# Visual Statistics: A Conceptual Primer

ISBN-10:
0205283179
ISBN-13:
9780205283170
Pub. Date:
11/20/1998
Publisher:
Allyn & Bacon, Inc.

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## Overview

Visual Statistics: A Conceptual Primer

Statistics can be seen by many as a difficult or intimidating subject. Yet, those same individuals that are intimidated by the subject often need to use statistics. This book serves to make sense out of seemingly complex concepts and to offer an easy, visual way to understanding and using statistics. This book is written in a clear, easy-to-read manner with the intention of making statistics simple. Through visual diagrams of the essential concepts used in statistical research, the book provides concise, short explanations designed to retain the readers' interest. The intelligent use of cartoons, figures, graphs, and charts make otherwise foreboding concepts easily understandable. Topics include correlation, regression, probability and measurements, amongst others. Statistics teachers, and anyone needing to use statistics in their work.

## Product Details

ISBN-13: 9780205283170 Allyn & Bacon, Inc. 11/20/1998 368 8.27(w) x 10.85(h) x 0.69(d)

PART I Sampling 1(48)
 SET 1 Samples, Sampling, and Sampling Distributions
1(48)
 Assumption
2(2)
 Figure 1.1 Are These Assumptions Warranted?
3(1)
 Population/Sample
4(2)
 Figure 1.2 Populations and Samples
5(1)
 Generalizability
6(2)
 Figure 1.3 Generalizing from a Sample
7(1)
 Unit
8(2)
 Figure 1.4 Units
9(1)
 Sampling Frame
10(2)
 Figure 1.5 A Sampling Frame
11(1)
 Variable
12(2)
 Figure 1.6 What Are the Variables Here?
13(1)
 Constant
14(2)
 Figure 1.7 A Constant in Social Security Numbers
15(1)
 Statistic/Parameter
16(2)
 Figure 1.8 Statistics and Parameters
17(1)
 Margin of Error
18(2)
 Figure 1.9 Margin of Error
19(1)
 Descriptive Statistics
20(2)
 Table 1.1 Frequency Distribution of Scores on a Midterm Exam in Medieval History
21(1)
 Figure 1.10 Pie Chart Showing Different Breakfast Preferences Expressed in Percents
21(1)
 Inferential Statistics
22(2)
 Figure 1.11 What Percent Approve?
23(1)
 Representative Sample
24(2)
 Figure 1.12 Representative Versus Nonrepresentative Samples
25(1)
 Random Sampling
26(2)
 Figure 1.13 Selecting a Random Sample
27(1)
 Table of Random Numbers
28(2)
 Table 1.2 A Table of Random Numbers
28(1)
 Figure 1.14 How to Use a Table of Random Numbers
29(1)
 Cluster Random Sample
30(2)
 Figure 1.15 Cluster Sampling
31(1)
 Stratified Random Sample
32(2)
 Figure 1.16 Stratified Sampling
33(1)
 Convenience Sample
34(2)
 Figure 1.17 A Convenience Sample
35(1)
 Purposive Sample
36(2)
 Figure 1.18 Purposive Sampling
37(1)
 Systematic Sample
38(2)
 Figure 1.19 Systematic Sampling
39(1)
 Multistage Sampling
40(2)
 Figure 1.20 Multistage Sampling
41(1)
 Sampling Distribution
42(2)
 Figure 1.21 A Sampling Distribution (of Means)
43(1)
 Sampling Error
44(2)
 Figure 1.22 Sampling Error
45(1)
 Sampling With and Without Replacement
46(3)
 Figure 1.23 Sampling with and without Replacement
47(2)
PART II Organizing and Summarizing Data 49(96)
 SET 2 Tables, Graphs, and Distributions
49(30)
 Frequency Distribution
50(2)
 Table 2.1 A Frequency Distribution Table with Ungrouped Data
51(1)
 Grouped Frequency Distribution
52(2)
