Purpose
This book provides you with what you need to know to manage JMP data and to perform the statistical analyses that are most commonly used in the social sciences and other areas of research. JMP for Basic Univariate and Multivariate Statistics: Methods for Researchers and Social Scientists shows you how to
- understand the basics of using JMP software
- enter and manage JMP data
- understand the correct statistic for a variety of study situations
- perform an analysis
- interpret the results
- prepare tables, figures, and text that summarize the results according to the guidelines of the Publication Manual of the American Psychological Association (the most widely used format in social science literature).
Audience
This book is designed for students and researchers who use Version 10 of JMP or JMP Pro and who have limited backgrounds in statistics, but this book can also be useful for more experienced researchers. An introductory chapter reviews basic concepts in statistics and research methods. The chapters on data and statistical analysis assume that the reader has no familiarity with JMP; all statistical concepts are conveyed at an introductory level. The chapters that deal with specific statistics clearly describe the circumstances under which each is used. Each chapter provides at least one detailed example of data, and describes how to analyze the data and interpret the results for a representative research problem. Even users whose only previous exposure to data analysis was an elementary statistics course should be able to use this book to perform statistical analyses successfully.
Organization
Although no single book can discuss every statistical procedure, this book covers the statistics that are most commonly used in research in psychology, sociology, marketing, organizational behavior, political science, communication, and the other sciences. Material covered in each chapter is summarized as follows.
Chapter 1: Basic Concepts in Research and Data Analysis
There are fundamental issues in research methodology, statistics, and JMP software that need to be reviewed before proceeding. This chapter defines and describes the differences between concepts such as variables and values, quantitative variables and classification variables, experimental research and nonexperimental research, and descriptive analysis and inferential analysis. Chapter 1 also describes the various scales of measurement, called modeling types in JMP (continuous, nominal, and ordinal), and covers the basic issues in hypothesis testing. This chapter gives you the fundamentals and terminology of data analysis needed to learn about using JMP for statistical analysis in the subsequent chapters.
Chapter 2: Getting Started with JMP
Students and researchers who are new to JMP should begin with this chapter. It discusses the general approach to analyzing data using JMP platforms. A step-by-step example takes you through a simple JMP session. You see how to start JMP, open a table, perform an exploratory analysis, and end the session. If you have used JMP previously and feel familiar with it, use this chapter as review and then proceed to Chapter 4, which begins with statistical explanations and examples.
Chapter 3: Working with JMP Data
All statistical analyses begin with data. This chapter covers the basics of data input and managing data in JMP. Topics include
- simple input such as keying in data
- how to copy and paste data
- reading simple and complex raw text files
- reading SAS data sets
- reading data from other external files
- creating data values with a formula
This chapter also introduces shaping JMP tables by stacking and splitting columns, creating subsets, concatenating tables, and joining tables.
Chapter 4: Exploring Data with the Distribution Platform
The first step in analyzing data is to become familiar with the data by looking at descriptive statistical information. This chapter illustrates the JMP Distribution platform, which is used to calculate means, standard deviations, and other descriptive statistics for quantitative variables, and construct frequency distributions for categorical variables. Features in the Distribution platform can test for normality and produce stem-and-leaf plots.
You see how the JMP Distribution platform can be used to screen data for errors, identify outliers, select subsets of data, and provide other useful preliminary information about a set of data.
Chapter 5: Measures of Bivariate Association
This chapter discusses ways to study the relationship between two variables and determine if the relationship is statistically significant. You see how the JMP Fit Y by X platform chooses the correct statistic based on the level of measurement (data type and modeling type) of the variables. There are examples of using the JMP Fit Y by X platform to prepare bivariate scatterplots and perform the chi-square test of independence, and using the JMP Multivariate platform to compute Pearson correlations and Spearman correlations.
Chapter 6: Assessing Scale Reliability with Coefficient Alpha
This chapter shows how to use the JMP Multivariate platform to compute the coefficient alpha reliability index (Cronbach’s alpha) for a multiple-item scale. You review basic issues regarding the assessment of reliability, and learn about the circumstances under which a measure of internal consistency is likely to be high. Fictitious questionnaire data are analyzed to demonstrate how you can perform an item analysis to improve the reliability of scale responses.
Chapter 7: t -Tests: Independent Samples and Paired Samples
You begin by learning the differences between the independent-samples t-test and the paired-samples t-test, and see how to perform both types of analysis. An example of a research design is developed that provides data appropriate for each type of t-test. With respect to the independent-samples test, this chapter shows how to use JMP to determine whether the equal-variances or unequal variances t-test is appropriate and how to interpret the results. There are analyses of data for paired-samples research designs with discussion of problems that can occur with paired data. You learn when it is appropriate to perform either the independent-samples or the paired-samples t-test, and you learn what steps to follow in performing both analyses.
Chapter 8: One-Way ANOVA with One Between-Subjects Factor
The one-way analysis of variance is one of the most flexible and widely used procedures in the social sciences and other areas of research. You learn how to prepare data using JMP to perform a one-way analysis of variance (ANOVA). This chapter focuses on the between-subjects design in which each participant is exposed to only one condition under the independent variable. This chapter discusses
- the R2 statistic from the results of an analysis of variance, which represents the percent of variance in the response that is accounted for or explained by variability in the predictor variable
- how to interpret the graphical results produced by JMP for a one-way ANOVA
- Tukey’s HSD multiple comparison test for comparing group means
- a systematic format to use when summarizing the results of an analysis
- the construction and meaning of the F statistic used in the ANOVA
Chapter 9: Factorial ANOVA with Two Between-Subjects Factors
The factorial design introduced in this chapter has a single dependent response variable and two independent predictor (between-subjects) variables. This chapter shows how to use the JMP Fit Model platform to perform a two-way ANOVA. The two predictor variables are manipulated so that treatment conditions include all combinations of levels of the predictor variables (a factorial design). Each subject is exposed to only one condition under each independent variable.
