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E-raamat: Applied Regression and ANOVA Using SAS

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  • Formaat: 428 pages
  • Ilmumisaeg: 07-Jun-2022
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781439869529
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Applied Regression and ANOVA Using SASSuurem pilt
  • Formaat: 428 pages
  • Ilmumisaeg: 07-Jun-2022
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781439869529
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Applied Regression and ANOVA Using SAS® has been written specifically for non-statisticians and applied statisticians who are primarily interested in what their data are revealing. Interpretation of results are key throughout this intermediate-level applied statistics book. The authors introduce each method by discussing its characteristic features, reasons for its use, and its underlying assumptions. They then guide readers in applying each method by suggesting a step-by-step approach while providing annotated SAS programs to implement these steps.

Those unfamiliar with SAS software will find this book helpful as SAS programming basics are covered in the first chapter. Subsequent chapters give programming details on a need-to-know basis. Experienced as well as entry-level SAS users will find the book useful in applying linear regression and ANOVA methods, as explanations of SAS statements and options chosen for specific methods are provided.

Features:

Statistical concepts presented in words without matrix algebra and calculus Numerous SAS programs, including examples which require minimum programming effort to produce high resolution publication-ready graphics Practical advice on interpreting results in light of relatively recent views on threshold p-values, multiple testing, simultaneous confidence intervals, confounding adjustment, bootstrapping, and predictor variable selection Suggestions of alternative approaches when a methods ideal inference conditions are unreasonable for ones data

This book is invaluable for non-statisticians and applied statisticians who analyze and interpret real-world data. It could be used in a graduate level course for non-statistical disciplines as well as in an applied undergraduate course in statistics or biostatistics.

Arvustused

"... A must for someone that wants to work with theaforementioned models using SAS and wants a step-by-step guide on how and when toimplement those models. Each chapter is organized in a very similar manner. Itprovides theminimum amount of theory in a non-technical way at first, including when to use a specificmodel, what should be checked as assumptions and what to do when assumptions are not met."

David Manteigas, ISCB News, May 2024

Preface xix
Author Biography xxi
1 Review of Some Basic Statistical Ideas
1(28)
1.1 Introducing Regression Analysis
1(1)
1.2 Classification of Variables
2(2)
1.2.1 Quantitative vs. Qualitative Variables
2(1)
1.2.2 Scale of Measurement Classification
2(1)
1.2.3 Overview of Variable Classification and the Methods to be Presented in this Book
3(1)
1.3 Probability Distributions
4(1)
1.3.1 The Normal Distribution
4(1)
1.4 Statistical Inference
5(1)
1.5 Missing Data
6(1)
1.6 Estimating Population Parameters Using Sample Data
7(1)
1.7 Basic Steps of Hypothesis Testing
8(3)
1.8 Why an Observed p-Value Should Be Interpreted with Caution
11(1)
1.9 A World Beyond 0.05?
12(1)
1.10 Caveats Regarding a Confidence Interval Estimate for an Effect Size
13(2)
1.11 Type I and Type II Errors, Power, and Robustness
15(1)
1.11.1 Type I and Type II errors
15(1)
1.12 Basic Types of Research Studies
16(3)
1.12.1 Observational Studies
16(1)
1.12.2 Controlled Randomized Trials
17(1)
1.12.3 Quasi-experiments
18(1)
1.13 Why Not Always Conduct a Controlled Randomized Trial?
19(1)
1.14 Importance of Screening for Data Entry Errors
19(1)
1.15 Example 1.1: Environmental Impact Study of a Mine Site
19(1)
1.16 Some SAS Basics: Key Commonalities that Apply to all SAS Programs
20(2)
1.16.1 Temporary and Permanent SAS Data Sets
22(1)
1.17
Chapter Summary
22(7)
Appendix
24(1)
1.A Program 1.1
24(1)
1.A.1 Explanation of SAS Statements in Program 1.1
24(2)
1.B The SAS Log
26(1)
1.C Listing of Data in the SAS Data File MINESET
27(2)
2 Introduction to Simple Linear Regression
29(18)
2.1 Characteristic Features
29(1)
