Introduction to Statistics
Online Edition 
Primary author and editor:
David M. Lane
1
Other authors:
David Scott
1
, Mikki Hebl
1
, Rudy Guerra
1
, Dan Osherson
1
, and Heidi Zimmer
2
1
Rice University; 
2
University of Houston, Downtown Campus
Section authors specified on each section.
........................................................................................
1. Introduction
10
..............................................................................................
What Are Statistics
11
......................................................................................
Importance of Statistics
13
...........................................................................................
Descriptive Statistics
15
.............................................................................................
Inferential Statistics
20
..............................................................................................................
Variables
26
...........................................................................................................
Percentiles
29
.......................................................................................
Levels of Measurement
34
........................................................................................................
Distributions
40
..........................................................................................
Summation Notation
52
......................................................................................
Linear Transformations
55
..........................................................................................................
Logarithms
58
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...............................................................................................
Statistical Literacy
61
..............................................................................................................
Exercises
62
.......................................................................
2. Graphing Distributions
65
..........................................................................
Graphing Qualitative Variables
66
........................................................................
Graphing Quantitative Variables
75
......................................................................................
Stem and Leaf Displays
76
..........................................................................................................
Histograms
82
............................................................................................
Frequency Polygons
86
.............................................................................................................
Box Plots
92
.........................................................................................................
Bar Charts
101
......................................................................................................
Line Graphs
105
...........................................................................................................
Dot Plots
109
.............................................................................................
Statistical Literacy
113
.........................................................................................................
References
115
............................................................................................................
Exercises
116
...............................................................
3. Summarizing Distributions
123
..............................................................................
What is Central Tendency?
124
.........................................................................
Measures of Central Tendency
131
............................................................................................
Median and Mean
134
.......................................................
Additional Measures of Central Tendency
136
.....................................................
Comparing Measures of Central Tendency
140
.....................................................................................
Measures of Variability
144
.....................................................................................
Shapes of Distributions
152
2
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....................................................................
Effects of Linear Transformations
154
.........................................................................................
Variance Sum Law I
156
.............................................................................................
Statistical Literacy
158
............................................................................................................
Exercises
159
.................................................................
4. Describing Bivariate Data
164
..........................................................................
Introduction to Bivariate Data
165
....................................................................
Values of the Pearson Correlation
170
....................................................................................
Properties of Pearson's r
175
......................................................................................
Computing Pearson's r
176
........................................................................................
Variance Sum Law II
178
.............................................................................................
Statistical Literacy
180
............................................................................................................
Exercises
181
.........................................................................................
5. Probability
185
........................................................
Remarks on the Concept of “Probability”
186
..................................................................................................
Basic Concepts
189
......................................................................
Permutations and Combinations
198
........................................................................................
Binomial Distribution
203
..........................................................................................
Poisson Distribution
207
..................................................................................
Multinomial Distribution
208
............................................................................
Hypergeometric Distribution
210
.........................................................................................................
Base Rates
212
.............................................................................................
Statistical Literacy
215
............................................................................................................
Exercises
216
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................................................................................
6. Research Design
222
..............................................................................................
Scientific Method
223
....................................................................................................
Measurement
225
..................................................................................
Basics of Data Collection
231
...................................................................................................
Sampling Bias
235
.......................................................................................
Experimental Designs
238
..........................................................................................................
Causation
243
.............................................................................................
Statistical Literacy
246
.........................................................................................................
References
247
............................................................................................................
Exercises
248
........................................................................
7. Normal Distributions
249
..............................................................
Introduction to Normal Distributions
250
..................................................................
History of the Normal Distribution
253
..................................................................
Areas Under Normal Distributions
257
..........................................................................
Standard Normal Distribution
260
..........................................................
Normal Approximation to the Binomial
264
.............................................................................................
Statistical Literacy
267
............................................................................................................
Exercises
268
..............................................................................
8. Advanced Graphs
273
............................................................................
Quantile-Quantile (q-q) Plots
274
....................................................................................................
Contour Plots
290
.............................................................................................................
3D Plots
293
.............................................................................................
Statistical Literacy
298
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............................................................................................................
Exercises
299
......................................................................
9. Sampling Distributions
300
............................................................
Introduction to Sampling Distributions
301
..................................................................
Sampling Distribution of the Mean
308
......................................
Sampling Distribution of Difference Between Means
312
................................................................
Sampling Distribution of Pearson's r
317
.................
Figure 2. The sampling distribution of r for N = 12 and ρ = 0.90.
319
...............................................................................
Sampling Distribution of p
320
.............................................................................................
Statistical Literacy
323
............................................................................................................
Exercises
324
.......................................................................................
10. Estimation
329
................................................................................
Introduction to Estimation
330
..........................................................................................
Degrees of Freedom
331
............................................................................
Characteristics of Estimators
334
.........................................................................................
Confidence Intervals
337
................................................................
Introduction to Confidence Intervals
338
.....................................................................................................
t Distribution
340
....................................................................
Confidence Interval for the Mean
344
................................................................................
