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Tables of Contents for Six Sigma and Beyond
Chapter/Section Title
Page #
Page Count
PART I Essential Concepts of Statistics
Introduction
3
1
What Are Data?
3
1
Describing Data
4
1
Testing Hypotheses
4
1
Describing Relationships
5
1
Asking a Question
5
1
What Information Do You Need?
6
1
Defining a Population
6
1
Designing a Study
7
1
Sampling
7
1
Random Samples
8
1
Volunteers
9
1
Using Surveys
9
1
Analyzing an Existing Survey
9
1
Designing Experiments
10
1
Random Assignment
10
2
``Blind'' Experiments
12
1
Control Groups
13
1
How Should You Proceed if You Want to Explore an Idea?
14
1
Selected Bibliography
14
1
Designing and Using Forms for Studies
15
6
Overview
15
1
Coding the Data
15
2
Tips on Form Design
17
1
Collecting the Data
17
1
What Comes Next?
18
1
Modifying the Data
18
1
Analyzing the Data
19
1
Printing the Results
19
1
Missing Data
19
2
Counting Frequencies
21
4
Overview
21
1
Interpreting a Frequency Table
21
1
Valid Percentages
21
1
Bar Charts
22
1
Cumulative Percentages
22
1
Levels of Measurement
22
1
Categories
22
1
Ordered Categories
23
1
Numbers
23
1
Nominal, Ordinal, Interval, and Ratio
23
2
Summarizing Data
25
16
Descriptive Statistics
25
6
Nominal Variables
25
1
Ordinal Variables
26
1
Interval or Ratio Variables
27
1
Differences between Bar Charts and Histograms
27
1
Uses of Histograms
28
1
Different Types of Distributions
28
1
More Descriptive Statistics
29
1
Other Percentiles
30
1
The Average or Arithmetic Mean
30
1
Mean, Median, or Mode?
31
1
How Much Do the Values Differ?
31
10
The Variance
32
1
The Standard Deviation
33
1
Frequency Tables Versus Cross-Classification Tables
33
2
Means
35
1
Means from Samples
36
1
Problems in Generalizing
36
1
Sampling Variability
37
1
A Computer Model
37
1
Other Statistics
38
1
Describing Data Sets with Boxplots
39
2
Working with the Normal Distribution
41
10
Overview
41
1
Areas in the Normal Distribution
41
2
Standard Scores
43
1
A Sample from the Normal Distribution
44
1
Distributions that Are Not Normal
44
1
More on the Distribution of the Means
45
1
More about Means of Means
45
1
The Standard Error of the Mean
46
1
Calculating a Confidence Interval
46
3
More Satisfied than Average?
49
2
Testing Hypotheses about Two Independent Means
51
6
Overview
51
1
Is the Difference Real?
52
1
Evaluating a Difference between Means
52
1
Why the Entire Area?
53
1
Drawing a Conclusion
53
1
More on Hypothesis Testing
54
1
Why Is That So Complicated?
54
3
Testing Hypotheses about Two Dependent Means
57
10
Overview
57
1
Using the T Distribution
57
1
Two Types of Errors
58
1
Interpreting a T Test
58
1
An Analogy: Coin Flips
59
1
Observed Significance Levels
59
1
Tails and Significance Tests
60
1
The Hypothesis-Testing Process
61
1
Assumptions Needed
62
1
Paired Experimental Designs
63
1
Significance vs. Importance
63
4
Comparing Several Means
67
6
Overview
67
1
Analysis of Variance
67
1
Necessary Assumptions
67
1
Within-Groups Variability
68
1
Between-Groups Variability
69
1
Calculating the F Ratio
69
1
Multiple Comparison Procedures
69
1
Interactions
70
1
Analysis of Variance in Computer Software
70
2
References
72
1
Measuring Association
73
18
Overview
73
1
The Strength of a Relationship
73
1
Why Not Chi-Square?
73
1
Measures of Association
74
1
Measures of Association for Variables
74
6
Measures Based on Chi-Square
75
1
Calculating the (Lambda)
75
1
Two Different Lambdas
76
1
Measures of Association for Ordinal Variables
77
1
Concordant and Discordant Pairs
77
1
Measures Based on Concordant and Discordant Pairs
78
1
Goodman and Kruskal's Gamma
78
1
Kendall's Tau-b
79
1
Tau-c
79
1
Somers' d
79
1
Measures Involving Interval Data
79
1
Testing Hypotheses
80
1
About Statistics for Crosstabs
80
1
Plotting
81
2
Covariance
83
1
Correlation
84
5
Does Significant Mean Important?
87
1
One-Tailed and Two-Tailed Significance Probabilities
87
1
Assumptions about the Data
87
1
Examining Many Coefficients
88
1
Reference
89
2
Calculating Regression Lines
91
20
Overview
91
1
Choosing the Best Line
91
1
The Equation of a Line
92
1
Predicting Values from the Regression Line
92
1
Choosing the Dependent Variable
92
1
Correlating Predicted and Observed Values
93
1
The Population Regression Line
93
2
Some Hypotheses of Interest
95
1
Are the Population Values Zero?
