Statistical Concepts - A Second Course

Debbie L. Hahs-Vaughn, Richard G. Lomax

• Publisher: Routledge
• Year: 2020
• ISBN:
  9781000134711
• Edition: 5
• Topic: Psychology
• Subtopic: Research & Methodology in Psychology
• Index: Psychology

Statistical Concepts — A Second Course presents the last 10 chapters from An Introduction to Statistical Concepts, Fourth Edition. Designed for second and upper-level statistics courses, this book highlights how statistics work and how best to utilize them to aid students in the analysis of their own data and the interpretation of research results.

In this new edition, Hahs-Vaughn and Lomax discuss sensitivity, specificity, false positive and false negative errors. Coverage of effect sizes has been expanded upon and more organizational features (to summarize key concepts) have been included. A final chapter on mediation and moderation has been added for a more complete presentation of regression models. In addition to instructions and screen shots for using SPSS, new to this edition is annotated script for using R.

This book acts as a clear and accessible instructional tool to help readers fully understand statistical concepts and how to apply them to data. It is an invaluable resource for students undertaking a course in statistics in any number of social science and behavioral science disciplines.

1
One-Factor Analysis of Variance—Fixed-Effects Model

Chapter Outline

1.1 What One-Factor ANOVA Is and How It Works

1.1.1 Characteristics

1.1.2 Power

1.1.3 Effect Size

1.1.4 Assumptions

1.2 Computing Parametric and Nonparametric Models Using SPSS

1.2.1 One-Way Analysis of Variance

1.2.2 Nonparametric Procedures

1.3 Computing Parametric and Nonparametric Models Using R

1.3.1 Introduction to R

1.3.2 Reading Data Into R

1.3.3 Generating the One-Way ANOVA Model

1.3.4 Generating the Welch Test

1.3.5 Generating the Kruskal-Wallis Test

1.4 Data Screening

1.4.1 Normality

1.4.2 Independence

1.4.3 Homogeneity of Variance

1.5 Power Using G*Power

1.5.1 Post Hoc Power for the One-Way ANOVA Using G*Power

1.5.2 A Priori Power for the One-Way ANOVA Using G*Power

1.6 Research Question Template and Example Write-Up

1.7 Additional Resources

Key Concepts

1. Between- and within-groups variability
2. Sources of variation
3. Partitioning the sums of squares
4. 4. The ANOVA model
5. 5. Expected mean squares

The first six chapters of this text are concerned with different analysis of variance (ANOVA) models. In this chapter, we consider the most basic ANOVA model, known as the one-factor analysis of variance model. Recall the independent t test where the means from two independent samples were compared. What if you wish to compare more than two means? The answer is to use the analysis of variance. At this point you may be wondering why the procedure is called the analysis of variance rather than the analysis of means, because the intent is to study possible mean differences. One way of comparing a set of means is to think in terms of the variability among those means. If the sample means are all the same, then the variability of those means would be zero. If the sample means are not all the same, then the variability of those means would be somewhat greater than zero. In general, the greater the mean differences are, the greater is the variability of the means. Thus, mean differences are studied by looking at the variability of the means; hence, the term analysis of variance is appropriate rather than analysis of means (further discussed in this chapter).

We use X to denote our single independent variable, which we typically refer to as a factor, and Y to denote our dependent (or criterion) variable. Thus, the one-factor ANOVA is a bivariate, or two variable, procedure. Our interest here is in determining whether mean differences exist on the dependent variable. Stated another way, the researcher is interested in the influence of the independent variable on the dependent variable (however, be cautious in inferring causality unless the design of your study allows that). For example, a researcher may want to determine the influence that method of instruction has on statistics achievement. The independent variable, or factor, would be method of instruction, and the dependent variable would be statistics achievement. Three different methods of instruction that might be compared are large lecture hall instruction, small-group instruction, and computer-assisted instruction. Students would be randomly assigned to one of the three methods of instruction and, at the end of the semester, evaluated as to their level of achievement in statistics. These results would be of interest to a statistics instructor in determining the most effective method of instruction (where “effective” is measured by student performance in statistics). Thus, the instructor may opt for the method of instruction that yields the highest mean achievement.

There are a number of new concepts introduced in this chapter as well as a refresher of concepts that you will likely remember from your previous statistics course. The concepts addressed in this chapter include the following: independent and dependent variables; between- and within-groups variability; fixed- and random-effects; the linear model; partitioning of the sums of squares; degrees of freedom, mean square terms, and F ratios; the ANOVA summary table; expected mean squares; balanced and unbalanced models; and alternative ANOVA procedures. Our objectives are that by the end of this chapter, you will be able to (a) understand the characteristics and concepts underlying a one-factor ANOVA, (b) generate and interpret the results of a one-factor ANOVA, and (c) understand and evaluate the assumptions of the one-factor ANOVA.

1.1 What One-Factor ANOVA Is and How It Works

Throughout the book, we will be following a group of superbly talented, creative, and energetic graduate research assistants (Challie Lenge, Ott Lier, Addie Venture, and Oso Wyse) working in their institution’s statistics and research lab, fondly known as CASTLE (Computing and Statistical Technology Laboratory). The group is supervised and mentored by a research methodology faculty member who empowers the group to lead their projects to infinity and beyond, so to speak. With each chapter, we will find the group, or a subset of members thereof, delving into a fantastical statistical journey. We now find Ott Lier assisting one of the region’s leading sports psychologists in examining elite athletes and vulnerability to psychological distress based on the type of sport in which they participate.

The statistics and research lab at the university serve clients within the institution, such as faculty and staff, and outside the institution, including a...