DISCOVERING STATISTICS USING SAS

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DISCOVERING STATISTICS USING SAS
ANDY FIELD
JEREMY MILES
2010
SAGE
753pages
This companion is designed for researchers who wish to perform linear models anal-
ysis using the definitional formulas. It can serve as a supplemental text for students
in a college-level theoretical or applied linear models course using The SAS System
(SAS) for computations. This book can also serve as the principal text for a special
topics course in a graduate program in statistics with linear models theory and appli-
cations courses as prerequisites. It may also serve as a useful reference for statistical
analysts who wish to use the SAS/IML product to work out the formulas for new
experimental methods of data analysis.
A linear models course can be taught from different approaches. Some of these
approaches are more theoretical and focus on computation and derivation of the
linear algebra formulations. Such a course might consist of theorem, proof, theorem,
proof, theorem, proof, theorem, lemma, proof, etc. Some theoretical approaches
focus on geometric interpretations of the linear model using projections. Yet other
approachesaremoreappliedandfocusonthecomputer-aidedappliedanalysisusing
high-level computational procedures such as PROC GLM, MIXED, REG, etc. in
SAS, with little time spent with the analytic formulas.
This companion illustrates the theoretical linear algebra approach to teaching
linear model analysis. This companion does not teach linear models concepts, but
demonstrates how SAS/IML can be used to evaluate numerical linear model prob-
lems. It is assumed that the reader does not have any experience using SAS/IML,
but is familiar with DATA steps and basic PROC steps in the SAS system.
All the SAS examples given in this companion are self-contained, and may be
executed as written, without additional programming. In most cases, there are other
SAS procedures that are more appropriate to use in the analysis of linear models
than the IML procedure. In many cases, the analysis will be performed in both IML
and another, more appropriate SAS procedure. This is done for the following reason:
The IML approach is directed at leaning and applying the linear models formulas.
The more “canned” procedures like REG and GLM do not allow students to see the
connection between formulas and the procedures. However, because REG and GLM
are more efficient and numerically accurate than SAS/IML in many applications of
the linear model, they will also be briefly demonstrated. The canned procedures
(such as REG and GLM) are considered the standard for analysis and are provided
to demonstrate that the results obtained using the IML procedures are the same as
those using the canned procedures. This allows students to go from written analytic
formula in say mixed models analysis to IML implementation of that same analytic
formula to high level analysis using PROC MIXED. Adding the step of PROC IML
implementation provides the missing link in the learning process.
Thetopicsselectedforthiscompanion arethetopicstheauthorfoundtobeuseful
in the academic learning of the analysis of linear models. There are many additional
topics useful in the study of linear models that were not included. However, this
should give the reader a complete treatise for a course on the subject.
Exercises have been included to aid the learner. Some exercises were developed
by withholding IML implementation steps for the reader to work through. Other
exercises are developed for perhaps repetitive application of concepts introduced in
the discussion.
The examples presented take advantage of the most recent advances in SAS/IML
and are current as of SAS version 9.2. However, most of the examples will work in
earlier versions of SAS.

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terryzhao1

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xxka917

2013-11-18 15:16:45

terryzhao1 发表于 2013-11-18 13:25
假的，别下载，请版主清理下！

如何假？
Preface
xix
How to use this book
xxiii
Acknowledgements
xxvii
Dedication
xxix
Symbols used in this book
xxx
Some maths revision
xxxii
1
Why is my evil lecturer forcing me to learn statistics?
1

1.1.
What will this chapter tell me? 1
1

1.2.
What the hell am I doing here? I don’t belong here 1
2

1.2.1. The research process 1
3

1.3.
Initial observation: finding something that needs explaining 1
3

1.4.
Generating theories and testing them 1
4

1.5.
Data collection 1: what to measure 1
7

1.5.1.
Variables 1
7

1.5.2.
Measurement error 1
10

1.5.3. Validity and reliability 1
11

1.6.
Data collection 2: how to measure 1
12

1.6.1. Correlational research methods 1
12

1.6.2. Experimental research methods 1
13

1.6.3. Randomization 1
17

1.7.
Analysing data 1
18

1.7.1. Frequency distributions 1
18

1.7.2. The centre of a distribution 1
20

1.7.3. The dispersion in a distribution 1
23

1.7.4. Using a frequency distribution to go beyond the data 1
24

1.7.5. Fitting statistical models to the data 1
26

What have I discovered about statistics? 1
28

Key terms that I’ve discovered
28

Smart Alex’s tasks
29

Further reading
29

Interesting real research
30
vi
DISCOVERING STATISTICS USING SAS
2
Everything you ever wanted to know about statistics
(well, sort of)
31