2.2 Why Use Simple Linear Regression?
29(1)
2.3 Example 2.1: Systolic Blood Pressure and Age
30(1)
2.4 Rationale Underlying a Simple Linear Regression Model
30(1)
2.5 An Equation for the Simple Linear Regression Model
31(1)
2.6 An Alternative Form of the Simple Linear Regression Model
32(1)
2.7 How Simple Linear Regression is Used with Sample Data
32(2)
2.7.1 Properties of Least Squares Estimators
34(1)
2.8 Prediction of a Y Value for an Individual having a Particular X Value
34(1)
2.9 Estimating the Mean Response in the Sampled Population Subgroup Having a Particular X Value
35(1)
2.10 Assessing Accuracy with Prediction Intervals and Confidence Intervals
35(1)
2.11 Ideal Inference Conditions for Simple Linear Regression
36(2)
2.12 Potential Consequences of Violations of Ideal Inference Conditions
38(1)
2.12.1 How Concerned Should We Be About Violations of Ideal Inference Conditions?
38(1)
2.13 What Researchers Need to Know about the Variance of Y Given X
39(1)
2.13.1 An Equation for Mean Square Error, A Model-Dependent Estimator of the Variance of Y given X
40(1)
2.14 Fixed vs. Random X in Simple Linear Regression
40(1)
2.15
Chapter Summary
41(6)
Appendix
42(1)
2.A Program 2.1
42(1)
2.A.1 Explanation of SAS Statements in Program 2.1
43(2)
2.A.2 A Message in SAS Log for Program 2.1
45(2)
3 Model Checking in Simple Linear Regression
47(42)
3.1 General Introduction
47(1)
3.2 Regression Outliers
47(2)
3.3 Influential Cases
49(1)
3.4 Residuals as Diagnostic Tools for Model Checking
50(1)
3.5 Obtaining Residuals from the REG Procedure
50(1)
3.5.1 Introduction
50(1)
3.5.2 Some Results from the REG Procedure for the Mine Site Example
50(1)
3.6 Raw (Unsealed) Residuals
51(2)
3.6.1 Example of a Raw Residual
51(1)
3.6.2 Estimated Standard Error (Standard Deviation) of a Raw Residual
52(1)
3.6.3 Difficulties Associated with Using Raw Residuals as a Diagnostic Tool
52(1)
3.7 Internally Studentized Residuals
53(1)
3.7.1 Advantages of Internally Studentized Residuals in Evaluating Ideal Inference Conditions
54(1)
3.8 Studentized Deleted Residuals
54(2)
3.8.1 Using a Studentized Deleted Residual to Identify a Regression Outlier
55(1)
3.8.2 Example
55(1)
3.8.3 Advantages of Studentized Deleted Residuals in Regression Outlier Dectection
56(1)
3.8.4 Caveat Regarding Studentized Deleted Residuals in Outlier Detection
56(1)
3.9 Graphical Evaluation of Ideal Inference Conditions in Simple Linear Regression
56(8)
3.9.1 Graphical Evaluation of Independence of Errors
56(1)
3.9.2 Graphical Evaluation of Linearity and Equality of Variances
57(2)
3.9.3 Graphical Evaluation of Normality
59(5)
3.10 Normality Tests and Gauging the Impact of Non-Normality
64(1)
3.11 Homogeneity of Variance Tests and Gauging the Impact of Unequal Variances in Regression
64(1)
3.12 Screening for Outliers to Detect Possible Recording Errors in Simple Linear Regression
65(1)
3.13 Overview of a Step-by-Step Approach for Checking Ideal Inference Conditions in Simple Linear Regression
66(2)
3.14 Example of Evaluating Ideal Inference Conditions
68(4)
3.15 Checking for Influential Cases
72(1)
3.16 DFBETA: Influence on an Estimated Regression Coefficient
73(1)
3.16.1 General Equation for DFBETA
73(1)
3.16.2 Equation for DFBETA for 8t in Simple Linear Regression
73(1)
3.16.3 Interpretation of DFBETA
74(1)
3.17 DFFITS: Influence of a Case on its Own Predicted Value
74(1)
3.17.1 Equation for DFFITS
74(1)
3.17.2 Interpretation of DFFITS
75(1)
3.18 Cook's Distance: Influence of a Case on All Predicted Values in the Sample
75(1)
3.18.1 Equation for Cook's D
