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9780805835540

Single-Case and Small-N Experimental Designs : A Practical Guide to Randomization Tests

by ;
  • ISBN13:

    9780805835540

  • ISBN10:

    0805835547

  • Format: Hardcover
  • Copyright: 2001-03-01
  • Publisher: Lawrence Erlbau
  • Purchase Benefits
List Price: $57.50

Summary

This book is a practical guide to help researchers draw valid causal inferences from small-scale clinical intervention studies. It should be of interest to teachers of, and students in, courses with an experimental clinical component, as well as clinical researchers. Inferential statistics used in the analysis of group data are frequently invalid for use with data from single-case experimental designs. Even non-parametric rank tests provide, at best, approximate solutions for only some single-case (and small-n ) designs. Randomization (Exact) tests, on the other hand, can provide valid statistical analyses for all designs that incorporate a random procedure for assigning treatments to subjects or observation periods, including single-case designs. These Randomization tests require large numbers of data rearrangements and have been seldom used, partly because desktop computers have only recently become powerful enough to complete the analyses in a reasonable time. Now that the necessary computational power is available, they continue to be under-used because they receive scant attention in standard statistical texts for behavioral researchers and because available programs for running the analyses are relatively inaccessible to researchers with limited statistical or computing interest. This book is first and foremost a practical guide, although it also presents the theoretical basis for Randomization tests. Its most important aim is to make these tests accessible to researchers for a wide range of designs. It does this by providing programs on CD-ROM that allow users to run analyses of their data within a standard package (Minitab, Excel, or SPSS) with which they are already familiar. No statistical or computing expertise is required to use these programs. This is the "new stats" for single-case and small-n intervention studies, and anyone interested in this research approach will benefit.

