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Integration of ANOVA and Multiple Regression for Beginning Statistics Students

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Abstract

Amelioration of the perpetual difficulty students have upon encountering typical statistical methods introduced in a first statistics course, or combined into a research methodology course, is the objective of this effort. In addition, an evaluation of the proposed method is included. rom student comments and in class experience, it is clear that difficulties students face on encountering statistical methods to address research questions are both conceptual and computational. Many of the conceptual problems students face are due to the fragmented "menu -style" manner in which inferential statistical methods are introduced in texts. "A t-test is on page 37; an ANOVA is on page 102, and a multiple regression is on page 150." But, as illustrated (Kerlinger & Pedhazur, 1973 , Pedhazur, 1982; or Cohen & Cohen, 1975 , 1983 ) these techniques, and many more, are intimately tied through the general linear model. Some would argue that such an integrative approach is too advanced for the beginning student; if handled gently, we disagree. A general introduction to the theory of the GLM is not suggested for the beginning student, but a method that allows easy illustration of how these techniques are computationally the same has been found to reduce confusion considerably. The computational difficulty students face is usually due to the user interface of commercial software packages. Students find the new computer interface challengingsometimes bewildering --especially at first. But all students are comfortable with and have immediate access to Excel, so an Excel software package, "Criterion.xlsx," was written, used, and evaluated herein. This software also has the advantage of "flexible immediacy" to illustrate the linkages among methods. We also wanted control over what is displayed and how. Specifically, we took this opportunity to embed contextual guidance toward correct understanding of analyses within the pages of this software, so that what the student reads as "output" is accompanied with narrative guidance. We want to educate while students calculate. As well, all relevant output is automatically generated in "camera-ready" APA cut-andpaste tables. We also point out errors made in commercial packages offering the same output. Criterion is divided into various spreadsheet "tabs" that execute various desired analyses; each with extensive embedded annotations that are used to teach in context and to provide clarification regarding often encountered interpretive errors. Methods are available for univariate through multivariate analyses, and the software has been used very successfully in a second multivariate statistics course, but that is not the interest here. Only the parts most relevant to ANOVA and multiple regression will be illustrated here. 1 [Note that the Excel statistical "Analysis Toolpak" that has received some criticism in the literature (e.g., McCullough & Wilson, but see amelioration with more recent versions, Melard, 2014) is not usedall programming is original. Moreover, with a very large set of examples, an exact match with SPSS, SAS, or Systat is always obtained.] . Data Source Relevant analyses will be displayed in Figures here using two data sets. A multiple regression data set in which graduate GPA is predicted from GRE (Quantitative and Verbal), the Miller Analogies Test, and the Average Rating of faculty (Kerlinger & Pedhazur, 1973, p. 292), and a group contrast ANOVA data set regarding the relationship of Religion to Attitude Toward Abortion (Cohen & Cohen, 1983, p. 185). The following will detail the use of the spreadsheet to analyze these data. To render the analysis, one only needs to enter the 1) N, 2) p (the number of variables), 3) α (we believe it is important for students to make a choice), 4) variable names, and 5) data (with the Criterion first in

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