2.1.
What will this chapter tell me? 1
31

2.2.
Building statistical models 1
32

2.3.
Populations and samples 1
34

2.4.
Simple statistical models 1
35

2.4.1. The mean: a very simple statistical model 1
35

2.4.2.  Assessing the fit of the mean: sums of squares, variance and standard
deviations 1
35

2.4.3. Expressing the mean as a model 2
38

2.5.
Going beyond the data 1
40

2.5.1.
The standard error 1
40

2.5.2. Confidence intervals 2
43

2.6.
Using statistical models to test research questions 1
48

2.6.1. Test statistics 1
52

2.6.2. One- and two-tailed tests 1
54

2.6.3.
Type I and Type II errors 1
55

2.6.4. Effect sizes 2
56

2.6.5. Statistical power 2
58

What have I discovered about statistics? 1
59

Key terms that I’ve discovered
59

Smart Alex’s tasks
59

Further reading
60

Interesting real research
60
3
The SAS environment
61

3.1.
What will this chapter tell me? 1
61

3.2.
Versions of SAS 1
62

3.3.
Getting started 1
62

3.4.
Libraries 1
63

3.5.
The program editor: getting data into SAS 1
65

3.5.1.
Entering words and numbers into SAS with the  program editor 1
66

3.5.2.
Entering dates 1
69

3.6.
Entering data with Excel 1
71

3.6.1.
Saving the data 1
72

3.6.2.
Date formats 1
72

3.6.3.
Missing values 1
73

3.7.
The DATA step 1
73

3.8.
SAS formats 1
74

3.8.1.
Built in formats 1
74

3.8.2.
User-defined formats 1
76

3.9.
Variable labels 1
77

3.10. More on DATA steps 1
79

3.10.1. Calculating a new variable 1
79

3.10.2. Conditional (If ...then...) statements 1
79

3.10.3. Getting rid of variables 1
81

3.10.4. Getting rid of cases 1
81
vii
CONTENTS

3.11.
Procs for checking data 1
81

3.12.
Output and results 1
82

3.13.
Looking at data with PROC COnTEnTS 1
85

3.14. What have I discovered about statistics? 1
85

3.15.
Key terms that I’ve discovered
86

3.16.
Smart Alex’s tasks
86

3.17.
Further reading
87
4
Exploring data with graphs
88

4.1.
What will this chapter tell me? 1
88

4.2.
The art of presenting data 1
88

4.2.1. What makes a good graph? 1
89

4.2.2. Lies, damned lies, and … erm … graphs 1
91

4.3.
Charts in SAS 1
92

4.4.
Histograms: a good way to spot obvious problems 1
93

4.5.
Boxplots (box–whisker diagrams) 1
95

4.6.
Graphing means: bar charts and error bars 1
100

4.6.1. Simple bar charts for independent means 1
100

4.6.2. Clustered bar charts for independent means 1
101

4.6.3. Simple bar charts for related means 1
102

4.6.4. Clustered bar charts for ‘mixed’ designs 1
104

4.7.
Graphing relationships: the scatterplot 1
106

4.7.1. Simple scatterplot 1
106

4.7.2. Grouped scatterplot 1
108

4.7.3. Simple and grouped 3-D scatterplots 1
108

4.7.4. Matrix scatterplot 1
110

What have I discovered about statistics? 1
111

Key terms that I’ve discovered 1
112

Smart Alex’s tasks
112

Further reading
112

Interesting real research
112
5
Exploring assumptions
113

5.1.
What will this chapter tell me? 1
113

5.2.
What are assumptions? 1
114

5.3.
Assumptions of parametric data 1
114

5.4.
The assumption of normality 1
115

5.4.1.  Oh no, it’s that pesky frequency distribution again: checking
normality visually 1
116

5.4.2. Quantifying normality with numbers 1
117

5.4.3. Exploring groups of data 1
121

5.5.
Testing whether a distribution is normal 1
127

5.5.1. Doing the Kolmogorov–Smirnov test on SAS 1
127

5.5.2. Output from the explore procedure 1
128

5.5.3. Reporting the K–S test 1
130

5.6.
Testing for homogeneity of variance 1