75(1)
3.18.2 Interpretation of Cook's Distance
76(1)
3.19 Caveats Regarding Cut-Off Values for Measures of Influence
76(1)
3.20 Detecting Multiple Influential Cases That Occur in a Cluster
76(1)
3.21 Checking for Potentially Influential Cases in Example 1.1
77(2)
3.21.1 DFBETAS Results for Example 1.1
77(1)
3.21.2 DFFITS Results for Example 1.1
78(1)
3.21.3 Cook's D Results for Example 1.1
79(1)
3.22 Discussion and Conclusion Regarding Influence in Example 1.1
79(1)
3.23 Summary of Model Checking for Example 1.1
80(1)
3.24
Chapter Summary
80(9)
Appendix
82(1)
3.A Program 3.1A
82(1)
3.A.1 Explanation of SAS Statements in Program 3.1A Not Encountered in Previous Programs
82(1)
3.B Program 3.1B
83(1)
3.B.1 Explanation of SAS statements in Program 3.1B
84(1)
3.C Program 3.1C
85(2)
3.C.1 Explanation of Program 3.1C
87(2)
4 Interpreting a Simple Linear Regression Analysis
89(16)
4.1 Introduction
89(1)
4.2 A Basic Question to Ask in Simple Linear Regression
89(1)
4.3 The Model F-Test
90(1)
4.3.1 The Test Statistic for the Model F-Test
90(1)
4.3.2 Mine Site Example
90(1)
4.4 The t-Test of β1 = 0 vs. β1 ≠ 0 in the Sampled Population
91(1)
4.4.1 Example
92(1)
4.5 Possible Interpretations of a Large p-Value from a Model F-Test or Equivalent t-Test of β1 vs. β1 ≠ in Simple Linear Regression
92(1)
4.6 Possible Interpretations of a Small p-Value from a Model F-Test or Equivalent t-test of β1 = 0 vs. β1 ≠ in Simple Linear Regression
93(1)
4.7 Evaluating the Extent of the Usefulness of X for Explaining Y in a Simple Linear Regression Model
94(1)
4.8 A Confidence Interval Estimate for β1, the Regression Coefficient for X in Simple Linear Regression
94(2)
4.8.1 Interpreting a 95% Confidence Interval Estimate for β1
95(1)
4.8.2 Example
95(1)
4.9 R2, the Coefficient of Determination
96(1)
4.9.1 An Equation for R2
96(1)
4.9.2 Some Issues Interpreting R2
97(1)
4.9.3 Example
97(1)
4.10 Root Mean Square Error
97(1)
4.11 Coefficient of Variation for the Model
98(1)
4.12 Estimating a Confidence Interval for the Subpopulation Mean of Y Given a Specified X Value
98(1)
4.12.1 Example
98(1)
4.12.2 Equation for Estimating the Endpoints of a 95% Conventional Confidence Interval for the Mean of Y for a Given X Value
99(1)
4.13 Estimating a Prediction Interval for an Individual Value of Y at a Particular X Value
99(2)
4.13.1 Example
100(1)
4.13.2 Equation for Estimating the Endpoints of a 95% Conventional Prediction Interval for an Individual Y Given X
100(1)
4.14 Concluding Comments
101(1)
4.15
Chapter Summary
102(3)
Appendix
103(1)
4.A Program 4.1
103(2)
5 Introduction to Multiple Linear Regression
105(12)
5.1 Characteristic Features of a Multiple Linear Regression Model
105(1)
5.2 Why Use a Multiple Linear Regression Model?
105(1)
5.3 Example 5.1
106(1)
5.4 Equation for a First Order Multiple Linear Regression Model
107(1)
5.5 Alternate Equation for a First Order Multiple Linear Regression Model
107(1)
5.6 How Multiple Linear Regression is Used with Sample Data
107(2)
5.7 Estimation of a Y Value for an Individual from the Sampled Population
109(1)
5.7.1 Equation for Estimating a Y Value for an Individual from the Sampled Population
109(1)
5.7.2 Example
109(1)
5.8 Using Multiple Linear Regression to Estimate the Mean Y Value in a Population Subgroup with Particular Values for the Explanatory Variables
110(1)
5.9 Assessing Accuracy of Predicted Values
110(1)
5.10 Ideal Inference Conditions for a Multiple Linear Regression Model
110(1)
5.11 Measurement Error in Explanatory Variables in Multiple Linear Regression
111(1)
