Statistical Methods: The Geometric Approach

Saville, David J.; Wood, Graham R.

doi:10.1007/978-1-4612-0971-3

Cited by 86 publications

(88 citation statements)

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“…This is a pre-specified contrast. For information on how to match ideas (hypotheses) to contrasts or comparisons, see Cochran and Cox (1957) or Saville and Wood (1991).…”

Section: Traditional Hypothesis Testing Scenariomentioning

confidence: 99%

Multiple Comparison Procedures—Cutting the Gordian Knot

Saville

2015

Agronomy Journal

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Multiple comparison procedures (MCPs), or mean separation tests, have been the subject of great controversy since the 1950s. Essentially, these procedures are an attempt at simultaneously formulating and testing pairwise comparison hypotheses using data from a single experiment. An unacceptable operating characteristic of most MCPs is their “inconsistency,” an idea that is illustrated in this article. This characteristic led to the development of a “practical solution” to the MCP problem, which is to “cut the Gordian knot” by abandoning any attempt at simultaneous formulation and testing. Instead, I recommend using the simplest multiple comparison procedure, the unrestricted least significant difference procedure, to (i) formulate new hypotheses at a known “false discovery rate” (in the null case) such as 5%, and (ii) independently test interesting new hypotheses in a second experiment. I also discuss the implications for sample size calculations of the choice of MCP.

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“…This is a pre-specified contrast. For information on how to match ideas (hypotheses) to contrasts or comparisons, see Cochran and Cox (1957) or Saville and Wood (1991).…”

Section: Traditional Hypothesis Testing Scenariomentioning

confidence: 99%

Multiple Comparison Procedures—Cutting the Gordian Knot

Saville

2015

Agronomy Journal

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“…However, as in many moderated regression analyses in the literature (e.g., Brock et al, 2006), introduction of the productterm increased the corresponding variable inflation factor (VIF), to 66, which is much above the recommended cut-off value of 5 or 10. Hence, we orthogonalized the product-term using the procedure suggested by Saville and Wood (1991). This procedure involves first running a simple regression with the product-term as the dependent variable and environmental performance and cost-to-turnover ratio as the independent variables.…”

Section: Resultsmentioning

confidence: 99%

“…There was evidence of multicollinearity with some variable-inflation factors (VIF) above the threshold of 5 (Hair et al, 2006) in our moderated regression analysis. To overcome this problem we employed an orthogonalizing procedure, which is based on replacing the interaction term with related residuals (Saville and Wood, 1991). This procedure will be explained during our discussion on moderated regression analysis later in this section.…”

Section: Testing the Hypothesesmentioning

confidence: 99%

The Moderating Effect of Operations Efficiency on the Links between Environmental Performance and Financial Performance: The UK Evidence

Ramanathan¹,

Akanni²

2015

KTIS

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Drawing upon the resource-based-view of a firm, we investigate the moderating role of operations efficiency on the link between environmental and financial performance. Extant literature has highlighted that operations efficiency is closely associated with the environmental/financial performance of firms, but no empirical study has investigated how operations efficiency affects the link between environmental and financial performance. We argue that operations efficiency could act as a moderator of this relationship. To test the hypothesized relationships, we have used available secondary quantitative UK data, namely data on the environmental/financial performance of Britain's most admired companies. By employing moderated regression analysis, we have found strong evidence for the moderating impact of operations efficiency. Our results are useful to managers in that they show that improvements in operations efficiency in a company can also help improve environmental/financial performance and vice versa.

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“…However, the problem with Figure 1 is that it is displaying in a 3-dimensional space which contradicts with the fact that ⃗, ⃗⃗ 1 and ⃗⃗ 2 are vectors in n-dimensional space . According to Saville and Wood (1991), this demonstration is not strictly correct as in higher dimensions (n>3), vectors cannot be shown pictorially in a strictly correct manner. To solve this contradiction, we establish a transformation matrix to map the n-dimensional vectors ⃗, ⃗⃗ 1 and ⃗⃗ 2 onto the 3-dimentional space.…”

Section: Drawing Graphs Onmentioning

confidence: 98%

Geometric Views of Partial Correlation Coefficient in Regression Analysis

Zeng¹,

Chen²

2017

IJSP

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By describing the geometric analogues of the concepts from various perspectives, this work aims to provide a richer and intuitive comprehension of the concept of partial correlation coefficient in the regression analysis, especially for beginning students. Based on a simple and strictly correct geometric framework, this article geometrically illustrates the concept of partial correlation coefficient in regression analysis from the views of the Frisch-Waugh-Lovell Theorem, partial F test statistics, and the comparisons with other levels of correlation coefficients. In our opinion, the geometric approach sheds lights on the regression analysis as it provides a richer and more concrete understanding for readers, especially for beginners. This paper can also be served as a supplementary reading material for serious beginners.

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Statistical Methods: The Geometric Approach

Abstract: Library of Congress Cataloging-in-Publication Data Saville, David J.Statistical methods: the geometric approach/David J. Saville, Graham R. Wood. p. cm. -(Springer texts in statistics) Includes bibliographical references and index.

Cited by 86 publications

References 0 publications

Multiple Comparison Procedures—Cutting the Gordian Knot

Multiple Comparison Procedures—Cutting the Gordian Knot

The Moderating Effect of Operations Efficiency on the Links between Environmental Performance and Financial Performance: The UK Evidence

Geometric Views of Partial Correlation Coefficient in Regression Analysis

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