 Table 2.2 A Grouped Frequency Distribution Table
53(1)
 Cumulative Frequency Distribution
54(2)
 Table 2.3 Number of Aggressive Acts Reported for a Group of 73 Boys at a Youth Guidance Center over a Three-Month Period
55(1)
 Percentile/Percentile Rank
56(2)
 Table 2.4 Hypothetical Example of Raw Scores and Percentile Ranks
57(1)
 Pie Chart
58(2)
 Figure 2.1 A Pie Chart Showing a City's Sources of Revenue
59(1)
 Dot Chart
60(2)
 Figure 2.2 A Dot Chart Showing Enrollment Percentages at a University
61(1)
 Bar Graph
62(2)
 Figure 2.3 Bar Graphs
63(1)
 Histogram
64(2)
 Figure 2.4 A Histogram Showing the Distribution of Ages of Members of a Drama Club
65(1)
 Frequency Polygon
66(2)
 Figure 2.5 A Frequency Polygon Showing the Distribution of Ages of 40 Children from Broken Homes
67(1)
 Stemplot
68(2)
 Figure 2.6 Two Stemplots Showing the Home Runs Hit by Babe Ruth and Roger Maris During Their Major League Careers
69(1)
 Time Series
70(2)
 Figure 2.7 Time Series Plot: Weekly Absences of a Class of Third Graders
71(1)
 Normal Distribution
72(2)
 Figure 2.8 Normal Distributions
73(1)
 Skewed Distribution
74(2)
 Table 2.5 Heights of Fourth Grade Boys
75(1)
 Table 2.6 Heights of Boys Baseball Team
75(1)
 Kurtosis
76(3)
 Figure 2.9 Examples of Kurtosis
77(2)
 SET 3 Centers and Spreads (Summary Measures)
79(26)
 Mean
80(2)
 Table 3.1 Distribution of 10 Scores on a Midterm
81(1)
 Figure 3.1 The Mean Height and Weight of a Group of Six Businesspeople
81(1)
 Algorithm
82(2)
 Figure 3.2 How Many Siblings Do You Have?
83(1)
 Weighted Mean
84(2)
 Table 3.2 Mean Salaries of Four Groups of People
84(1)
 Figure 3.3 When a Weighted Mean Is Called For
85(1)
 Median
86(2)
 Table 3.3 Median Age of a Group of 18 Boys and Girls in an Elementary School
87(2)
 Mode
88(2)
 Figure 3.4 The Mode
89(1)
 Range
90(2)
 Table 3.4 Typical Temperatures During the Month of August in Omaha, Nebraska
91(1)
 Interquartile Range (IQR)
92(2)
 Figure 3.5 Scores for 20 Students on a Statistics Quiz
93(1)
 Boxplot
94(2)
 Figure 3.6 Boxplot Comparing the Number of Facelifts Performed by 15 Male and 15 Female Physicians
95(1)
 Variance
96(2)
 Table 3.5 A Comparison of the Average Number of Free Throws Made Per Game Early and Late in the Season by Five Players on a High School Basketball Team
97(1)
 Standard Deviation
98(2)
 Figure 3.7 Standard Deviations for Boys' and Mens' Basketball Teams
99(1)
 Standard Score
100(2)
 Table 3.6 Amy's Midterm Exam Scores in Three Subjects
101(1)
 Figure 3.8 Standard Scores
101(1)
 Standardized Normal Distribution
102(3)
 Figure 3.9 A Standardized Normal Distribution
103(2)
 SET 4 Measurement
105(40)
 Data
106(2)
 Figure 4.1 Weights as Data
107(1)
 Measurement
108(2)
 Figure 4.2 Examples of Measurement
109(1)
 Percentage/Proportion
110(2)
 Table 4.1 Proportion/Percentage of Different Kinds of Majors in a University Graduating Class
111(1)
 Rates Versus Counts
112(2)
 Figure 4.3 Rate versus Count
113(1)
 Ratio
114(2)
 Figure 4.4 Ratio of Vans to Cars in a City Parking Lot
115(1)
 Likert Scale
116(2)
 Figure 4.5 Examples of Items from a Likert Scale Measuring Attitude toward teacher Empowerment
117(1)
 Index Number
118(2)
 Table 4.2 Yearly Increase in Costs of Attending a Small Private College
119(1)
 Figure 4.6 Can You Believe the Price of Bread?
