Categorical Distributions
by Lee Creighton, Mia Stephens, Ann Lehman, Ph.D., John Sall
JMP Start Statistics, 5th Edition
- Preface
- Preliminaries
- JMP Right In
- Data Tables, Reports, and Scripts
- Formula Editor Adventures
- What Are Statistics?
- Simulations
- Univariate Distributions: One Variable, One Sample
- Overview
- Looking at Distributions
- Describing Distributions of Values
- Statistical Inference on the Mean
- Practical Significance vs. Statistical Significance
- Examining for Normality
- Special Topic: Practical Difference
- Special Topic: Simulating the Central Limit Theorem
- Seeing Kernel Density Estimates
- Exercises
- The Difference Between Two Means
- Overview
- Two Independent Groups
- When the Difference Isn’t Significant
- Check the Data
- Launch the Fit Y by X Platform
- Examine the Plot
- Display and Compare the Means
- Inside the Student’s t-Test
- Equal or Unequal Variances?
- One-Sided Version of the Test
- Analysis of Variance and the All-Purpose F-Test
- How Sensitive Is the Test? How Many More Observations Are Needed?
- When the Difference Is Significant
- Normality and Normal Quantile Plots
- Testing Means for Matched Pairs
- Two Extremes of Neglecting the Pairing Situation: A Dramatization
- A Nonparametric Approach
- Exercises
- Comparing Many Means: One-Way Analysis of Variance
- Fitting Curves through Points: Regression
- Categorical Distributions
- Categorical Models
- Overview
- Fitting Categorical Responses to Categorical Factors: Contingency Tables
- Two-Way Tables: Entering Count Data
- If You Have a Perfect Fit
- Special Topic: Correspondence Analysis— Looking at Data with Many Levels
- Continuous Factors with Categorical Responses: Logistic Regression
- Surprise: Simpson's Paradox: Aggregate Data versus Grouped Data
- Generalized Linear Models
- Exercises
- Multiple Regression
- Fitting Linear Models
- Overview
- The General Linear Model
- Kinds of Effects in Linear Models
- Coding Scheme to Fit a One-Way anova as a Linear Model
- Regressor Construction
- Interpretation of Parameters
- Predictions Are the Means
- Parameters and Means
- Analysis of Covariance: Continuous and Categorical Terms in the Same Model
- The Prediction Equation
- The Whole-Model Test and Leverage Plot
- Effect Tests and Leverage Plots
- Least Squares Means
- Lack of Fit
- Separate Slopes: When the Covariate Interacts with a Categorical Effect
- Two-Way Analysis of Variance and Interactions
- Optional Topic: Random Effects and Nested Effects
- Exercises
- Design of Experiments
- Bivariate and Multivariate Relationships
- Exploratory Modeling
- Control Charts and Capability
- Mechanics of Statistics
- Analyze and Graph Menu Commands
- Answers to Selected Exercises
- Chapter 4, "Formula Editor Adventures"
- Chapter 7, "Univariate Distributions: One Variable, One Sample"
- Chapter 8, "The Difference Between Two Means"
- Chapter 9, "Comparing Many Means: One-Way Analysis of Variance"
- Chapter 10, "Fitting Curves through Points: Regression"
- Chapter 11, "Categorical Distributions"
- Chapter 12, "Categorical Models"
- Chapter 13, "Multiple Regression"
- Chapter 14, "Fitting Linear Models"
- Chapter 15, "Design of Experiments"
- Chapter 16, "Bivariate and Multivariate Relationships"
- Chapter 17, "Exploratory Modeling"
- Chapter 18, "Control Charts and Capability"
- References and Data Sources
- Technology License Notices
- Index
11
Categorical Distributions
Overview
When a response is categorical, a different set of tools is needed to analyze the data. This chapter focuses on simple categorical responses and introduces these topics:
• There are two ways to approach categorical data. This chapter refers to them as choosing and counting. They use different tools and conventions for analysis.
• The concept of variability in categorical responses is more difficult than in continuous responses. Monte Carlo simulation helps demonstrate how categorical variability works.
• The chi-square test is the fundamental statistical tool for categorical models. There are two kinds of chi-square tests. They test the same thing in a different way and get similar results.
Fitting models to categorical response data is covered in Categorical Models.
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