Difference between Means
350
........................................................................................................
Correlation
357
.........................................................................................................
Proportion
359
.............................................................................................
Statistical Literacy
361
............................................................................................................
Exercises
363
5
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...........................................................
11. Logic of Hypothesis Testing
370
......................................................................................................
Introduction
371
..........................................................................................
Significance Testing
376
..........................................................................................
Type I and II Errors
378
..............................................................................
One- and Two-Tailed Tests
380
........................................................................
Interpreting Significant Results
384
................................................................
Interpreting Non-Significant Results
386
..............................................................................
Steps in Hypothesis Testing
389
.................................................
Significance Testing and Confidence Intervals
390
.................................................................................................
Misconceptions
392
.............................................................................................
Statistical Literacy
393
.........................................................................................................
References
394
............................................................................................................
Exercises
395
.................................................................................
12. Testing Means
399
.......................................................................................
Testing a Single Mean
400
..................................
Differences between Two Means (Independent Groups)
407
........................................................
All Pairwise Comparisons Among Means
413
...................................................
Specific Comparisons (Independent Groups)
419
..........................................
Difference Between Two Means (Correlated Pairs)
429
.............................................
Specific Comparisons (Correlated Observations)
433
............................................
Pairwise Comparisons (Correlated Observations)
437
.............................................................................................
Statistical Literacy
439
.........................................................................................................
References
440
6
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............................................................................................................
Exercises
441
...............................................................................................
13. Power
448
.......................................................................................
Introduction to Power
449
.......................................................................................
Example Calculations
451
....................................................................................
Factors Affecting Power
455
.............................................................................................
Statistical Literacy
459
............................................................................................................
Exercises
460
.......................................................................................
14. Regression
462
....................................................................
Introduction to Linear Regression
463
.....................................................................
Partitioning the Sums of Squares
469
........................................................................
Standard Error of the Estimate
474
.........................................................................
Inferential Statistics for b and r
477
....................................................................................
Influential Observations
483
...........................................................................
Regression Toward the Mean
488
.................................................................
Introduction to Multiple Regression
497
.............................................................................................
Statistical Literacy
509
.........................................................................................................
References
510
............................................................................................................
Exercises
511
........................................................................
15. Analysis of Variance
517
......................................................................................................
Introduction
518
............................................................................
Analysis of Variance Designs
520
.............................................................
Between- and Within-Subjects Factors
521
..........................................................
One-Factor ANOVA (Between Subjects)
523
7
...........................................................
Multi-Factor Between-Subjects Designs
534
......................................................................................
Unequal Sample Sizes
546
..........................................................................
Tests Supplementing ANOVA
555
..................................................................................
Within-Subjects ANOVA
564
.............................................................................................
Statistical Literacy
571
............................................................................................................
Exercises
572
..............................................................................
16. Transformations
578
........................................................................................
Log Transformations
579
...................................................................................
Tukey Ladder of Powers
582
................................................................................
Box-Cox Transformations
590
.............................................................................................
Statistical Literacy
596
.........................................................................................................
References
597
............................................................................................................
Exercises
598
......................................................................................
17. Chi Square
599
....................................................................................
Chi Square Distribution
600
......................................................
One-Way Tables (Testing Goodness of Fit)
603
..........................................................................................
Contingency Tables
607
.............................................................................................
Statistical Literacy
610
.........................................................................................................
References
611
............................................................................................................
Exercises
612
....................................................................
18. Distribution-Free Tests
618
..............................................................................................................
Benefits
619
............................................................
Randomization Tests: Two Conditions
620
8
..............................................
Randomization Tests: Two or More Conditions
622
................................................
Randomization Tests: Association (Pearson's r)
624
.....................
Randomization Tests: Contingency Tables: (Fisher's Exact Test)
626
Rank Randomization: Two Conditions (Mann-Whitney U, Wilcoxon Rank 
..................................................................................................................
Sum)
628
...................
Rank Randomization: Two or More Conditions (Kruskal-Wallis)
633
......................................
Rank Randomization for Association (Spearman's ρ)
635
.............................................................................................
Statistical Literacy
638
............................................................................................................
Exercises
639
........................................................................................
19. Effect Size
641
........................................................................................................
Proportions
642
.......................................................................
Difference Between Two Means
645
....................................................................
Proportion of Variance Explained
649
.........................................................................................................
References
655
.............................................................................................
Statistical Literacy
656
............................................................................................................
Exercises
657
....................................................................................
20. Case Studies
659
...........................................................................................
21. Glossary
661
9
1. Introduction
This chapter begins by discussing what statistics are and why the study of statistics 
is important. Subsequent sections cover a variety of topics all basic to the study of 
statistics. The only theme common to all of these sections is that they cover 
concepts and ideas important for other chapters in the book.
A.What are Statistics?
B.Importance of Statistics
C.Descriptive Statistics
D.Inferential Statistics
E. Variables
F. Percentiles
G.Measurement
H.Levels of Measurement
I. Distributions
J. Summation Notation
K.Linear Transformations
L. Logarithms
M.Exercises
10
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