Statistical Misconceptions

by Huck; Schuyler W.

• ISBN13: 9780805859027
• ISBN10: 0805859020
• Format: Hardcover
• Copyright: 2008-11-03
• Publisher: Routledge

Summary

Brief and inexpensive, this engaging book helps readers identify and then discard 52 misconceptions about data and statistical summaries. The focus is on major concepts contained in typical undergraduate and graduate courses in statistics, research methods, or quantitative analysis. Fun interactive Internet exercises that further promote undoing the misconceptions are found on the book's website. The author's accessible discussion of each misconception has five parts: The Misconception - a brief description of the misunderstanding Evidence that the Misconception Exists examples and claimed prevalence Why the Misconception is Dangerous consequence of having the misunderstanding Undoing the Misconception - how to think correctly about the concept Internet Assignment - an interactive activity to help readers gain a firm grasp of the statistical concept and overcome the misconception. The book's statistical misconceptions are grouped into 12 chapters that match the topics typically taught in introductory/intermediate courses. However, each of the 52 discussions is self-contained, thus allowing the misconceptions to be covered in any order without confusing the reader. Organized and presented in this manner, the book is an ideal supplement for any standard textbook. Statistical Misconceptionsis appropriate for courses taught in a variety of disciplines including psychology, medicine, education, nursing, business, and the social sciences. The book also will benefit independent researchers interested in undoing their statistical misconceptions.

Table of Contents

Preface	p. xiii
Descriptive Statistics	p. 1
Measures of Central Tendency	p. 3
The Mean of Means	p. 9
The Mode's Location	p. 13
The Standard Deviation	p. 15
Recommended Reading	p. 18
Distributional Shape	p. 19
The Shape of the Normal Curve	p. 21
Skewed Distributions and Measures of Central Tendency	p. 25
Standard Scores and Normality	p. 29
Rectangular Distributions and Kurtosis	p. 33
Recommended Reading	p. 37
Bivariate Correlation	p. 39
Correlation Coefficients	p. 41
Correlation and Causality	p. 45
The Effect of a Single Outlier on Pearson's r	p. 49
Relationship Strength and r	p. 55
The Meaning of r = 0	p. 59
Recommended Reading	p. 63
Reliability and Validity	p. 65
Statistical Indices of Reliability and Validity	p. 67
Interrater Reliability	p. 71
Cronbach's Alpha and Unidimensionality	p. 77
Range Restriction and Predictive Validity	p. 83
Recommended Reading	p. 87
Probability	p. 89
The Binomial Distribution and N	p. 91
A Random Walk With a Perfectly Fair Coin	p. 95
Two Goats and a New Car	p. 99
Identical Birthdays	p. 103
The Sum of an Infinite Number of Numbers	p. 107
Being Diagnosed With a Rare Disease	p. 111
Risk Ratios and Odds Ratios	p. 115
Recommended Reading	p. 119
Sampling	p. 121
The Character of Random Samples	p. 123
Random Replacements When Sampling	p. 127
Precision and the Sampling Fraction	p. 131
Matched Samples	p. 135
Finite Versus Infinite Populations	p. 139
Recommended Reading	p. 143
Estimation	p. 145
Interpreting a Confidence Interval	p. 147
Overlapping Confidence Intervals	p. 151
The Mean [plus or minus] the Standard Error	p. 155
Confidence Intervals and Replication	p. 159
Recommended Reading	p. 163
Hypothesis Testing	p. 165
Alpha and Type I Error Risk	p. 167
The Null Hypothesis	p. 171
Disproving H[subscript 0]	p. 175
The Meaning of p	p. 179
Directionality and Tails	p. 183
The Relationship Between Alpha and Beta Errors	p. 189
Recommended Reading	p. 193
t-Tests Involving One or Two Means	p. 195
Correlated t-Tests	p. 197
The Difference Between Two Means If p < .0001	p. 201
The Robustness of a t-Test When n[subscript 1] = n[subscript 2]	p. 205
Recommended Reading	p. 208
ANOVA and ANCOVA	p. 209
Pairwise Comparisons	p. 211
The Cause of a Significant Interaction	p. 215
Equal Covariate Means in ANCOVA	p. 219
Recommended Reading	p. 223
Practical Significance, Power, and Effect Size	p. 225
Statistical Significance Versus Practical Significance	p. 227
A Priori and Post Hoc Power	p. 231
Eta Squared and Partial Eta Squared	p. 237
Recommended Reading	p. 241
Regression	p. 243
Comparing Two r's; Comparing Two b's	p. 245
R[superscript 2]	p. 249
Predictor Variables That Are Uncorrelated With Y	p. 253
Beta Weights	p. 257
Recommended Reading	p. 261
Citations for Material Referenced in the Preface	p. 263
References for Quotations Presented in the Sections Entitled "Evidence That This Misconception Exists"	p. 265
Subject Index	p. 279
Author Index	p. 285
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