119(1)
 Bias
120(2)
 Figure 4.7 Examples of Bias
121(1)
 Halo Effect
122(2)
 Figure 4.8 A Halo Effect
123(1)
 Ceiling Effect
124(2)
 Figure 4.9 The Ceiling Effect
125(1)
 Reliability
126(2)
 Figure 4.10 Reliability and Validity
127(1)
 Reliability Coefficient
128(2)
 Figure 4.11 Reliability of a Measurement
129(1)
 Standard Error of Measurement
130(2)
 Figure 4.12 Standard Error of Measurement
131(1)
 Validity
132(2)
 Table 4.3 Valid versus Invalid Measurement
133(1)
 Norm
134(2)
 Figure 4.13 What's The Norm?
135(1)
 Nominal Scale/Level of Measurement
136(2)
 Figure 4.14 Nominal Scales
137(1)
 Ordinal Scale/Level of Measurement
138(2)
 Figure 4.15 An Ordinal Scale: The Winner of a Horse Race
139(1)
 Interval Scale/Level of Measurement
140(2)
 Figure 4.16 Interval Scales
141(1)
 Ratio Scale/Level of Measurement
142(3)
 Figure 4.17 A Ratio Scale
143(2)
PART III Experimentation 145(26)
 SET 5 Experiments
145(26)
 Experiment
146(2)
 Figure 5.1 The Physician's Health Study
147(1)
 Dependent/Independent Variables
148(2)
 Figure 5.2 Mathematical Achievement Shown as a Dependent Variable
149(1)
 Treatment
150(2)
 Figure 5.3 The Physician's Health Study Revisited
151(1)
 Control Group
152(2)
 Figure 5.4 How Fast Do Cars Go on One-Way Compared to Two-Way Streets?
153(1)
 Placebo
154(2)
 Figure 5.5 A Placebo
155(1)
 Extraneous Variable
156(1)
 Figure 5.6 Extraneous Variables
157(1)
 Extraneous Variables
157(1)
 Confounding
158(2)
 Figure 5.7 Confounding
159(1)
 Double-Blind Procedure
160(2)
 Figure 5.8 A Double-Blind Experiment
161(1)
 Matched Pairs Design
162(2)
 Figure 5.9 A Matched Pairs Design
163(1)
 Block Design
164(2)
 Figure 5.10 A Block Design
165(1)
 Observational Study
166(2)
 Figure 5.11 Some Observational Studies
167(1)
 Hawthorne Effect
168(3)
 Figure 5.12 The Hawthorne Effect
169(2)
PART IV Looking for Relationships in Data 171(72)
 SET 6 Relationships between Quantitative Variables: Correlation
171(38)
 Quantitative Variable
172(2)
 Figure 6.1 Quantitative Variables
173(1)
 Continuous Variable
174(2)
 Figure 6.2 The Measurement of Continuous Variables
175(1)
 Positive Correlation
176(2)
 Figure 6.3 A Positive Correlation between Height and Weight Figure 6.4 Cancer Rates Plotted against Fat in the Diet: A Positive Correlation
177(1)
 Negative Correlation
178(2)
 Figure 6.5 A Very Strong Negative Correlation
179(1)
 Figure 6.6 A Perfect Negative Correlation
179(1)
 X-Y Axes
180(2)
 Figure 6.7 x-y Axes
181(1)
 Scatterplot
182(2)
 Figure 6.8 Scatterplot When r = .37
183(1)
 Outlier
184(2)
 Table 6.1 Scores on a Drivers' Test
185(1)
 Figure 6.9 Relationship between Sales and Profit in a Hypothetical Group of Companies
185(1)
 Correlation Coefficient
186(2)
 Figure 6.10 Scatterplots of Correlations of Varying Strength
187(1)
 Biserial/Point Biserial Correlation
188(2)
 Table 6.2 Scores of 14 Students on a Civics Test
189(1)
 Figure 6.11 Relationship between Total Score on a Test and Score on One Particular Item
189(1)
 Spearman Rank-Order Correlation Coefficient
190(2)
 Table 6.3 Swimsuit and Musical Talent Ratings
191(1)
 Restricted Range Effect
192(2)