5.12 Collinearity -- Why Worry?
112(1)
5.13 Why the Estimation of Variance of Y Given the X Variables is Critical in Multiple Linear Regression
113(1)
5.14
Chapter Summary
114(3)
Appendix
115(1)
5.A Program 5.1
115(1)
5.B Example 5.1 Data Values
116(1)
6 Before Interpreting a Multiple Linear Regression Analysis
117(20)
6.1 Introduction
117(1)
6.2 Evaluating Collinearity
117(3)
6.2.1 A Method for Diagnosing Collinearity
118(1)
6.2.2 Interpreting Collinearity Diagnostics from the Method Proposed by Belsley (1991)
118(1)
6.2.3 Variance Inflation Factor: Another Measure of Collinearity
119(1)
6.2.4 Further Comments Regarding Collinearity Diagnosis
120(1)
6.3 A Ten-Step Approach for Checking Ideal Inference Conditions in Multiple Linear Regression
120(3)
6.4 Example -- Evaluating Ideal Inference Conditions
123(4)
6.5 Identifying Influential Cases
127(1)
6.6 Summary of Results Regarding Potentially Influential Cases based on Cook's D, DFBETAS, and DFFITS Values Output from Program 6.1C
128(3)
6.6.1 DFBETAS
129(1)
6.6.2 DFFITS
129(2)
6.6.3 Potentially Influential Cases
131(1)
6.7
Chapter Summary
131(6)
Appendix
133(1)
6.A Program 6.1A
133(1)
6.B Program 6.1B
134(1)
6.C Program 6.1C
135(2)
7 Interpreting an Additive Multiple Linear Regression Model
137(20)
7.1 Introduction
137(1)
7.2 Height at Age 18 Example
137(1)
7.3 The Model F-Test
138(2)
7.3.1 Model F-Test and Some Other Results Generated by the Model Statement of the REG Procedure for the Height at Age 18 Example
138(1)
7.3.2 Interpretation When the Model F-Test Statistic for a Multiple Linear Regression Model Has a Small p-Value
139(1)
7.3.3 Possible Interpretations When the Model F-Test Statistic for an Additive Multiple Linear Regression Model Has a Large p-Value
140(1)
7.4 R2 in Multiple Linear Regression
140(1)
7.4.1 Equation
140(1)
7.4.2 Issues Regarding R2
141(1)
7.4.3 Example
141(1)
7.5 Adjusted R2
141(1)
7.5.1 Equation for Adjusted R2
141(1)
7.5.2 Issues Regarding Adjusted R2
142(1)
7.5.3 Example
142(1)
7.6 Root Mean Square
142(1)
7.7 Coefficient of Variation for the Model
142(1)
7.8 Partial t-Tests in a Multiple Linear Regression Model
143(2)
7.8.1 Equation of the Test Statistic for a Partial t-Test of a Regression Coefficient
143(1)
7.8.2 Partial t-Test Examples
144(1)
7.9 Partial t-Tests and the Issue of Multiple Testing
145(1)
7.10 The Model F-Test, Partial t-Tests, and Collinearity
145(1)
7.11 Why Estimate a Confidence Interval for Bp
145(2)
7.11.1 Example
146(1)
7.11.2 Equation for a Conventional Confidence Interval Estimate for Bj
146(1)
7.12 Estimating a Conventional Confidence Interval for the Mean Y Value in a Population Subgroup with a Particular Combination of the Predictor Variables
147(1)
7.12.1 Example
147(1)
7.13 Estimating a Prediction Interval for an Individual Y Value Given Specified Values for the Predictor Variables
148(1)
7.14 Further Evaluation of Influence in the Height at Age 18 Example
149(1)
7.15 Extrapolation in Multiple Regression
150(3)
7.15.1 Delivery Time Data Example
151(1)
7.15.2 Cases Sorted by Hat Values from Program 7.2
151(2)
7.16
Chapter Summary
153(4)
Appendix
154(1)
7.A Program 7.1
154(1)
7.B Program 7.2
154(1)
7.B.1 Explanation of Program 7.2
155(2)
8 Modelling a Two-Way Interaction Between Continuous Predictors in Multiple Linear Regression
157(24)
8.1 Introduction to a Two-Way Interaction
157(1)
8.2 A Two-Way Interaction Model in Multiple Linear Regression
158(2)
8.3 Investigating a Two-Way Interaction Using Sample Data
160(1)
8.4 Example 8.1: Physical Endurance as a Linear Function of Age, Exercise, and their Interaction
161(1)
8.5 Facilitating Interpretation in Two-Way Interaction Regression via Centring
161(2)
8.5.1 Example of Centring to Facilitate Interpretation
163(1)
8.6 A Suggested Approach for Applying a Multiple Linear Regression Two-Way Interaction Model with Two Continuous Predictors
163(2)
8.7 An Example Using the Suggested Approach for Applying an Interaction Model with Two Continuous Predictors
165(1)
8.8 Results from Application of a Multiple Regression Interaction Analysis with Centred AGE and Uncentered EXER in the Physical Endurance Example
166(1)
8.9 Interpretation of Regression Coefficient Estimates for the Interaction Model Fitted to Example 8.1
167(1)