Table of Contents

Preface xix
Data Analysis in Single-Case and Small-n Experiments
1(11)
Varieties of Clinical Design
1(2)
Random Allocation of Treatments to Participants or Test Occasions
3(2)
Random Sampling Versus Random Allocation
4(1)
Participants Versus Exposures
5(1)
Testing Hypotheses in Single-Case and Small-n Designs
5(3)
Time-Series Analysis Using ARIMA
5(1)
Adaptations of Classical ANOVA and Regression Procedures
6(1)
Nonparametric Tests
7(1)
Randomization Tests and the Validity of Statistical Conclusions
8(1)
The Versatility of Randomization Tests
9(1)
Guidelines for Statistical Hypothesis Testing
9(3)
Statistical and Visual Analysis
12(15)
Arguments Against Statistical Analysis of Single-Case Designs
12(1)
The Operant Viewpoint
13(10)
Control
13(3)
Response-Guided Experimentation
16(2)
An Illustration of Response-Guidance Bias
18(3)
An Experimental Test of Response-Guided Bias
21(1)
Statistical Consequences of Response-Guided Experimentation
21(1)
Replication
22(1)
Clinical and Statistical Significance
23(2)
When to Use Statistical Analysis
25(2)
Approaches to Statistical Inference
27(11)
Randomization Tests
27(1)
The Classical Theory
28(2)
Bayesian Inference
30(1)
Randomization Tests Revisited
30(1)
Assumptions of Randomization Tests
31(5)
Distributional Assumptions
32(1)
Autocorrelation
33(3)
The Current Suitability of Randomization Tests
36(2)
Principles of Randomization Tests
38(12)
The Lady Tasting Tea Experiment
38(2)
Examples with Scores as Data
40(5)
Alternating Treatments (3 Observation Times for Each of 2 Treatments)
40(3)
Alternating Treatments (4 Observation Times for Each of 2 Treatments)
43(1)
A Phase (Baseline-Treatment) Design
43(2)
Generalized Application of Principles of Randomization Tests
45(4)
A Randomization Procedure
45(1)
Selection of a Test Statistic
46(1)
Computation of the Test Statistic for Arrangements of the Data
46(1)
Systematic Arrangements of the Data
46(1)
Random Samples of Arrangements of the Data
47(1)
Reporting the Statistical Decision
48(1)
Summary of Randomization Test Requirements
49(1)
Randomization Designs for Single-Case and Small-n Studies
50(23)
Design 1 (AB)
51(4)
Example for Design 1
53(2)
Design 2 (ABA Reversal)
55(2)
Example for Design 2
55(2)
Design 3 (AB Multiple Baseline)
57(3)
Example for Design 3
57(3)
Design 4 (ABA Multiple Baseline)
60(1)
Example for Design 4
60(1)
Design 5
61(4)
Design 5 (One-Way Small Groups)
62(1)
Example for Design 5 (Small Groups)
62(1)
Design 5 (Single-Case Randomized Treatment)
63(1)
Example for Design 5 (Single-Case)
63(1)
Design 5a (Small Groups or Single-Case--2 Randomized Treatments)
64(1)
Example for Design 5a
64(1)
Design 6
65(3)
Design 6 (One-Way Small Group Repeated Measures)
65(1)
Example for Design 6 (Small Group)
65(1)
Design 6 (Single-Case Randomized Blocks)
66(1)
Example for Design 6 (Single-Case)
66(1)
Design 6a (2 Repeated Measures or 2 Randomized Blocks)
67(1)
Example for Design 6a
67(1)
Design 7 (Two-Way Factorial Single-Case)
68(2)
Example for Design 7
68(2)
Design 8 (Ordinal Predictions)
70(3)
Example for Design 8
71(2)
Randomization Tests Using Minitab
73(34)
Design 1 (AB)
75(2)
Specifications for Design 1 Example
75(1)
Commented Macro for Design 1 (Macro File Name: des1.txt)
75(1)
Location of Sample Size (2000 and 2001 Entries) in Macro
76(1)
Location of Design 1 Test Results
77(1)
Randomization Test Results for Design 1 Example
77(1)
Statistical Conclusion for Design 1 Example (Assuming a Directional Prediction)
77(1)
Design 2 (ABA Reversal)
77(3)
Specifications for Design 2 Example
77(1)
Commented Macro for Design 2 (Macro File Name: des2.txt)
78(1)
Location of Sample Size (2000 and 2001 Entries) in Macro
79(1)
Location of Design 2 Test Results
80(1)
Randomization Test Results for Design 2 Example
80(1)
Statistical Conclusion for Design 2 Example (Assuming a Directional Prediction)
80(1)
Design 3 (AB Multiple Baseline)
80(4)
Specifications for Design 3 Example
80(1)
Commented Macro for Design 3 (Macro File Name: des3.txt)
81(2)
Location of Sample Size (2000 and 2001 Entries) in Macro
83(1)
Location of Design 3 Test Results
