Lies, Damned Lies, or Statistics- How to Tell the Truth with Statistics, 2017a

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8 1. ONE-VARIABLE STATISTICS: BASICS EXAMPLE 1.2.2. The relative frequency version of the above bar chart in Example 1.2.1 would look like 1.2.3. Bar Charts III: Cautions. Notice that with bar charts (of either frequency or relative frequency) the variable values along the x-axis can appear in any order whatsoever. This means that any conclusion you draw from looking at the bar chart must not depend upon that order. For example, it would be foolish to say that the graph in the above Example 1.2.1 “shows and increasing trend,” since it would make just as much sense to put the bars in the other order and then “show a decreasing trend” – both are meaningless. For relative frequency bar charts, in particular, note that the total of the heights of all the bars must be 1 (or 100%). If it is more, something is weird; if it is less, some data has been lost. Finally, it makes sense for both kinds of bar charts for the y-axis to run from the logical minimum to maximum. For frequency charts, this means it should go from 0 to n (the sample size). For relative frequency charts, it should go from 0 to 1 (or 100%). Skimping on how much of this appropriate y-axis is used is a common trick to lie with statistics. EXAMPLE 1.2.3. The coin we looked at in Example 1.2.1 and Example 1.2.2 could well be a fair coin – it didn’t show exactly half heads and half tails, but it was pretty close. Someone who was trying to claim, deceptively, that the coin was not fair might have shown only a portion of the y axis, as
1.2. VISUAL REPRESENTATION OF DATA, I 9 This is actually, in a strictly technical sense, a correct graph. But, looking at it, one might conclude that T seems to occur more than twice as often as H, so the coin is probably not fair ... until a careful examination of the y-axis shows that even though the bar for T is more than twice as high as the bar for H, that is an artifact of how much of the y-axis is being shown. In summary, bar charts actually don’t have all that much use in sophisticated statistics, but are extremely common in the popular press (and on web sites and so on). 1.2.4. Pie Charts. Another way to make a picture with categorical data is to use the fractions from a relative frequency bar chart, but not for the heights of bars, instead for the sizes of wedges of a pie. EXAMPLE 1.2.4. Here’s a pie chart with the relative frequency data from Example 1.2.2.
Page 1: Lies, Damned Lies, or Statistics: H
Page 5 and 6: Contents Release Notes Preface iii
Page 7: CONTENTS vii 5.3.2. Informed Consen
Page 10 and 11: x PREFACE of this book to help you
Page 12 and 13: The first instinct of the scientist
Page 15 and 16: CHAPTER 1 One-Variable Statistics:
Page 17: 1.2. VISUAL REPRESENTATION OF DATA,
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Page 27 and 28: 1.4. NUMERICAL DESCRIPTIONS OF DATA
Page 41 and 42: EXERCISES 31 EXERCISE 1.5. Twenty s
Page 43 and 44: CHAPTER 2 Bi-variate Statistics: Ba
Page 45 and 46: 2.2. SCATTERPLOTS 35 2.2. Scatterpl
Page 47 and 48: 2.3. CORRELATION 37 Many electronic
Page 49 and 50: CHAPTER 3 Linear Regression Quick r
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Page 59: EXERCISES 49 Exercises EXERCISE 3.1
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64 4. PROBABILITY THEORY The final
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76 4. PROBABILITY THEORY FACT 4.3.1
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82 4. PROBABILITY THEORY One nice t
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84 4. PROBABILITY THEORY In order t
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88 4. PROBABILITY THEORY EXERCISE 4
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90 4. PROBABILITY THEORY EXERCISE 4
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92 5. BRINGING HOME THE DATA guidel
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94 5. BRINGING HOME THE DATA Simila
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100 5. BRINGING HOME THE DATA and s
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102 5. BRINGING HOME THE DATA 5.2.5
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104 5. BRINGING HOME THE DATA 5.3.
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106 5. BRINGING HOME THE DATA In th
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Part 3 Inferential Statistics
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CHAPTER 6 Basic Inferences The purp
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6.1. THE CENTRAL LIMIT THEOREM 113
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6.2. BASIC CONFIDENCE INTERVALS 115
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6.3. BASIC HYPOTHESIS TESTING 117 6
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6.3. BASIC HYPOTHESIS TESTING 119 N
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6.3. BASIC HYPOTHESIS TESTING 121 M
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The two hypotheses then are 6.3. BA
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EXERCISES 125 Exercises EXERCISE 6.
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Bibliography [Gal17] Gallup, Presid
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130 INDEX causation, 46 center of a
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132 INDEX population standard devia
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Lies, Damned Lies, or Statistics- How to Tell the Truth with Statistics, 2017a

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