130

5.6.1. Levene’s test 1
131

5.7.
Correcting problems in the data 2
133
viii
DISCOVERING STATISTICS USING SAS

5.7.1. Dealing with outliers 2
133

5.7.2. Dealing with non-normality and unequal variances 2
134

5.7.3. Transforming the data using SAS 2
136

5.7.4. When it all goes horribly wrong 3
140

What have I discovered about statistics? 1
142

Key terms that I’ve discovered
143

Smart Alex’s tasks
143

Further reading
143
6
Correlation
144

6.1.
What will this chapter tell me? 1
144

6.2.
Looking at relationships 1
145

6.3.
How do we measure relationships? 1
145

6.3.1. A detour into the murky world of covariance 1
145

6.3.2.
Standardization and the correlation coefficient 1
147

6.3.3.
The significance of the correlation coefficient 3
149

6.3.4. Confidence intervals for r 3
150

6.3.5. A word of warning about interpretation: causality 1
151

6.4.
Data entry for correlation analysis using SAS 1
152

6.5.
Bivariate correlation 1
152

6.5.1. General procedure for running correlations on SAS 1
152

6.5.2. Pearson’s correlation coefficient 1
154

6.5.3. Spearman’s correlation coefficient 1
157

6.5.4. Kendall’s tau (non-parametric) 1
159

6.6.
Partial correlation 2
160

6.6.1.
The theory behind part and partial correlation 2
160

6.6.2.
Partial correlation using SAS 2
162

6.6.3.
Semi-partial (or part) correlations 2
163

6.7.
Comparing correlations 3
164

6.7.1. Comparing independent rs 3
164

6.7.2. Comparing dependent rs 3
165

6.8.
Calculating the effect size 1
166

6.9.
How to report correlation coefficents 1
166

What have I discovered about statistics? 1
168

Key terms that I’ve discovered
169

Smart Alex’s tasks
169

Further reading
170

Interesting real research
170
7
Regression
171

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xxka917

2013-11-18 15:18:00

terryzhao1 发表于 2013-11-18 13:25
假的，别下载，请版主清理下！

7.1.
What will this chapter tell me? 1
171

7.2.
An introduction to regression 1
172

7.2.1. Some important information about straight lines 1
173

7.2.2.
The method of least squares 1
174

7.2.3.
Assessing the goodness of fit: sums of squares, R and R2 1
175

7.2.4. Assessing individual predictors 1
178
ix
CONTENTS

7.3.
Doing simple regression on SAS 1
179

7.4.
Interpreting a simple regression 1
180

7.4.1. Overall fit of the model 1
180

7.4.2. Model parameters 1
181

7.4.3. Using the model 1
182

7.5.
Multiple regression: the basics 2
183

7.5.1.
An example of a multiple regression model 2
184

7.5.2.
Sums of squares, R and R2 2
185

7.5.3. Methods of regression 2
186

7.6.
How accurate is my regression model? 2
188

7.6.1. Assessing the regression model I: diagnostics 2
188

7.6.2.
Assessing the regression model II: generalization 2
194

7.7.
How to do multiple regression using SAS 2
199

7.7.1.
Some things to think about before the analysis 2
199

7.7.2.
Main options 2
200

7.7.3.
Statistics 2
201

7.7.4. Saving regression diagnostics 2
202

7.8.
Interpreting multiple regression 2
203

7.8.1. Simple statistics 2
204

7.8.2.
Model parameters 2
207

7.8.3.
Comparing the models 1
211

7.8.4. Assessing the issue of multicollinearity 1
211

7.8.5. Casewise diagnostics 1
214

7.8.6.
Checking assumptions 2
216

7.9.
What if I violate an assumption? 2
221

7.10. How to report multiple regression 2
221

7.11. Categorical predictors and multiple regression 3
222

7.11.1. Dummy coding 3
222

7.11.2. SAS output for dummy variables 3