83(1)
Randomization Test Results for Design 3 Example
84(1)
Statistical Conclusion for Design 3 Example (Assuming a Directional Prediction)
84(1)
Design 4 (ABA Multiple Baseline)
84(4)
Specifications for Design 4 Example
84(1)
Commented Macro for Design 4 (Macro File Name: des4.txt)
85(2)
Location of Sample Size (2000 and 2001 Entries) in Macro
87(1)
Location of Design 4 Test Results
88(1)
Randomization Test Results for Design 4 Example
88(1)
Statistical Conclusion for Design 4 Example (Assuming a Directional Prediction)
88(1)
Design 5 (One-Way Small Groups and Single-Case Randomized Treatment)
88(2)
Specifications for Design 5 Example
88(1)
Commented Macro for Design 5 (Macro File Name: des5.txt)
89(1)
Location of Sample Size (2000 and 2001 Entries) in Macro
90(1)
Location of Design 5 Test Results
90(1)
Randomization Test Results for Design 5 Example
90(1)
Statistical Conclusion for Design 5 (One-Way Small Groups) Example
90(1)
Design 5a (Small Groups or Single-Case--Two Randomized Treatments)
90(3)
Specifications for Design 5a Example
90(1)
Commented Macro for Design 5a (Macro File Name: des5a.txt)
91(1)
Location of Sample Size (2000 and 2001 Entries) in Macro
92(1)
Location of Design 5a Test Results
92(1)
Randomization Test Results for Design 5a Example
92(1)
Statistical Conclusion for Design 5a (One-Tailed Single-Case) Example
92(1)
Design 6 (One-Way Small Group Repeated Measures and Single-Case Randomized Blocks)
93(2)
Specifications for Design 6 Example
93(1)
Commented Macro for Design 6 (Macro File Name: des6.txt)
93(1)
Location of Sample Size (2000 and 2001 Entries) in Macro
94(1)
Location of Design 6 Test Results
94(1)
Randomization Test Results for Design 6 Example
95(1)
Statistical Conclusion for Design 6 (One-Way Small Groups) Example
95(1)
Design 6a (2 Repeated Measures on Small Group or Single-Case Blocks)
95(3)
Specifications for Design 6a Example
95(1)
Commented Macro for Design 6a (Macro File Name: des6a.txt)
95(2)
Location of Sample Size (2000 and 2001 Entries) in Macro
97(1)
Location of Design 6a Test Results
97(1)
Randomization Test Results for Design 6a Example
97(1)
Statistical Conclusion for Design 6a (One-Tailed Single-Case) Example
97(1)
Design 7 (Two-Way Factorial Single Case)
98(5)
Specifications for Design 7 Example
98(1)
Commented Macro for Design 7 (Macro File Name: des7.txt)
98(3)
Location of Sample Size (2000 and 2001 Entries) in Macro
101(1)
Location of Design 7 Test Results
101(1)
Randomization Test Results for Design 7 Example
101(1)
Statistical Conclusions for Design 7 (One-Tailed Main Effects) Example
102(1)
Testing Simple Effects in the Factorial Design
102(1)
Randomization Test Results for Design 7 (Simple Effect of Display Mode with Touch-Screen Interface) Example
103(1)
Statistical Conclusion for One-Tailed Test of a Simple Effect
103(1)
Design 8 (Ordinal Predictions Within Nonexperimental Designs)
103(4)
Specifications for Design 8 Example
104(1)
Commented Macro for Design 8 (Macro File Name: des8.txt)
104(1)
Location of Sample Size (2000 and 2001 Entries) in Macro
105(1)
Location of Design 8 Test Results
105(1)
Randomization Test Results for Design 8 Example
105(1)
Statistical Conclusion for Design 8 (Unique Order Prediction of Small Group Data) Example
105(1)
Statistical Conclusion for Design 8 (Partial Order Prediction of Single-Case Data) Example
106(1)
Randomization Tests Using Excel
107(48)
Design 1 (AB)
109(5)
Specifications for Design 1 Example
109(1)
Commented Macro for Design 1 (Macro File Name: design1.xls)
110(3)
Location of Design 1 Test Results
113(1)
Randomization Test Results for Design 1 Example
113(1)
Statistical Conclusion for Design 1 Example (Assuming a Directional Prediction)
114(1)
Design 2 (ABA Reversal)
114(5)
Specifications for Design 2 Example
114(1)
Commented Macro for Design 2 (Macro File Name: design2.xls)
114(4)
Location of Design 2 Test Results
118(1)
Randomization Test Results for Design 2 Example
119(1)
Statistical Conclusion for Design 2 Example (Assuming a Directional Prediction)
119(1)
Design 3 (AB Multiple Baseline)
119(6)