8.10 Visualization of the Interaction Effect Observed in Example 8.1
168(2)
8.11 Predicting Endurance on a Treadmill
170(1)
8.12
Chapter Summary
171(10)
Appendix
173(1)
8.A Summary of Evaluation of Ideal Inference Conditions for the Physical Endurance Example with a Two-Way Interaction Model
173(3)
8.B Summary of Influence Diagnostics for the Physical Endurance Example with a Two-Way Interaction Model
176(1)
8.C Program 8.1
177(1)
8.D Program 8.2
178(2)
8.D.1 Explanation of SAS Statements in Program 8.2
180(1)
9 Evaluating a Two-Way Interaction Between a Qualitative and a Continuous Predictor in Multiple Linear Regression
181(20)
9.1 Introduction
181(1)
9.2 How to Include a Qualitative Variable in a Multiple Linear Regression Model
181(1)
9.3 Full Rank Reference Cell Coding
182(1)
9.4 Example 9.1: Mussel Weight
182(1)
9.5 Example Using a Nine-Step Approach for Applying a Multiple Linear Regression with a Two-Way Interaction between a Continuous and Qualitative Predictor
183(1)
9.6 Evaluating Influence in Multiple Regression Models which Involve Qualitative Variables
184(1)
9.7 Summary of Influence Evaluation in the Multiple Regression Interaction Analysis for the Mussel Example
185(1)
9.8 Results from Program 9.2: Two-Way Interaction Regression Analysis between a Qualitative Predictor (Reference Cell Coding) and a Centred Continuous Predictor
186(1)
9.9 Interpreting Results of the Model F-Test and Parameter Estimates Reported in Section 9.8
187(4)
9.9.1 Introduction
187(1)
9.9.2 Interpretation of Model F-Test
187(1)
9.9.3 Interpretation of the Estimated Regression Coefficient for AGECILOC
187(2)
9.9.4 Interpretation of the Estimated Regression Coefficient for AGEC
189(1)
9.9.5 Interpretation of the Estimated Regression Coefficient for ILOC
189(1)
9.9.6 Interpretation of the Sample Model Intercept
190(1)
9.10
Chapter Summary
191(10)
Appendix
192(1)
9.A Evaluation of Ideal Inference Conditions for the Mussel Example
192(2)
9.B Program 9.1: Getting to Know the Mussel Data
194(1)
9.B.1 Explanation of Statements in Program 9.1
195(1)
9.C Program 9.2: Two-Way Interaction Regression Analysis between a Qualitative Predictor (Reference Cell Coding) and a Centred Continuous Predictor
196(2)
9.C.1 Explanation of Selected SAS Statements in Program 9.2
198(1)
9.D Program 9.3
199(2)
10 Subset Selection of Predictor Variables in Multiple Linear Regression
201(26)
10.1 Introduction
201(1)
10.2 Under-Fitting, Over-Fitting, and the Bias-Variance Trade-Off
202(1)
10.3 Overview of Traditional Model Selection Algorithms
202(2)
10.3.1 Forward Selection
202(1)
10.3.2 Backward Elimination
203(1)
10.3.3 Stepwise Selection
203(1)
10.3.4 All Subsets Selection Algorithm
203(1)
10.3.5 The Impact of Collinearity on Traditional Sequential Selection Algorithms
203(1)
10.4 Fit Criteria Used in Model Selection Methods
204(4)
10.4.1 Adjusted R2
204(1)
10.4.2 Akaike's Information Criterion
205(1)
10.4.3 The Corrected Akaike's Information Criterion
205(1)
10.4.4 Average Square Error
206(1)
10.4.5 Mallows' Cp Statistic
206(1)
10.4.6 Mean Square Error
206(1)
10.4.7 The PRESS Statistic
207(1)
10.4.8 Schwarz's Bayesian Information Criterion
207(1)
10.4.9 Significance Level (p-Value) Criterion
207(1)
10.5 Post-Selection Inference Issues
208(1)
10.6 Predicting Percentage Body Fat: Naval Academy Example
208(3)
10.7 Model Selection and the REG Procedure
211(2)
10.8 Model Selection and the GLMSELECT Procedure
213(8)
10.8.1 Example of Subset Selection in GLMSELECT
214(1)
10.8.2 Model Information: Program 10.2
214(1)
10.8.3 Model Building Summary Results: Program 10.2
215(1)
10.8.4 Comments Regarding Model Building Summary Results
216(1)
10.8.5 Selected Model Results: Program 10.2
217(1)
10.8.6 Comments Regarding Standard Errors of the Partial Regression Coefficients for the Selected Model
218(1)
10.8.7 Average Square Error Plot: Program 10.2
218(1)
10.8.8 Criteria Panel Plot: Program 10.2
218(3)
10.9 Other Features Available in GLMSELECT
221(1)
10.10
Chapter Summary
221(6)
Appendix
223(1)
10.A Program 10.1
223(2)
10.B Program 10.2
225(2)
11 Evaluating Equality of Group Means with a One-Way Analysis of Variance
227(26)
11.1 Characteristic Features of a One-Way Analysis of Variance Model
227(1)
11.2 Fixed Effects vs. Random Effects in One-Way ANOVA
227(2)