225

What have I discovered about statistics? 1
228

Key terms that I’ve discovered
229

Smart Alex’s tasks
229

Further reading
230

Interesting real research
230
8
Logistic regression
231

8.1.
What will this chapter tell me? 1
231

8.2.
Background to logistic regression 1
232

8.3.
What are the principles behind logistic regression? 3
232

8.3.1.
Assessing the model: the log-likelihood statistic 3
234

8.3.2.
Assessing the model: R, R2 and c 3
235

8.3.3.
Assessing the contribution of predictors: the Wald statistic 2
237

8.3.4. The odds ratio 3
238

8.4.
Assumptions and things that can go wrong 4
239

8.4.1. Assumptions 2
239

8.4.2. Incomplete information from the predictors 4
240

8.4.3. Complete separation 4
240

8.5.
Binary logistic regression: an example that will make you feel eel 2
242
x
DISCOVERING STATISTICS USING SAS

8.5.1.
The main analysis 2
243

8.5.2. Obtaining predicted probabilities and residuals 2
244

8.5.3. Final syntax
245

8.6.
Interpreting logistic regression 2
245

8.6.1. The initial output 2
245

8.6.2.
Intervention
246

8.6.3. Listing predicted probabilities 2
250

8.6.4. Interpreting residuals 2
251

8.6.5. Calculating the effect size 2
253

8.7.
How to report logistic regression 2
253

8.8.
Testing assumptions: another example 2
254

8.8.1. Testing for linearity of the logit 3
255

8.8.2. Testing the assumption of linearity of the logit
256

8.9.
Predicting several categories: multinomial logistic regression 3
258

8.9.1.
Running multinomial logistic regression in SAS 3
259

8.9.2. The final touches 3
260

8.9.3. Interpreting the multinomial logistic regression output 3
260

8.9.4. Reporting the results 3
264

What have I discovered about statistics? 1
265

Key terms that I’ve discovered
265

Smart Alex’s tasks
265

Further reading
267

Interesting real research
267
9
Comparing two means
268

9.1.
What will this chapter tell me? 1
268

9.2.
Looking at differences 1
269

9.3.
The t-test 1
269

9.3.1. Two example data sets 1
270

9.3.2. Rationale for the t-test 1
271

9.3.3. Assumptions of the t-test 1
273

9.4.
The dependent t-test 1
273

9.4.1. Sampling distributions and the standard error 1
274

9.4.2. The dependent t-test equation explained 1
274

9.4.3. The dependent t-test and the assumption of normality 1
276

9.4.4. Dependent t-tests using SAS 1
276

9.4.5. Output from the dependent t-test 1
277

9.4.6. Calculating the effect size 2
278

9.4.7. Reporting the dependent t-test 1
279

9.5.
The independent t-test 1
280

9.5.1. The independent t-test equation explained 1
280

9.5.2. The independent t-test using SAS 1
284

9.5.3. Output from the independent t-test 1
285

9.5.4. Calculating the effect size 2
286

9.5.5. Reporting the independent t-test 1
287

9.6.
Between groups or repeated measures? 1
288

9.7.
The t-test as a general linear model 2
288

9.8.
What if my data are not normally distributed? 2
290

What have I discovered about statistics? 1
291

Key terms that I’ve discovered
291
xi
CONTENTS

Smart Alex’s task
291

Further reading
292

Interesting real research
292
10 Comparing several means: ANOVA (GLM 1)
293

10.1. What will this chapter tell me? 1
293

10.2. The theory behind AnOVA 2
294

10.2.1.
Inflated error rates 2
294

10.2.2.
Interpreting f 2
295

10.2.3.
AnOVA as regression 2
295

10.2.4.
Logic of the f-ratio 2
300

10.2.5.
Total sum of squares (SST) 2
302

10.2.6.
Model sum of squares (SSM) 2
302