96
1
Confidence Intervals for Regression Coefficients
96
1
Goodness of Fit of the Model
96
2
Multiple Regression
98
1
Residuals
99
1
Judging the Size of the Residuals
99
1
Looking for Outliers
100
2
Checking Assumptions with Residuals
102
2
Normality
102
1
Linearity
103
1
Independence
103
1
Multiple Linear Regression
104
1
Selecting Independent Variables
105
1
Discriminant Analysis
105
1
Log-Linear Models
106
1
Factor Analysis
107
2
Cluster Analysis
109
1
Testing Hypotheses about Many Means
109
1
Selected Bibliography
110
1
Common Miscellaneous Statistical Tests
111
18
Binomial Test
111
1
Remarks on the Binomial Test
112
1
Chi-Square (I) Test
112
1
Chi-Square (II) Test
113
1
A Word of Caution on χ2
113
1
McNemar Test
114
1
Cochran Q Test
115
1
Kolmogorov-Smirnov Test
115
1
Use of the Mann-Whitney U Test
116
1
Comment about the Mann-Whitney U
117
1
Sign Test
117
1
Comments about the Sign Test
118
1
Wilcoxon Signed-Ranks Test
118
1
Sample Sizes Larger Than 25
119
1
Kruskal-Wallis Test
119
1
The Effect of Ties
120
1
Friedman Test
120
1
T Test
121
1
Comments about the T Distribution
122
1
T Test (II)
123
1
Importance of Requirements Three and Four
123
1
T Test (III)
124
1
Scheffe's Test
125
1
Correlation
125
1
Pearson Product-Moment Coefficient
126
1
What Is the Pearson r?
126
1
Spearman Rank Coefficient (rho)
127
1
Coefficient of Contingency
128
1
References
128
1
Advanced Topics in Statistics
129
40
What Are Discriminant Analysis and Logistic Regression?
129
5
Analogy with Regression and MANOVA
131
1
Discriminant Analysis (DA)
132
1
SSCP
132
1
Elements of DA
133
1
Measures of Association
134
2
A Note on Multiple Discriminant Analysis
136
1
Multivariate Analysis of Variance (MANOVA)
136
7
Testing the Assumptions of Multivariate Analysis
136
1
Assessing Individual Variables Versus the Variate
137
1
Normality
137
3
Homoscedasticity
140
2
Linearity
142
1
Identifying Nonlinear Relationships
142
1
What Is Factor Analysis'?
143
1
Multiple Regression Analysis
144
4
Representing Curvilinear Effects with Polynomials
144
2
Standardizing the Regression Coefficients: Beta Coefficients
146
1
Assessing Multicollinearity
146
2
What Is Multivariate Analysis of Variance?
148
5
Univariate Procedures for Assessing Group Differences
148
1
The T Test
148
2
Analysis of Variance
150
1
Multivariate Analysis of Variance
151
1
The Two-Group Case: Hotelling's T2
151
1
Differences between MANOVA and Discriminant Analysis
152
1
What Is Conjoint Analysis?
153
1
Unique Aspects of Conjoint Analysis
153
1
Uses of Conjoint Analysis
154
1
What Is Canonical Correlation?
154
1
What Is Cluster Analysis?
155
1
What Is Multidimensional Scaling?
156
1
What Is Structural Equation Modeling?
157
9
Accommodating Multiple Interrelated Dependence Relationships
158
1
Incorporating Variables that We Do Not Measure Directly
158
1
Improving Statistical Estimation
159
1
Overall Goodness-of-Fit Measures for Structural Equation Modeling
159
1
Measures of Absolute Fit
160
1
Likelihood-Ratio Chi-Square Statistic
160
1
Noncentrality and Scaled Noncentrality Parameters
161
1
Goodness-of-Fit Index
162
1
Root Mean Square Residual (RMSR)
162
1
Root Mean Square Error of Approximation
162
1
Expected Cross-Validation Index
162
1
Cross-Validation Index
163
1
Incremental Fit Measures
163
1
Adjusted Goodness-of Fit Index
163
1
Tucker-Lewis Index
163
1
Normed Fit Index
164
1
Other Incremental Fit Measures
164
1
Parsimonious Fit Measures
164
1
Parsimonious Normed Fit Index
164
1
Parsimonious Goodness-of-Fit Index
165
1
Normed Chi-Square
165
1
Akaike Information Criterion
165
1
References
166
3
Time Series and Forecasting
169
14
Extrapolation Methods
169
7
Exponential Trend
169
1
Autocorrelation
170
2
Exponential Smoothing
172
1
Simple Exponential Smoothing
173
1
Holt's Model for Trend
174
1
Winters' Model for Seasonality
175
1
Econometric Models
176
4
A Final Comment on Combining Forecasts
180
1
References
180
3
PART II Essential Concepts of Probability
Functions of Real and Random Variables
183
12
Deterministic Mathematics (Replicated by Mean)
183
1
Statistical Mathematics
183
1
Sum or Difference of Two Real Variables: X1 and X2
183
1