11.3 Why Use a One-Way Fixed Effects Analysis of Variance?
229(1)
11.4 Task Study Example
229(1)
11.5 The Means Model for a One-Way Fixed Effects ANOVA
230(1)
11.6 Basic Concepts Underlying a One-Way Fixed Effects ANOVA
230(2)
11.7 Ideal Inference Conditions for One-Way Fixed Effects ANOVA
232(1)
11.8 Potential Consequences of Violating Ideal Inference Conditions for One-Way Fixed Effects ANOVA Test of Equality of Group Means
232(2)
11.9 Overview of General Approaches for Evaluating Ideal Inference Conditions for a One-Way Fixed Effects ANOVA
234(1)
11.10 Suggestions for Alternative Approaches When Ideal Inference Conditions are Not Reasonable
234(1)
11.11 Testing Equality of Group Variances
235(1)
11.12 Some Earlier Tests for Equality of Variances
235(1)
11.12.1 Bartlett's Test
235(1)
11.12.2 Hartley's Fmax Test
236(1)
11.13 ANOVA-Based Tests for Equality of Variances
236(2)
11.13.1 Levene's Approach for Testing Equality of Variances
236(1)
11.13.2 Brown's and Forsythe's Tests of Variances
237(1)
11.13.3 O'Brien's Test
237(1)
11.14 Simulation Studies on ANOVA-Based Equality of Variances Tests
238(1)
11.15 Additional Comments about ANOVA-Based Equality of Variances Tests
239(1)
11.16 Overview of a Step-by-Step Approach for Checking Ideal Inference Conditions
239(1)
11.17 Nine-Step Approach for Evaluating Ideal Inference Conditions: Task Study Example
240(3)
11.18 One-Way ANOVA Model F-Test of Means
243(2)
11.18.1 Task Study Example
243(1)
11.18.2 What is a Linear Contrast?
244(1)
11.18.3 Comments on Model F-Test in One-Way Fixed Effects ANOVA
244(1)
11.19 Testing Equality of Population Means When Population Variances Are Unequal
245(1)
11.19.1 Welch's Test
245(1)
11.19.2 Fitting Unequal Variance ANOVA Models
246(1)
11.19.3 Other Suggestions
246(1)
11.20
Chapter Summary
246(7)
Appendix
248(1)
11.A Program 11.1: Data Screening
248(1)
11.B Program 11.2
249(1)
11.C Explanation of Statements in Program 11.2
250(3)
12 Multiple Testing and Simultaneous Confidence Intervals
253(34)
12.1 Multiple Testing and the Multiplicity Problem
253(1)
12.2 Measures of Error Rates
253(1)
12.3 Overview of Multiple Testing Procedures
254(2)
12.4 The Least Significant Difference: A Multiplicity-Unadjusted Procedure
256(2)
12.4.1 Introduction
256(1)
12.4.2 Ideal Inference Conditions
256(1)
12.4.3 Fisher's LSD
257(1)
12.4.4 SAS and the LSD Procedure
257(1)
12.5 Examples of Familywise Error Rate Controlling Procedures
258(1)
12.6 The Bonferroni Method
259(3)
12.6.1 Introduction
259(1)
12.6.2 Example 12.1: An Application of the Bonferroni Method
260(1)
12.6.3 Why the Bonferroni Method Can Be Conservative
261(1)
12.6.4 The Bonferroni Method and All Possible Pairwise Comparisons of Group Means
261(1)
12.7 The Tukey-Kramer Method for All Pairwise Comparisons
262(2)
12.7.1 Introduction
262(1)
12.7.2 SAS and the Tukey-Kramer Method
263(1)
12.8 A Simulation-Based Method for All Pairwise Comparisons
264(1)
12.8.1 Introduction
264(1)
12.8.2 SAS and Simulation-Based Adjusted p-Value Estimates
264(1)
12.8.3 Task Study Example of Simulation-Based Adjusted p-Values Estimates
265(1)
12.9 Dunnett's Method for "Treatment" vs. "Control" Comparisons
265(2)
12.9.1 Introduction
265(1)
12.9.2 SAS and Dunnett's Test
266(1)
12.10 Scheffe's Method for "Data Snooping"
267(2)
12.10.1 Introduction
267(1)
12.10.2 Application of Scheffe's Method
268(1)
12.10.3 SAS and Scheffe's method
268(1)
12.11 Ordinary Confidence Intervals and the Multiplicity Issue
269(1)
12.11.1 Introduction
269(1)