 Figure 6.12 Restricted Range Effect
193(1)
 Correlation Ratio
194(2)
 Figure 6.13 A Curvilinear Relationship
195(1)
 Multiple Correlation
196(2)
 Figure 6.14 Multiple Correlation
197(1)
 Coefficient of Determination
198(2)
 Figure 6.15 Coefficients of Determination
199(1)
 Factor Analysis
200(2)
 Table 6.4 Variables Related to Male Marital Satisfaction at Age 55
201(1)
 Path Analysis
202(2)
 Figure 6.16 A Path Analysis
203(1)
 Partial Correlation
204(2)
 Figure 6.17 Eliminating the Effects of Age through Partial Correlation
205(1)
 Correlation versus Causation
206(3)
 Table 6.5 Pairs of Numbers Selected from a Table of Random Numbers: I
207(1)
 Table 6.6 Pairs of Numbers Selected from a Table of Random Numbers: II
207(1)
 Table 6.7 Pairs of Numbers Selected from a Table of Random Numbers: III
207(2)
 SET 7 Relationships between Quantitative Variables: Regression
209(18)
 Regression
210(2)
 Table 7.1 Heights and Weights of a Group of 14 Bicyclists
210(1)
 Figure 7.1 Predicting the Size of Carrots Based on the Amount of Fertilizer Used Weekly
211(1)
 Regression Equation
212(2)
 Figure 7.2 Using a Regression Equation to Predict Weight of a Truck and Its Load
213(1)
 Beta Weights/Beta Coefficient
214(2)
 Figure 7.3 Beta Weights
215(1)
 Regression Line
216(2)
 Table 7.2 Relationship between Number of Library Books Checked Out by a Group of 25 Students and Their History Test Scores
216(1)
 Figure 7.4 A Regression Line
217(1)
 Slope/Intercept
218(2)
 Figure 7.5 Positive and Negative Slope
219(1)
 Figure 7.6 The y-Intercept
219(1)
 Least Squares Criterion (or Principle)
220(2)
 Table 7.3 Using the Mean as the Least Squares Criterion
220(1)
 Figure 7.7 Using the Least Squares Criterion
221(1)
 Standard Error of Estimate
222(2)
 Figure 7.8 Predicting Productivity
223(1)
 Discriminant Function Analysis
224(3)
 Figure 7.9 Discriminant Function Analysis
225(2)
 SET 8 Relationships between Categorical Variables
227(16)
 Categorical Variable
228(2)
 Figure 8.1 Categorical Variables
229(1)
 Numbers and Categorical Variables
230(2)
 Figure 8.2 Counting Categorical Variables
231(1)
 Crossbreak Table
232(2)
 Table 8.1 Relationship between Gender and Political Party
233(1)
 Table 8.2 Relationship between Type of Illness and Geographic Area of Occurrence
233(1)
 Table 8.3 Relationship between Attitude toward Welfare and a Belief in Human Goodness
233(1)
 Degrees of Freedom
234(2)
 Table 8.4 Degrees of Freedom in a 3 x 2 Table
235(1)
 Figure 8.3 Degrees of Freedom
235(1)
 Chi-Square Test
236(2)
 Table 8.5 Relationship between Gender of Viewer and Type of Television Show Preferred
237(1)
 Contingency Coefficient: C
238(2)
 Table 8.6 Relationship Between Level of Service Provided and Type of Retail Store
239(1)
240(3)
 Table 8.7 Survival Rates for Two Drugs at Two Hospitals
241(1)
 Table 8.8 Risk Compared for Old and New Drugs
241(1)
 Table 8.9 Estimating Overall Risk Reduction from Using Two Different Drugs for Prostate Cancer
241(2)
PART V Drawing Conclusions from Data 243(110)
 SET 9 Probability
243(30)
 Probability
244(2)
 Figure 9.1 What's the Change of Getting a 4 ?