10.2.7.
Residual sum of squares (SSR) 2
303

10.2.8.
Mean squares 2
304

10.2.9.
The f-ratio 2
304

10.2.10. Assumptions of AnOVA 3
305

10.2.11. Planned contrasts 2
306

10.2.12. Post hoc procedures 2
317

10.3. Running one-way AnOVA on SAS 2
319

10.3.1.
Planned comparisons using SAS 2
320

10.3.2.
Post hoc tests in SAS 2
322

10.3.3.
Options 2
322

10.3.4.
ODS graphics 2
323

10.4. Output from one-way AnOVA 2
324

10.4.1.
Output for the main analysis 2
324

10.4.2.
Output for trends and planned comparisons 2
327

10.4.3.
Output for post hoc tests 2
328

10.4.4.
Graph output for one-way AnOVA using PROC GLM 2
330

10.5. Calculating the effect size 2
331

10.6. Reporting results from one-way independent AnOVA 2
333

10.7. Violations of assumptions in one-way independent AnOVA 2
333

What have I discovered about statistics? 1
334

Key terms that I’ve discovered
334

Smart Alex’s tasks
335

Further reading
336

Interesting real research
336
11 Analysis of covariance, ANCOVA (GLM 2)
337

11.1. What will this chapter tell me? 2
337

11.2. What is AnCOVA? 2
338

11.3. Assumptions and issues in AnCOVA 3
339

11.3.1.
Independence of the covariate and treatment effect 3
339

11.3.2.
Homogeneity of regression slopes 3
341

11.4. Conducting AnCOVA on SAS 2
341

11.4.1.
Inputting data 1
341

11.4.2.  Initial considerations: testing the independence of the independent
variable and covariate 2
343

11.4.3.
The main analysis 2
344
xii
DISCOVERING STATISTICS USING SAS

11.4.4.
Contrasts and other options 2
344

11.5. Interpreting the output from AnCOVA 2
345

11.5.1.
What happens when the covariate is excluded? 2
345

11.5.2.
The main analysis 2
346

11.5.3.
Contrasts 2
348

11.5.4.
Interpreting the covariate 2
349

11.6. AnCOVA run as a multiple regression 2
351

11.7. Testing the assumption of homogeneity of regression slopes 3
351

11.8. Calculating the effect size 2
353

11.9.
Reporting results 2
355

11.10. What to do when assumptions are violated in AnCOVA 3
356

What have I discovered about statistics? 2
356

Key terms that I’ve discovered
357

Smart Alex’s tasks
357

Further reading
358

Interesting real research
358
12 Factorial ANOVA (GLM 3)
359

12.1. What will this chapter tell me? 2
359

12.2. Theory of factorial AnOVA (between groups) 2
360

12.2.1.
Factorial designs 2
360

12.2.2.
An example with two independent variables 2
361

12.2.3.
Total sums of squares (SST) 2
362

12.2.4.
The model sum of squares (SSM) 2
364

12.2.5.
The residual sum of squares (SSR) 2
366

12.2.6.
The f-ratios 2
367

12.3. Factorial AnOVA using SAS 2
368

12.3.1.
Exploring the data: PROC MEAnS 2
368

12.3.2.
Contrasts and estimates 2
369

12.3.3.
Post hoc tests 2
370

12.3.4.
Simple effects 2
371

12.3.5.
ODS graphics 2
371

12.4. Output from factorial AnOVA 2
372

12.4.1.
The main AnOVA tables 2
372

12.4.2.
Contrasts
375

12.4.3.
Least squares means and post hoc analysis 2
375

12.4.4.
Simple effects
377

12.4.5.
Summary
378

12.5. Interpreting interaction graphs 2
379

12.6. Calculating effect sizes 3
382

12.7. Reporting the results of two-way AnOVA 2
384

12.8. Factorial AnOVA as regression 3
384

12.9. What to do when assumptions are violated in factorial AnOVA 3
388

What have I discovered about statistics? 2
390

Key terms that I’ve discovered
390

Smart Alex’s tasks
390

Further reading
391

Interesting real research
392
xiii
CONTENTS
13 Repeated-measures designs (GLM 4)
393