Sum or Difference of Two Random Variables: X1 and X2
184
1
Rank and Stack Observed Data
185
1
Other Measures of Central Tendencies
185
1
Summary of Various Data Presentations
186
1
Probability Density Function (pdf)
187
1
Mean of Frequency Grouped Data
188
1
Observations
188
1
Mean of Probability Density Function
188
1
Formulas for Mean or Average
189
1
Cumulative Frequency Function
190
1
Cumulative Distribution Function (cdf)
191
1
Probability of Exceeding Threshold
192
1
Continuous Probability
193
1
Deviations of Data about Mean
193
1
Measures of Dispersion
193
1
Sample Variance (Unbiased → E(σ2) = σ2)
193
1
Standard Deviation (Unbiased)
194
1
Probability Density and Expected Values
194
1
Set Theory
195
30
Definitions
195
1
Example of Universal Set
195
1
Subsets of Elements of Universal Set
196
1
Example of Subset A of a Universal Set U
196
1
``Or'' Set of Operation: Union of Two Subsets
197
1
``And'' Set of Operation: Intersection of Two Subsets
197
1
Complementary Set, A* (Other Notation: A, A')
198
1
De Morgan's Laws of Complements
198
1
``Disjoint'' Sets (Mutually Exclusive Events)
199
1
Sample Space: S
199
4
Examples of Sets
200
3
Probability Concepts
203
21
Reference
224
1
Permutations and Combinations
225
10
Rules
225
1
Permutations and Combinations
226
9
Sampling
226
1
Permutations
226
1
Each Ordering Is Unique
226
2
Permutations Are Choosing ``Without Replacement''
228
1
Permutations of Different Types of Objects
228
2
Combinations - Ordering Is Irrelevant
230
1
Permutation or Combination?
230
2
Binomial Expansion
232
1
Combinations
232
1
Properties of Binomial Coefficients
232
1
Binomial Expansion
232
3
Discrete and Continuous Random Variables
235
96
Introduction
235
1
Samples Assigned the Same Random Variable
236
1
Random Variables Grouped into Cells
236
2
Random Experiment
237
1
Discrete Probability Distribution
238
2
Random Experiment
239
1
Discrete Cumulative Distribution Function
240
4
Random Experiment
240
1
Random Experiment
241
3
Mean or Expected Value
244
1
Random Experiment
244
1
Continuous Random Variables
245
3
Advantages of Continuous Random Variables
246
1
Properties of Continuous Distributions
247
1
Standardized Random Variable
248
1
Typical Unstandardized Form of Tabulated CDF
248
1
Leading Tail Interval
248
1
Trailing Tail Interval
249
1
Upper Range from Mean Value
249
1
Probability Distribution
249
1
Uniform Distribution
250
3
Normal Distribution - Otherwise Known as the ``Bell Curve''
253
9
Typical Comments about the Normal Curve
254
2
Differential Equation (DE)
256
1
Standardized Random Variables - Tabulated Function
256
1
Standardized Normal Distribution (SND)
257
5
Normal Approximation of Binomial
262
4
Central Limit Theorem (CLT) - Mean of Means Is Normal
266
1
Comments on the SND
266
1
Normalized Transforms
267
1
Discrete Probability Distributions
267
12
Binomial Distribution (Bernoulli)
267
5
Hypergeometric Distribution
272
1
Overview
272
1
General Comments
273
1
Alternate Parameters and Properties
273
1
Comments
273
1
Comparison of Hypergeometric and Binomial Distributions
274
1
Sample Size
274
1
Discrete Two Options
274
1
Computations
274
1
Hypergeometric Distribution Applications
275
1
Probability Considerations
276
1
Random Variable
277
2
Poisson Distribution: Limit of Binomial Distribution for Rare Occurrence
279
3
Comparison of Binomial and Poisson
280
2
Selected Bibliography
282
3
PART III Appendices
Appendix A --- Matrix Algebra: An Introduction
285
12
Basic definitions
285
2
Matrix operations
287
1
Addition and Subtraction
287
1
Multiplication
288
3
Determinants
291
1
Applications of Determinants
292
1
Linear Dependence
293
1
Matrix Inverse
293
3
References
296
1
Appendix B --- The Simplex Method in Two Dimensions
297
6
Appendix C --- Bernoulli Trials
303
6
Appendix D --- Markov Chains
309
6
Appendix E --- Optimization
315
2
Appendix F --- Randomized Strategies
317
2
Appendix G --- Lagrange Multipliers
319
6
Comment
322
3
Appendix H --- Monte Carlo Simulation
325
4
Selected Bibliography
328
1
Appendix I --- Statistical Reporting Content
329
2
Example of a Typical Statistical Report Format
330
1
Selected Bibliography
331
6
Index
337