Guidelines are provided for interpreting results that do not display a significant interaction, and separate guidelines are provided for interpreting results that do display a significant interaction. After completing this chapter, you should be able to determine whether an interaction is significant and to summarize the results involving main effects in the case of a nonsignificant interaction. For significant interactions, you should be able to display the interaction in a figure and perform tests for simple effects (test slices).
Chapter 10: Multivariate Analysis of Variance (MANOVA) with One Between-Subjects Factor
This chapter examines the situation where groups of subjects produce response measurements for two responses. The focus is on the between-subjects design—in which each subject is exposed to only one condition (level) of a single nominal (grouping) independent predictor variable.
You see how to use the JMP Fit Model platform to perform a one-way multivariate analysis of variance (MANOVA). You can think of MANOVA as an extension of ANOVA that allows for the inclusion of multiple response variables in a single test. Examples show how to summarize both significant and nonsignificant MANOVA results.
Chapter 11: One-Way ANOVA with One Repeated-Measures Factor
This chapter focuses on repeated-measures designs in which each participant is exposed to every condition (level) of the independent variable. This design is compared to the between-subjects design described in Chapter 8, “One-Way ANOVA with One Between-Subjects Factor.” You also learn how problems such the lack of a control group, order effects, and carry-over effects can affect the validity of this kind of design.
This chapter also introduces both the univariate approach and the multivariate approach to analysis of repeated measures designs, and discusses the homogeneity of variance necessary for a valid univariate analysis.
After completing this chapter, you should be familiar with
- necessary conditions for performing a valid repeated-measures ANOVA
- alternative analyses to use when the validity conditions are not met
- strategies for minimizing sequence effects
Chapter 12: Factorial ANOVA with Repeated-Measures Factors and Between-Subjects Factors
This chapter introduces designs that have both repeated-measures factors and between-subjects factors. This two-way mixed design extends the one-way repeated-measures design presented in the previous chapter by adding one or more groups. Example data includes one additional group, which is used as a control group. Adding a control group lets you test the plausibility of alternative explanations that could account for study results.
There are example analyses for data with significant interaction and with nonsignificant interaction. The analyses illustrate using multivariate fitting (MANOVA) and explain how the MANOVA approach to analysis of repeated-measures data automatically uses the correct error term for statistical tests. A detailed description shows how to perform the analysis and interpret the MANOVA results.
When there is a significant main effect with no interaction, you learn how to test each level of the main effect with a one-way repeated-measures ANOVA.
A univariate approach to analyzing a two-way mixed design is shown as an alternative analysis method.
Chapter 13: Multiple Regression
This chapter discusses the situation in which a response variable is being predicted from continuous predictor variables, all of which display a linear relationship with the response. You learn how to use the JMP Fit Model platform to perform multiple regression analysis that investigates the relationship between the continuous response variable and multiple continuous predictor variables.
This chapter describes the principle of least squares, describes the different components of the multiple regression equation, and discusses the meaning of R2 and other results from a multiple regression analysis. It also shows how bivariate correlations, multiple-regression coefficients, and uniqueness indices can be reviewed to assess the relative importance of predictor variables.
After completing the chapter, you should be able to use the JMP Fit Model platform to conduct the multiple regression analysis, and be able to summarize the results of a multiple regression analysis in tables and in text.
Chapter 14: Principal Component Analysis
This chapter presents principal component analysis as a way to reduce the number of observed variables to a smaller number of uncorrelated variables that account for most of the variance in a set of data. You learn how to use the Principal Components command in the JMP Multivariate platform to do a principal component analysis. Several methods are presented to determine the subset of meaningful components to retain and use for further analysis. Example data (fictitious) show that factor rotation can facilitate interpretation of the relationship between the components and possible underlying characteristics in the data.
By the end of the chapter, you should be able to perform a principal component analysis, determine the correct number of components to retain, interpret the rotated solution, create component scores, and summarize the results.
Note: This chapter deals only with the creation of orthogonal (uncorrelated) components. Oblique (correlated) solutions are covered in the exploratory factor analysis chapter from A Step-by-Step Approach to Using the SAS System for Factor Analysis and Structural Equation Modeling (Hatcher, 1994).
Appendix A: Choosing the Correct Statistic
Although JMP uses the correct statistics for analyses based on the data type and modeling of the variables you are analyzing, it is useful to see a structured overview of the correct statistical procedure for use when analyzing data. This approach bases the choice of a specific statistic upon the number of response variables and on the modeling type of the response (criterion or dependent) variables and the predictor (independent) variables. The chapter groups commonly used statistics into three tables based on the number of criterion and predictor variables in the analysis.
General References
American Psychological Association (2001). Publication Manual of the American Psychological Association (5th edition). Washington, DC.
Hatcher, L. (1994). A Step-by-Step Approach to Using the SAS System for Factor Analysis and Structural Equation Modeling. Cary, NC: SAS Institute Inc.
Rusbult, C. E. (1980). Commitment and Satisfaction in Romantic Associations: A Test of the Investment Model. Journal of Experimental Social Psychology, 16, 172–186.