13.1. What will this chapter tell me? 2
393

13.2. Introduction to repeated measures designs 2
394

13.2.1.
The assumption of sphericity 2
395

13.2.2.
How is sphericity measured? 2
395

13.2.3.
Assessing the severity of departures from sphericity 2
396

13.2.4.
What is the effect of violating the assumption of sphericity? 3
396

13.2.5.
What do you do if you violate sphericity? 2
397

13.3. Theory of one-way repeated measures AnOVA 2
398

13.3.1.
The total sum of squares (SST) 2
400

13.3.2.
The within-participant sum of squares (SSW) 2
401

13.3.3.
The model sum of squares (SSM) 2
402

13.3.4.
The residual sum of squares (SSR) 2
403

13.3.5.
The mean squares 2
403

13.3.6.
The f-ratio 2
403

13.3.7.
The between-participant sum of squares 2
404

13.4. One-way repeated-measures AnOVA using SAS 2
404

13.4.1.
The main analysis 2
404

13.4.2.
Defining contrasts for repeated measures 2
405

13.5. Output for one-way repeated-measures AnOVA 2
407

13.5.1.
Model description
407

13.5.2.
Assessing and correcting for sphericity: Mauchly’s test 2
408

13.5.3.
The main AnOVA 2
409

13.5.4.
Contrasts 2
411

13.6. Effect sizes for repeated-measures AnOVA 3
414

13.7. Reporting one-way repeated-measures AnOVA 2
415

13.8. Repeated-measures with several independent variables 2
416

13.8.1.
Calculating and comparing means 2
418

13.8.2.
The main analysis 2
419

13.9. Output for factorial repeated-measures AnOVA 2
421

13.9.1.
Descriptive statistics 2
421

13.9.2.
Main analysis 2
422

13.9.3.
The effect of drink 2
424

13.9.4.
The effect of imagery 2
424

13.9.5.
The interaction effect (drink × imagery) 2
424

13.9.6.
Contrasts for repeated-measures variables 2
426

13.10. Effect sizes for factorial repeated-measures AnOVA 3
430

13.11. Reporting the results from factorial repeated-measures AnOVA 2
431

13.12. What to do when assumptions are violated in repeated-measures AnOVA 3 432

What have I discovered about statistics? 2
432

Key terms that I’ve discovered
433

Smart Alex’s tasks
433

Further reading
434

Interesting real research
435

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xxka917

2013-11-18 15:18:55

14 Mixed design ANOVA (GLM 5)
436

14.1. What will this chapter tell me? 1
436

14.2. Mixed designs 2
437
xiv
DISCOVERING STATISTICS USING SAS

14.3. What do men and women look for in a partner? 2
438

14.4. Mixed AnOVA on SAS 2
438

14.5. Output for mixed factorial AnOVA: main analysis 3
441

14.5.1.
The main effect of gender 2
443

14.5.2.
The main effect of looks 2
445

14.5.3.
The main effect of charisma 2
447

14.5.4.
The interaction between gender and looks 2
447

14.5.5.
The interaction between gender and charisma 2
449

14.5.6.
The interaction between attractiveness and charisma 2
550

14.5.7.
The interaction between looks, charisma and gender 3
453

14.5.8.
Conclusions 3
457

14.6. Calculating effect sizes 3
458

14.7. Reporting the results of mixed AnOVA 2
459

14.8. What to do when assumptions are violated in mixed AnOVA 3
462

What have I discovered about statistics? 2
462

Key terms that I’ve discovered
463

Smart Alex’s tasks
463

Further reading
464

Interesting real research
464
15 Non-parametric tests
465

15.1. What will this chapter tell me? 1
465

15.2. When to use non-parametric tests 1
466

