Statistical Analysis

Conrad Carlberg started writing about Excel, and its use in quantitative analysis, before workbooks had worksheets. As a graduate student he had the great good fortune to learn something about statistics from the wonderfully gifted Gene Glass. He remembers much of it and has learned more since–and has exchanged the discriminant function for logistic regression–but it still looks like a rodeo. This is a book he has been wanting to write for years, and he is grateful for the opportunity. He expects to refer to it often while running his statistical consulting business.

Introduction

Chapter 1 About Variables and Values

Variables and Values

    Recording Data in Lists

Scales of Measurement

    Category Scales

    Numeric Scales

    Telling an Interval Value from a Text Value

Charting Numeric Variables in Excel

    Charting Two Variables

Understanding Frequency Distributions

    Using Frequency Distributions

    Building a Frequency Distribution from a Sample

    Building Simulated Frequency Distributions

Chapter 2 How Values Cluster Together

Calculating the Mean

    Understanding Functions, Arguments, and Results

    Understanding Formulas, Results, and Formats

    Minimizing the Spread

Calculating the Median

    Choosing to Use the Median

Calculating the Mode

    Getting the Mode of Categories with a Formula

From Central Tendency to Variability

Chapter 3 Variability: How Values Disperse

Measuring Variability with the Range

The Concept of a Standard Deviation

    Arranging for a Standard

    Thinking in Terms of Standard Deviations

Calculating the Standard Deviation and Variance

    Squaring the Deviations

    Population Parameters and Sample Statistics

    Dividing by N - 1

Bias in the Estimate

    Degrees of Freedom

Excel’s Variability Functions

    Standard Deviation Functions

    Variance Functions

Chapter 4 How Variables Move Jointly: Correlation

Understanding Correlation

    The Correlation, Calculated

    Using the CORREL() Function

    Using the Analysis Tools

    Using the Correlation Tool

    Correlation Isn’t Causation

Using Correlation

    Removing the Effects of the Scale

    Using the Excel Function

    Getting the Predicted Values

    Getting the Regression Formula

Using TREND() for Multiple Regression

    Combining the Predictors

    Understanding “Best Combination”

    Understanding Shared Variance

    A Technical Note: Matrix Algebra and Multiple Regression in Excel

Moving on to Statistical Inference

Chapter 5 How Variables Classify Jointly: Contingency Tables

Understanding One-Way Pivot Tables

    Running the Statistical Test

Making Assumptions

    Random Selection

    Independent Selections

    The Binomial Distribution Formula

    Using the BINOM.INV() Function

Understanding Two-Way Pivot Tables

    Probabilities and Independent Events

    Testing the Independence of Classifications

The Yule Simpson Effect

    Summarizing the Chi-Square Functions

Chapter 6 Telling the Truth with Statistics

Problems with Excel’s Documentation

A Context for Inferential Statistics

    Understanding Internal Validity

The F-Test Two-Sample for Variances

    Why Run the Test?

Chapter 7 Using Excel with the Normal Distribution

About the Normal Distribution

    Characteristics of the Normal Distribution

    The Unit Normal Distribution

Excel Functions for the Normal Distribution

    The NORM.DIST() Function

    The NORM.INV() Function

Confidence Intervals and the Normal Distribution

    The Meaning of a Confidence Interval

    Constructing a Confidence Interval

    Excel Worksheet Functions That Calculate Confidence Intervals

    Using CONFIDENCE.NORM() and CONFIDENCE()

    Using CONFIDENCE.T()

    Using the Data Analysis Add-in for Confidence Intervals

    Confidence Intervals and Hypothesis Testing

The Central Limit Theorem

    Making Things Easier

    Making Things Better

Chapter 8 Testing Differences Between Means: The Basics

Testing Means: The Rationale

    Using a z-Test

    Using the Standard Error of the Mean

    Creating the Charts

Using the t-Test Instead of the z-Test

    Defining the Decision Rule

    Understanding Statistical Power

Chapter 9 Testing Differences Between Means: Further Issues

Using Excel’s T.DIST() and T.INV() Functions to Test Hypotheses

    Making Directional and Nondirectional Hypotheses

    Using Hypotheses to Guide Excel’s t-Distribution Functions

    Completing the Picture with T.DIST()