12.11.2 Why Does the Overall Confidence Level Decrease as the Number of Ordinary Confidence Intervals Increases?
269(1)
12.12 Controlling Familywise Error Rate for Confidence Intervals
270(3)
12.12.1 Introduction
270(1)
12.12.2 Task Study Example
271(1)
12.12.3 SAS and Controlling Familywise Error Rate for Confidence Intervals
272(1)
12.13 Confidence Bands for Simple Linear Regression
273(5)
12.13.1 The Working-Hotelling Method
274(1)
12.13.2 SAS and Working-Hotelling's Confidence Band
274(1)
12.13.3 A Discrete Simulation-Based Method
275(3)
12.14 Single Step vs. Sequential Multiplicity-Adjusted Procedures
278(1)
12.15 The Holm-Bonferroni Sequential Procedure
278(3)
12.15.1 Introduction
278(1)
12.15.2 How to Compute Holm-Bonferroni Multiplicity-Adjusted p-Values
279(1)
12.15.3 SAS and the Holm-Bonferroni Method
280(1)
12.15.4 Familywise Adjusted p-Values for Partial t-Tests from Program 12.2
281(1)
12.16 Adjusting for Multiplicity Using Resampling Methods
281(1)
12.17 Benjamini-Hochberg's False Discovery Rate Method
281(3)
12.17.1 Introduction
281(1)
12.17.2 Benjamini-Hochberg's Adjusted p-Values
282(1)
12.17.3 SAS and Benjamini-Hochberg's FDR-Controlling Method
283(1)
12.17.4 Interpreting Results from a FDR-Controlling Procedure
284(1)
12.18 Recent Advances in FDR-Controlling Procedures
284(1)
12.19
Chapter Summary
285(2)
13 Analysis of Covariance: Adjusting Group Means for Nuisance Variables Using Regression
287(64)
13.1 Introduction
287(1)
13.2 Characteristic Features of a One-Way Analysis of Covariance Linear Model
287(1)
13.3 Why Apply an Analysis of Covariance?
288(1)
13.4 Example 13.1: Exercise Programs and Heart Rate
288(1)
13.5 General Equation for a One-Way Analysis of Covariance with a Single Continuous Covariate
289(1)
13.6 Two Critical Decisions in an Analysis of Covariance
290(4)
13.7 Implementing a One-Way ANCOVA A Step-by-Step Approach
294(3)
13.8 An Example of Implementing an Analysis of Covariance
297(11)
13.9 What If an Equal Slopes Analysis Had Been Applied to the Exercise Program Data?
308(2)
13.9.1 What Is Going On?
309(1)