15.3.  Comparing two independent conditions: the Wilcoxon rank-sum test and
Mann–Whitney test 1
466

15.3.1.
Theory 2
468

15.3.2.
Inputting data and provisional analysis 1
471

15.3.3.
Running the analysis 1
473

15.3.4.
Output from the Wilcoxon two-sample test 1
474

15.3.5.
Calculating an effect size 2
476

15.3.6.
Writing the results 1
476

15.4. Comparing two related conditions: the Wilcoxon signed-rank test 1
478

15.4.1.
Theory of the Wilcoxon signed-rank test 2
478

15.4.2.
Running the analysis 1
481

15.4.3.
Output for the alcohol group 1
481

15.4.4.
Output for the ecstasy group 1
482

15.4.5.
Writing the results 1
482

15.5.
Differences between several independent groups: the Kruskal–Wallis test 1
483

15.5.1.
Theory of the Kruskal–Wallis test 2
484

15.5.2.
Inputting data and provisional analysis 1
486

15.5.3.
Doing the Kruskal–Wallis test on SAS 1
487

15.5.4.
Output from the Kruskal–Wallis test 1
487

15.5.5.
Post hoc tests for the Kruskal–Wallis test 2
488

15.5.6.
Writing and interpreting the results 1
492

15.6. Differences between several related groups: Friedman’s AnOVA 1
493

15.6.1.
Theory of Friedman’s AnOVA 2
494

15.6.2.
Inputting data and provisional analysis 1
495

15.6.3.
Doing Friedman’s AnOVA on SAS 1
496
xv
CONTENTS

15.6.4.
Output from Friedman’s AnOVA 1
497

15.6.5.
Post hoc tests for Friedman’s AnOVA 2
498

15.6.6.
Writing and interpreting the results 1
500

What have I discovered about statistics? 1
500

Key terms that I’ve discovered
501

Smart Alex’s tasks
501

Further reading
502

Interesting real research
502
16 Multivariate analysis of variance (MANOVA)
503

16.1. What will this chapter tell me? 2
503

16.2. When to use MAnOVA 2
504

16.3. Introduction: similarities and differences to AnOVA 2
504

16.3.1.
Words of warning 2
506

16.3.2.
The example for this chapter 2
506

16.4. Theory of MAnOVA 3
507

16.4.1.
Introduction to matrices 3
507

16.4.2.
Some important matrices and their functions 3
509

16.4.3.
Calculating MAnOVA by hand: a worked example 3
510

16.4.4.
Principle of the MAnOVA test statistic 4
517

16.5. Practical issues when conducting MAnOVA 3
522

16.5.1.
Assumptions and how to check them 3
522

16.5.2.
Choosing a test statistic 3
523

16.5.3.
Follow-up analysis 3
524

16.6. MAnOVA on SAS 2
524

16.6.1.
The main analysis 2
525

16.6.2.
Multiple comparisons in MAnOVA 2
525

16.7. Output from MAnOVA 3
526

16.7.1.
Preliminary analysis and testing assumptions 3
526

16.7.2.
MAnOVA test statistics 3
527

16.7.3.
Univariate test statistics 2
528

16.7.4.
SSCP matrices 3
529

16.7.5.
Contrasts 3
530

16.8. Box’s test 3

531

16.9. Reporting results from MAnOVA 2
532

16.10. Following up MAnOVA with discriminant function analysis 3
533

16.11. Output from the discriminant function analysis 4
533

16.12. Reporting results from discriminant function analysis 2
536

16.13. Some final remarks 4
536

16.13.1. The final interpretation 4
536

16.13.2. Univariate AnOVA or discriminant function analysis?
537

16.14. What to do when assumptions are violated in MAnOVA 3
537

What have I discovered about statistics? 2
539

Key terms that I’ve discovered
539

Smart Alex’s tasks
540

Further reading
540

Interesting real research
540
xvi
DISCOVERING STATISTICS USING SAS
17 Exploratory factor analysis
541