Specifications for Design 3 Example
119(1)
Commented Macro for Design 3 (Macro File Name: design3.xls)
120(4)
Location of Design 3 Test Results
124(1)
Randomization Test Results for Design 3 Example
124(1)
Statistical Conclusion for Design 3 (Assuming a Directional Prediction)
125(1)
Design 4 (ABA Multiple Baseline Design)
125(6)
Specifications for Design 4 Example
125(1)
Commented Macro for Design 4 (Macro File Name: design4.xls)
125(5)
Location of Design 4 Test Results
130(1)
Randomization Test Results for Design 4 Example
131(1)
Statistical Conclusion for Design 4 Example (Assuming a Directional Prediction)
131(1)
Design 5 (One-Way Small Groups and Single-Case Randomized Treatment)
131(3)
Specifications for Design 5 Example
131(1)
Commented Macro for Design 5 (Macro File Name: design5.xls)
132(1)
Location of Design 5 Test Results
133(1)
Randomization Test Results for Design 5 Example
134(1)
Statistical Conclusion for Design 5 (One-Way Small Groups) Example
134(1)
Design 5a (Small Groups or Single-Case--Two Randomized Treatments)
134(3)
Specifications for Design 5a Example
134(1)
Commented Macro for Design 5a (Macro File Name: design5a.xls)
135(2)
Location of Design 5a Test Results
137(1)
Randomization Test Results for Design 5a Example
137(1)
Statistical Conclusion for Design 5a (One-Tailed Single-Case) Example
137(1)
Design 6 (One-Way Small Group Repeated Measures and Single-Case Randomized Blocks)
137(4)
Specifications for Design 6 Example
137(1)
Commented Macro for Design 6 (Macro File Name: design6.xls)
138(2)
Location of Design 6 Test Results
140(1)
Randomization Test Results for Design 6 Example
140(1)
Statistical Conclusion for Design 6 (One-Way Small Groups) Example
140(1)
Design 6a (Two Repeated Measures on Small Group or Single-Case Blocks)
141(3)
Specifications for Design 6a Example
141(1)
Commented Macro for Design 6a (Macro File Name: design6a.xls)
141(2)
Location of Design 6a Test Results
143(1)
Randomization Test Results for Design 6a Example
144(1)
Statistical Conclusion for Design 6a (One-Tailed Single-Case) Example
144(1)
Design 7 (Two-Way Factorial Single Case)
144(7)
Specifications for Design 7 Example
144(1)
Commented Macro for Design 7 (Macro File Name: design7.xls)
145(3)
Location of Design 7 Test Results
148(1)
Randomization Test Results for Design 7 Example
149(1)
Statistical Conclusions for Design 7 (One-Tailed Main Effects) Example
149(1)
Testing Simple Effects in the Factorial Design
150(1)
Randomization Test Results for Design 7 (Simple Effect of Display Mode with Touch-Screen Interface) Example
150(1)
Statistical Conclusion for One-Tailed Test of a Simple Effect
151(1)
Design 8 (Ordinal Predictions Within Nonexperimental Designs)
151(4)
Specifications for Design 8 Example
151(1)
Commented Macro for Design 8 (Macro File Name: design8.xls)
151(2)
Location of Design 8 Test Results
153(1)
Randomization Test Results for Design 8 Example
153(1)
Statistical Conclusion for Design 8 (Unique Order Prediction of Small Group Data) Example
153(1)
Statistical Conclusion for Design 8 (Partial Order Prediction of Single-Case Data) Example
154(1)
Randomization Tests Using SPSS
155(41)
Design 1 (AB)
157(4)
Specifications for Design 1 Example
157(1)
Commented Program for Design 1 (Program File Name: design1.sps)
158(2)
Randomization Test Results for Design 1 Example
160(1)
Statistical Conclusion for Design 1 Example (Assuming a Directional Prediction)
160(1)
Design 2 (ABA Reversal)
161(3)
Specifications for Design 2 Example
161(1)
Commented Program for Design 2 (Program File Name: design2.sps)
161(3)
Randomization Test Results for Design 2 Example
164(1)
Statistical Conclusion for Design 2 Example (Assuming a Directional Prediction)
164(1)
Design 3 (AB Multiple Baseline)
164(4)
Specifications for Design 3 Example
164(1)
Commented Program for Design 3 (Program File Name: design3.sps)
165(3)
Randomization Test Results for Design 3 Example
168(1)
Statistical Conclusion for Design 3 Example (Assuming a Directional Prediction)
168(1)
Design 4 (ABA Multiple Baseline)
168(4)
Specifications for Design 4 Example
168(1)