Using the T.TEST() Function

    Degrees of Freedom in Excel Functions

    Equal and Unequal Group Sizes

    The T.TEST() Syntax

Using the Data Analysis Add-in t-Tests

    Group Variances in t-Tests

    Visualizing Statistical Power

    When to Avoid t-Tests

Chapter 10 Testing Differences Between Means: The Analysis of Variance

Why Not t-Tests?

The Logic of ANOVA

    Partitioning the Scores

    Comparing Variances

    The F Test

Using Excel’s F Worksheet Functions

    Using F.DIST() and F.DIST.RT()

    Using F.INV() and FINV()

    The F Distribution

Unequal Group Sizes

Multiple Comparison Procedures

    The Scheffé Procedure

    Planned Orthogonal Contrasts

Chapter 11 Analysis of Variance: Further Issues

Factorial ANOVA

    Other Rationales for Multiple Factors

    Using the Two-Factor ANOVA Tool

The Meaning of Interaction

    The Statistical Significance of an Interaction

    Calculating the Interaction Effect

The Problem of Unequal Group Sizes

    Repeated Measures: The Two Factor Without Replication Tool

Excel’s Functions and Tools: Limitations and Solutions

    Power of the F Test

    Mixed Models

Chapter 12 Multiple Regression Analysis and Effect Coding: The Basics

Multiple Regression and ANOVA

    Using Effect Coding

    Effect Coding: General Principles

    Other Types of Coding

Multiple Regression and Proportions of Variance

    Understanding the Segue from ANOVA to Regression

    The Meaning of Effect Coding

Assigning Effect Codes in Excel

Using Excel’s Regression Tool with Unequal Group Sizes

Effect Coding, Regression, and Factorial Designs in Excel

    Exerting Statistical Control with Semipartial Correlations

    Using a Squared Semipartial to get the Correct Sum of Squares

Using TREND() to Replace Squared Semipartial Correlations

    Working with the Residuals

    Using Excel’s Absolute and Relative Addressing to Extend the Semipartials

Chapter 13 Multiple Regression Analysis: Further Issues

Solving Unbalanced Factorial Designs Using Multiple Regression

    Variables Are Uncorrelated in a Balanced Design

    Variables Are Correlated in an Unbalanced Design

    Order of Entry Is Irrelevant in the Balanced Design

    Order Entry Is Important in the Unbalanced Design

    About Fluctuating Proportions of Variance

Experimental Designs, Observational Studies, and Correlation

Using All the LINEST() Statistics

    Using the Regression Coefficients

    Using the Standard Errors

    Dealing with the Intercept

    Understanding LINEST()’s Third, Fourth, and Fifth Rows

Managing Unequal Group Sizes in a True Experiment

Managing Unequal Group Sizes in Observational Research

Chapter 14 Analysis of Covariance: The Basics

The Purposes of ANCOVA

    Greater Power

    Bias Reduction

Using ANCOVA to Increase Statistical Power

    ANOVA Finds No Significant Mean Difference

    Adding a Covariate to the Analysis

Testing for a Common Regression Line

Removing Bias: A Different Outcome

Chapter 15 Analysis of Covariance: Further Issues

Adjusting Means with LINEST() and Effect Coding

Effect Coding and Adjusted Group Means

Multiple Comparisons Following ANCOVA

    Using the Scheffé Method

    Using Planned Contrasts

The Analysis of Multiple Covariance

    The Decision to Use Multiple Covariates

    Two Covariates: An Example

 

9780789747204    TOC    4/6/2011