrati‐Kopaei & Sadooghi‐Alvandi (), Franck et al (), Malik et al () and Kharrati‐Kopaei & Miller (). See also Alin & Kurt () who provided an overview of many methods.…”

Section: Introductionmentioning

confidence: 99%

“…Indeed, Kharrati‐Kopaei & Sadooghi‐Alvandi () formally showed that there is no test that has high power against all interaction patterns Therefore, it is reasonable to combine multiple tests to test additivity. However, the main problem is how to combine multiple dependent tests into a single test procedure for testing additivity such that it controls the type I error rate and has an acceptably high power (Franck et al , ; Kharrati‐Kopaei & Miller, ).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Method for Testing Additivity in Unreplicated Two‐Way Layouts Based on Combining Multiple Interaction Tests

Shenavari

Kharrati-Kopaei

2018

Int Statistical Rev

Self Cite

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There are several non-functional-form-based interaction tests for testing additivity in unreplicated two-way layouts. The distinctness of the various tests in this setting is somewhat unfortunate, as no single test can detect all patterns of possible interaction, and the tests are sensitive to a particular pattern of interaction. Therefore, it is reasonable to combine multiple interaction tests for testing additivity. The main problem is how we can combine multiple dependent tests into a single test such that it has an acceptable performance in terms of controlling the type I error rate and maximizing the power. In this paper, we review six methods for combining interaction tests which utilize six different non-functional-form-based interaction tests. We also propose two novel combination methods based on the Jacobi polynomial expansion and the Gaussian copula. We first compare these eight combination methods in terms of controlling the type I error rate via a simulation study. We then compare the six interaction tests and four combination methods in terms of power. The simulation results show that our proposed combination method that is based on the Jacobi polynomial expansion has the best performance in terms of controlling the type I error rate and maximizing the power. Therefore, we recommend this combination method as a test procedure for testing additivity. The major contribution of this work is to provide researchers with a testing approach which leverages many existing methods to detect disparate forms of non-additivity. This alleviates the need for researchers to naively choose among highly specialized methods by instead allowing for a general approach that captures a number of interaction effects with reasonable power.

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Section: A Review Of the Utilized Interaction Testsmentioning

confidence: 99%

“…KM16. Kharrati‐Kopaei & Miller () provided a test statistic based on inspecting all pairwise interaction contrasts (PICs); that is,

μ_{i j} - μ_{i^{'} j} - μ_{i j^{'}} + μ_{i^{'} j^{'}}, i \neq i^{'}

Section: A Review Of the Utilized Interaction Testsmentioning

confidence: 99%

“…Note that n = a b ( a −1)( b −1)/4. Let

S_{0} = m e d i a n ({}, (||, Z_{k}); k = 1, \dots, n) / c_{0}

, where c 0 is an unbiasing constant given by Kharrati‐Kopaei & Miller (), and Z k is the k ‐th element of Z . Let

P S E = m e d i a n ({}, (||, Z_{k}); (||, Z_{k}) \leq 5 S_{0})

and

T_{K M 16} = m a x ({}, (||, Z_{k}); k = 1, \dots, n) / P S E

.…”

Section: A Review Of the Utilized Interaction Testsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Method for Testing Additivity in Unreplicated Two‐Way Layouts Based on Combining Multiple Interaction Tests

Shenavari

Kharrati-Kopaei

2018

Int Statistical Rev

Self Cite

View full text Add to dashboard Cite

show abstract

combinIT: A Combined Interaction Test for Unreplicated Two-Way Tables

Shenavari,

Haghbin,

Kharrati-Kopaei

et al. 2022

CRAN: Contributed Packages

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combinIT: An R Package for Combining Interaction Tests for Unreplicated Two-Way Tables

Kharrati-Kopaei,

Shenavari,

Haghbin

2023

The R Journal

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Several new tests have been proposed for testing interaction in unreplicated two-way analysis of variance models. Unfortunately, each test is powerful for detecting a pattern of interaction. Therefore, it is reasonable to combine multiple interaction tests to increase the power of detection for significant interactions. We introduce the package combinIT that provides researchers the results of six existing recommended interaction tests, including: the value of test statistics, exact Monte Carlo p-values, approximated or adjusted p-values, the results of four combined tests and explanations of interaction types if the discussed tests are significant. The software combinIT is a more comprehensive R package in comparison with the two existing packages. In addition, the software is executed quickly to obtain the exact Monte Carlo p-values, even for large Monte Carlo runs, in contrast to existing packages.

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A method for testing interaction in unreplicated two-way tables: using all pairwise interaction contrasts

Cited by 3 publications

References 16 publications

A Method for Testing Additivity in Unreplicated Two‐Way Layouts Based on Combining Multiple Interaction Tests

A Method for Testing Additivity in Unreplicated Two‐Way Layouts Based on Combining Multiple Interaction Tests

combinIT: A Combined Interaction Test for Unreplicated Two-Way Tables

combinIT: An R Package for Combining Interaction Tests for Unreplicated Two-Way Tables

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