245(1)
 P Value
246(2)
 Figure 9.2 p Value
247(1)
 Theoretical Probability
248(2)
 Figure 9.3 Theoretical Probability
249(1)
 Empirical (Actual) Probability
250(2)
 Figure 9.4 Three Different Kinds of Probability
251(1)
 Subjective Probability
252(2)
 Figure 9.5 Subjective Probability
253(1)
 Independence
254(2)
 Figure 9.6 You've Got about a 50-50 Chance of Having Another Girl!
255(1)
 Mutually Exclusive Outcomes
256(2)
 Figure 9.7 Mutually Exclusive Outcomes
257(1)
 Gambler's Fallacy
258(2)
 Figure 9.8 The Gambler's Fallacy
259(1)
 Probability Rules
260(6)
 Figure 9.9 The Probability of Only Two Possible Outcomes Always Equals 1.00
263(1)
 Figure 9.10 The Probability of Drawing Either the King of Hearts or the Queen of Spades in One Draw from an Honest Deck of 52 Playing Cards
263(1)
 Figure 9.11 The Likelihood of Selecting a Woman of Color
264(1)
 Figure 9.12 The Probability of Drawing Both the King of Hearts and the Queen of Spades in Two Draws from an Honest Deck of 52 Playing Cards
265(1)
 Figure 9.13 The Probability of an Individual Completing a Ph.D. Degree
265(1)
 Binomial Distribution
266(2)
 Table 9.1 Probability Distribution of Getting Different Numbers of Heads in Four Tosses
267(1)
 Odds
268(2)
 Figure 9.14 What Are the Odds?
269(1)
 Odds Ratio
270(3)
 Table 9.2 Relationship between Age of Mother When First Child Was Born and the Development of Breast Cancer
271(2)
 SET 10 Inferential Reasoning
273(51)
 Point Versus Interval Estimate
274(2)
 Figure 10.1 Point versus Interval Estimates
275(1)
 Confidence Interval
276(2)
 Figure 10.2 We Can Be 99% Confident
277(1)
 Standard Error
278(2)
 Figure 10.3 Standard Errors
279(1)
 Research Hypothesis
280(2)
 Figure 10.4 Research Hypotheses
281(1)
 Null Hypothesis
282(2)
 Figure 10.5 Two Kinds of Hypotheses
283(1)
 Statistical Significance
284(2)
 Figure 10.6 Is It Statistically Significant?
285(1)
 Type I Error
286(2)
 Figure 10.7 A Possible Type I Error
287(1)
 Critical Region
288(2)
 Figure 10.8 Critical Regions
289(1)
 Alpha Level
290(2)
 Figure 10.9 An Alpha Level of 0.5
291(1)
 Type II Error
292(2)
 Figure 10.10 A Possible Type II Error
293(1)
 Power of a Statistical Test
294(2)
 Figure 10.11 A Power Curve
295(1)
 One-versus Two-Tailed Tests of Statistical Significance
296(2)
 Figure 10.12 A Two-Tailed Test
297(1)
 Figure 10.13 One-Tailed Test
297(1)
 Parametric/Nonparametric Test
298(2)
 Figure 10.14 Should You Use a Parametric or Nonparametric Test?