13.10 What If a One-Way ANOVA Had Been Applied to the Exercise Program Data?
310(2)
13.11 Example 13.2: Effect of Study Methods on Exam Scores Adjusted for Pretest Scores
312(1)
13.12 A Step-by-Step Analysis of Covariance for Example 13.2
312(9)
13.13 References for Other Approaches for Covariate Adjustment
321(1)
13.14
Chapter Summary
321(30)
Appendix
323(1)
13.A Details of a Nine-Step Evaluation of Ideal Inference Conditions for Simple Linear Regressions in Exercise Programs A and B in Example 13.1
323(6)
13.B Details of Evaluation of Ideal Inference Conditions for Simple Linear Regressions of Postscore vs. Prescore in Example 13.2
329(6)
13.C Program 13.1
335(1)
13.D Program 13.2
336(2)
13.E Program 13.3A
338(1)
13.F Program 13.3B
339(1)
13.G Program 13.4
340(2)
13.H Program 13.5
342(1)
13.I Program 13.6
343(1)
13.J Program 13.7
344(1)
13.K Summary of SAS Programs for Example 13.2
345(1)
13.L Program 13.8
345(1)
13.M Program 13.9
346(2)
13.N Program 13.10A
348(1)
13.O Program 13.10B
349(1)
13.P Program 13.11
349(1)
13.Q Program 13.12
350(1)
14 Alternative Approaches If Ideal Inference Conditions Are Not Satisfied
351(38)
14.1 Introduction
351(1)
14.2 When Random Sampling Is Not an Option
351(1)
14.3 When Errors Are Not All Independent
352(2)
14.3.1 Introduction
352(1)
14.3.2 Fitting a Model for Correlated Data
353(1)
14.4 Transformations
354(5)
14.4.1 Advantages and Disadvantages of a Data Transformation Approach
354(1)
14.4.2 Power Transformations
355(1)
14.4.3 Applying Power Transformations in SAS
356(1)
14.4.4 Log Transformations
357(2)
14.5 Alternative Approaches When Linearity Is Not Satisfied
359(8)
14.5.1 Introduction
359(1)
14.5.2 Adding One or More Predictor Variable(s) to the Model to Achieve Linearity
359(1)
14.5.3 Transformations and the Linearity Assumption
359(5)
14.5.4 Overview of Rank Regression
364(1)
14.5.5 Polynomial Regression and Nonlinearity
365(2)
14.5.6 Overview of Fitting a Nonlinear Model
367(1)
14.6 Alternative Approaches When Variances Are Not All Equal
367(3)
14.6.1 Introduction
367(1)
14.6.2 Transforming Data to Achieve Equality of Variances
368(1)
14.6.3 Overview of Weighted Least Squares for Unequal Variances
369(1)
14.7 Alternative Approaches If Model Errors Are Not Normal
370(1)
14.7.1 Introduction
370(1)
14.7.2 Reducing Skewness with Power Transformations
370(1)
14.8 Robust Statistics
371(1)
14.9 Bootstrapping
371(2)
14.9.1 Case Resampling
372(1)
14.9.2 The Bootstrap Estimate of Standard Error
372(1)
14.9.3 The Bootstrap Percentile Confidence Interval
373(1)
14.10 When Is n Too Small And What Is An Adequate Number Of Bootstrap Samples?
373(4)
14.10.1 Example of a Bootstrapping Application
374(3)
14.11 Alternative Approaches If Harmful Collinearity Is Detected
377(1)
14.12
Chapter Summary
378(11)
Appendix
380(1)
14.A Program 14.A
380(1)
14.B Program 14.B
380(2)
14.C Program 14.C
382(1)
14.D Program 14.D
383(1)
14.E Program 14.E
384(1)
14.E.1 Explanation of SAS Statements in Program 14.E
385(4)
References 389(12)
Index 401
Patricia F. Moodie is a Research Scholar in the Department of Mathematics and Statistics at the University of Winnipeg, Manitoba, Canada. Prior to that she was Head of Biostatistics in the Computer Department for Health Sciences in the College of Medicine, University of Manitoba, an adjunct lecturer in Biometry in the Department of Social and Preventive Medicine at the University of Manitoba, and a biostatistician in the Epidemiology and Biostatistics Department at the Manitoba Cancer Treatment and Research Foundation. Her statistical consulting and collaboration for over three decades as well as her substantive background in the biomedical sciences have made her appreciate the challenges in analyzing and interpreting real-life data. She received a BSc (Hons) in Biology at Memorial University of Newfoundland, an MSc in Zoology at the University of Alberta, and an MS in Biostatistics at the University of Illinois at Chicago. She has been an enthusiastic SAS user since 1980.

Dallas E. Johnson, Professor Emeritus in the Department of Statistics, Kansas State University, has published extensively in the areas of linear models, multiplicative interaction models, experimental design, and messy data analysis. He is the author of Applied Multivariate Methods for Data Analysts and co-author with George A. Milliken of the following books: Analysis of Messy Data, Vol. I - Designed Experiments, Vol. II - Nonreplicated Experiments, Vol. III - Analysis of Covariance, and Vol. I - Designed Experiments 2nd Edition. An active presenter of short courses, and a statistical consultant for over 50 years, he was the recipient of ASA's award for Excellence in Statistical Consulting in 2010. He received his B.S. degree in Mathematics Education, Kearney State College, a M.A.T. degree in Mathematics, Colorado State University, a M.S. degree in Mathematics, Western Michigan University, and a Ph.D. degree in Statistics, Colorado State University. He has been a SAS user and mentor since 1976.
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