17.1. What will this chapter tell me? 1
541

17.2. When to use factor analysis 2
542

17.3. Factors 2

542

17.3.1.
Graphical representation of factors 2
544

17.3.2.
Mathematical representation of factors 2
545

17.3.3.
Factor scores 2
547

17.4. Discovering factors 2
548

17.4.1.
Choosing a method 2
548

17.4.2.
Communality 2
549

17.4.3.
Factor analysis vs. principal component analysis 2
550

17.4.4.
Theory behind principal component analysis 3
551

17.4.5.
Factor extraction: eigenvalues and the scree plot 2
552

17.4.6.
Improving interpretation: factor rotation 3
554

17.5. Research example 2
557

17.5.1.
Before you begin 2
559

17.6. Running the analysis 2
562

17.6.1.
Factor extraction on SAS 2
562

17.6.2.
Rotation 2
563

17.6.3.
Saving factor scores
563

17.7. Interpreting output from SAS
564

17.7.1.
Preliminary analysis 2
566

17.7.2.
Factor extraction 2
567

17.7.3.
Factor rotation 2
573

17.7.4.
Factor scores 2
578

17.7.5.
Summary 2
579

17.8. How to report factor analysis 1
579

17.9. Reliability analysis 2
582

17.9.1.
Measures of reliability 3
582

17.9.2.
Interpreting Cronbach’s α (some cautionary tales) 2
583

17.9.3.
Reliability analysis on SAS 2
585

17.9.4.
Interpreting the output 2
585

17.10. How to report reliability analysis 2
589

What have I discovered about statistics? 2
590

Key terms that I’ve discovered
590

Smart Alex’s tasks
591

Further reading
593

Interesting real research
593
18 Categorical data
594

18.1. What will this chapter tell me? 1
594

18.2. Analysing categorical data 1
595

18.3. Theory of analysing categorical data 1
595

18.3.1.
Pearson’s chi-square test 1
596

18.3.2.
Fisher’s exact test 1
598

18.3.3.
The likelihood ratio 2
598

18.3.4.
Yates’s correction 2
599
xvii
CONTENTS

18.4. Assumptions of the chi-square test 1
599

18.5. Doing chi-square on SAS 1
600

18.5.1.
Entering data: raw scores 1
600

18.5.2.
Entering data: weight cases 1
600

18.5.3.
Running the analysis 1
601

18.5.4.
Output for the chi-square test 1
601

18.5.5.  Breaking down a significant chi-square test with standardized residuals 2
604

18.5.6.
Calculating an effect size 2
606

18.5.7.
Reporting the results of chi-square 1
607

18.6. Several categorical variables: loglinear analysis 3
609

18.6.1.
Chi-square as regression 4
609

18.6.2.
Loglinear analysis 3
615

18.7. Assumptions in loglinear analysis 2
617

18.8. Loglinear analysis using SAS 2
617

18.8.1.
Initial considerations 2
617

18.8.2.
The loglinear analysis 2
619

18.9. Output from loglinear analysis 3
620

18.10. Following up loglinear analysis 2
624

18.11. Effect sizes in loglinear analysis 2
625

18.12. Reporting the results of loglinear analysis 2
626

What have I discovered about statistics? 1
626

Key terms that I’ve discovered
627

Smart Alex’s tasks
627

Further reading
628

Interesting real research
628
19 Multilevel linear models
629

19.1. What will this chapter tell me? 1
629

19.2. Hierarchical data 2
630

19.2.1.
The intraclass correlation 2
632

19.2.2.
Benefits of multilevel models 2
633

19.3. Theory of multilevel linear models 3
634

19.3.1.
An example 2
634

19.3.2.
Fixed and random coefficients 3
636

19.4. The multilevel model 4
638

19.4.1.
Assessing the fit and comparing multilevel models 4
641

19.4.2.
Types of covariance structures 4
641

19.5. Some practical issues 3
643

19.5.1.
Assumptions 3
643

19.5.2.
Sample size and power 3
644

19.5.3.
Centring variables 4
644

19.6. Multilevel modelling on SAS 4
645

19.6.1.
Entering the data 2
646

19.6.2.
Ignoring the data structure: AnOVA 2
646

19.6.3.
Ignoring the data structure: AnCOVA 2
648

19.6.4.
Factoring in the data structure: random intercepts 3
650

19.6.5.
Factoring in the data structure: random intercepts and slopes 4
652

19.6.6.
Adding an interaction to the model 4
659
xviii
DISCOVERING STATISTICS USING SAS

19.7. Growth models 4
662

19.7.1.
Growth curves (polynomials) 4
662

19.7.2.
An example: the honeymoon period 2
663

19.7.3.
Restructuring the data 3
664

19.7.4.
Running a growth model on SAS 4
667

19.7.5.
Further analysis 4
670

19.8. How to report a multilevel model 3
672

What have I discovered about statistics? 2
673

Key terms that I’ve discovered
674

Smart Alex’s tasks
674

Further reading
674

Interesting real research
675
Epilogue: Life after Discovering Statistics
676
Glossary
679
Appendix
695

A.1.
Table of the standard normal distribution
695

A.2.
Critical values of the t-distribution
701

A.3.
Critical values of the f-distribution
702

A.4.
Critical values of the chi-square distribution
706
References
707
Index
713

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terryzhao1

2013-11-18 15:40:25

我下不了

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terryzhao1

2013-11-18 15:41:52

花币买了，就是下不了，我擦，是不是版主要过来参与下，不然我币白花了

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terryzhao1

2013-11-18 16:51:30

能发份到我qq邮箱吗，我已经购买过了！请查看消息

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xxka917

2013-11-18 17:23:25

terryzhao1 发表于 2013-11-18 13:25
假的，别下载，请版主清理下！

1. 下载不了请与网站联系
2.如果所有人都下载不了，该帖子肯定不会被版主审核通过（版主应该先下载过）
3.楼主没有骗人
4.已发你邮箱

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terryzhao1

2013-11-18 17:31:47

谢谢！

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tyui11

2014-3-24 22:24:32

good book

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tamtam7010

2014-4-9 00:19:21

downloaded to learn, thanks for your sharing.

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wh7064rg

2015-3-29 01:10:26

谢谢分享

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ydbin

2015-4-4 17:51:13

太有帮助了谢谢楼主

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