299(1)
 t-Test
300(2)
 Figure 10.15 t-Tests
301(1)
 Analysis of Variance (ANOVA)
302(2)
 Figure 10.16 Typical Situation in Which ANOVA Would be Used
303(1)
 Between-Group Differences
304(2)
 Table 10.1 Between-Group Differences
304(1)
 Figure 10.17 Between-Group Differences
305(1)
 Interaction Effect
306(2)
 Figure 10.18 Interaction between Student Characteristics and Teaching Method
307(1)
 Figure 10.19 An Interaction Effect
307(1)
 Pairwise Comparison
308(2)
 Table 10.2 Relationship of Type of Occupation to Level of Stress
309(1)
 Multivariate Analysis of Variance (MANOVA)
310(2)
 Figure 10.20 MANOVA
311(1)
 Analysis of Covariance (ANCOVA)
312(2)
 Figure 10.21 Analysis of Covariance
313(1)
 Sign Test
314(2)
 Figure 10.22 A Sign Test
315(1)
 Mann-Whitney U Test
316(2)
 Table 10.3 Ranking the Scores of Boys and Girls
317(1)
 Figure 10.23 The Mann-Whitney U Test
317(1)
 Practical (Substantive) Significance
318(2)
 Figure 10.24 Practical Significance
319(1)
 Effect Size
320(2)
 Figure 10.25 When Does a Difference Make a Difference?
321(1)
 Meta Analysis
322(2)
 Figure 10.26 Meta Analysis
323(1)
 Appendix Contents
324(29)
 A-1: How to Percentage a Table
325(2)
 Figure A-1 Percentaging a Table
326(1)
 A-2: How to Construct a Scatterplot
327(1)
 Figure A-2 Constructing a Scatterplot
327(1)
 A-3: How to Simulate an Outcome
328(2)
 Table A-1 A Table of Random Numbers
328(1)
 Figure A-3 Simulating an Outcome
329(1)
 A-4: How to Read an ANOVA Table
330(1)
 Table A-2 An ANOVA Table
330(1)
 A-5: How to Read an ANCOVA Table
331(1)
 Table A-3 An ANCOVA Table
331(1)
 A-6: How to Read a Chi-Square Table
332(1)
 Table A-4 Critical Region for the Chi-Square Test
332(1)
 Figure A-4 Critical Region for the Chi-Square Test
332(1)
 A-7: How to Read a Correlation Matrix
333(1)
 Table A-5 A Correlation Matrix: I
333(1)
 Table A-6 A Correlation Matrix: II
333(1)
 A-8: How to Read a Normal Curve Table
334(1)
 Figure A-5 Critical Region for the Normal Curve
334(1)
 Table A-7 Portion of a Normal Curve Table
334(1)
 A-9: How to Read a t Table
335(1)
 Figure A-6 Critical Region for the t-Test
335
 Table A-8 Portion of a t Table
335
 A-10: How to Read an F Table
336(2)
 Table A-9 Portion of an F Table Figure A-7 Critical Region for the F-Test
337(1)
 A-11: How to Read a Significance Table for the Pearson Correlation
338(1)
 Table A-10 Portion of a Pearson r Table
338(1)
 A-12: How to Draw a Regression Line
339(2)
 Figure A-8 Scatterplot and the Regression Line for Predicting Spelling Scores from Reading Scores
340(1)
 A-13: How to Calculate a Correlation Coefficient
341(2)
341(1)
 Table A-12 Clocks versus Radios Revisited
342(1)
 A-14: How to Calculate a Standard Deviation
343(2)
 Table A-13 Calculation of the Standard Deviation of a Distribution
343(2)
 A-15: How to Perform a Chi-Square Test
345(3)
 Table A-14 Number of Chain Compared to Non-Chain Restaurants in Different Cities: I Table A-15 Number of Chain Compared to Non-Chain Restaurants in Different Cities: II
346(2)
 A-16: How to Perform a t-Test for Independent Means
348(2)
 Table A-16 Inches of Rainfall in Two Cities
348(1)
 Table A-17 Daily Inches of Rainfall in Two Cities
349(1)
 A-17: How to Calculate a One-Way Analysis of Variance
350(3)
 Table A-18 Identified Ruins in Three Forests
350(1)
 Table A-19 An ANOVA Table
351(2)
Bibliography 353(2)
Glossary 355(10)
Index 365

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