Commented Program for Design 4 (Program File Name: design4.sps)
169(3)
Randomization Test Results for Design 4 Example
172(1)
Statistical Conclusion for Design 4 Example (Assuming a Directional Prediction)
172(1)
Design 5 (One-Way Small Groups and Single-Case Randomized Treatment)
172(3)
Specifications for Design 5 Example
172(1)
Commented Program for Design 5 (Program File Name: design5.sps)
173(2)
Randomization Test Results for Design 5 Example
175(1)
Statistical Conclusion for Design 5 (One-Way Small Groups) Example
175(1)
Design 5a (Small Groups or Single-Case--Two Randomized Treatments)
175(4)
Specifications for Design 5a Example
175(1)
Commented Program for Design 5a (Program File Name: design5a.sps)
176(2)
Randomization Test Results for Design 5a Example
178(1)
Statistical Conclusion for Design 5a (One-Tailed Single-Case) Example
178(1)
Design 6 (One-Way Small Group Repeated Measures and Single-Case Randomized Blocks)
179(3)
Specifications for Design 6 Example
179(1)
Commented Program for Design 6 (Program File Name: design6.sps)
179(3)
Randomization Test Results for Design 6 Example
182(1)
Statistical Conclusion for Design 6 (One-Way Small Groups) Example
182(1)
Design 6a (Two Repeated Measures on Small Group or Single-Case Blocks)
182(4)
Specifications for Design 6a Example
182(1)
Commented Program for Design 6a (Program File Name: design6a.sps)
183(2)
Randomization Test Results for Design 6a Example
185(1)
Statistical Conclusion for Design 6a (One-Tailed Single-Case) Example
185(1)
Design 7 (Two-Way Factorial Single Case)
186(6)
Specifications for Design 7 Example
186(1)
Commented Program for Design 7 (Program File Name: design7.sps)
186(4)
Randomization Test Results for Design 7 Example
190(1)
Statistical Conclusions for Design 7 (One-Tailed Main Effects) Example
191(1)
Testing Simple Effects in the Factorial Design
191(1)
Randomization Test Results for Design 7 (Simple Effect of Display Model with Touch-Screen Interface) Example
192(1)
Statistical Conclusion for One-Tailed Test of a Simple Effect
192(1)
Design 8 (Ordinal Predictions Within Nonexperimental Designs)
192(4)
Specifications for Design 8 Example
193(1)
Commented Program for Design 8 (Program File Name: design8.sps)
193(2)
Randomization Test Results for Design 8 Example
195(1)
Statistical Conclusion for Design 8 (Unique Order Prediction of Small Group Data) Example
195(1)
Statistical Conclusion for Design 8 (Partial Order Prediction of Single-Case Data) Example
195(1)
Other Sources of Randomization Tests
196(6)
Books and Journal Articles
196(1)
Statistical Packages
197(5)
Randibm
197(1)
SCRT
198(1)
StatXact
199(1)
SPSS for Windows
200(1)
SAS
200(2)
The Use of Randomization Tests with Nonrandomized Designs
202(6)
Nonrandomized Designs
204(4)
Nonrandomized Classification Variables
204(1)
Nonrandomized Phase Designs with Specific Predictions
205(3)
The Power of Randomization Tests
208(15)
The Concept of Power
208(2)
The Determinants of Power
210(7)
The Probability of Type I Error (a Level)
210(1)
Effect Size
211(1)
Sample Size
212(1)
Other Factors Influencing Power
212(1)
Control of Random Nuisance Variables
212(2)
Increased Reliability of Measuring Instruments
214(1)
Maximizing Effect Size
214(1)
Choice of Statistic
215(1)
Increased Precision of Prediction
215(1)
Estimating Power and Required Sample Size
216(1)
Power in Single-Case Designs
217(6)
Power for a Single-Case Randomized Treatment Design
218(1)
Power for an AB Design with a Randomized Intervention Point
219(2)
Power for a Phase Design with Random Assignment to Phases
221(1)
Conclusions
221(2)
Creating Your Own Randomization Tests
223(12)
Steps in Creating a Macro for a Randomization Test
224(1)
Writing Your Own Macros
225(2)
Tinkering: Changing Values Within a Macro
227(1)
Design Modifications Without Macro Changes
227(1)
Data Modification Prior to Analysis
227(7)
Downward Slope During Baseline
228(3)
Upward Slope During Baseline
231(3)
Sources of Design Variants and Associated Randomization Tests
234(1)
References 235(4)
Author Index 239(2)
Subject Index 241

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