An Introduction to Critical Thinking and Creativity - always yours

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152 STATISTICS AND PROBABILITY On the face of it, the picture seems to indicate that there was a sudden surge in cake sales. But this is actually an illusion because the horizontal time axis is not evenly scaled. The period 2002 to 2007 is compressed compared to the other periods, giving the erroneous impression that the rate of growth has abruptly increased when in fact the growth in sales might have been rather steady. » (D 1980: 9,947 calls 2000: 50,105 calls The diagram above shows that the number of emergency calls received by a hospital has increased about fivefold between 1980 and 2000. This is represented pictorially by the fact that the diagram on the right is five times taller than the left one. But the problem is that subjectively, our perception of the relative difference depends on the area instead of just the height. Since the diagram on the right is also five times wider, its area is actually 5 x 5 = 25 times larger than the diagram on the left. The result is that looking at such the diagram, the readers have the impression that the increase is a lot more than just five times. 17.4 PROBABILITY It is no exaggeration to say that probability is the very guide to life. Life is full of uncertainty, but we have to plan ahead based on assumptions about what is likely or unlikely to happen. In all kinds of professions, assessments of probability and risks are of critical importance—forecasting sales, calculating insurance needs and premiums, determining safety standards in engineering, and so on. In this section, we are not going to discuss the mathematics of probability. If you are interested, there are many textbooks and websites you can consult (including the companion website). Instead we shall focus on some of the main reasoning mistakes about probability. 17.4.1 Gambler's fallacy The gambler's fallacy is the mistaken belief that the probability of an event might increase or decrease depending on the pattern of its recent occurrences, even though these events are independent of each other. The name comes from the
PROBABILITY 153 fact that lots of people make this mistake when they gamble. For example, the probability of a fair coin landing on heads is V2. But suppose you toss the coin four times and it landed on heads each time. Someone who thinks it is more likely to be tails next time so that things will "balance out" is committing the gambler's fallacy. This is because the probability of a fair coin landing heads is just the same as the probability of landing tails, whatever the past results might have been. Similarly, it is also a fallacy to think that a series of four tails is more likely to be followed by yet another tail because the tail side is "hot." A good real-life example of the gambler's fallacy might be when people choose numbers for a lottery. Let's say the winning numbers of the last lottery are 2,4,18, 27, 29, 36. Most people would choose a different set of numbers when they play the lottery, thinking that their combination is more likely to win than the previous winning combination. But this is a fallacy, because if the lottery is a fair one, all combinations are equally likely, or better, equally unlikely! A very dangerous manifestation of the gambler's fallacy is the hot hand fallacy. This happens when a gambler wins a few times in a row, and he thinks he is on a lucky streak. As a result, he thinks he is more likely to win than lose if he continues to gamble. But this is a fallacy because the probability of him winning the next round is independent of his past record. It is a dangerous fallacy because very often these gamblers start to feel they are invincible and so they increase their wager and end up losing all their money. 17.4.2 Regression fallacy Regression fallacy is a mistake of causal reasoning due to the failure to consider how things fluctuate randomly, typically around some average condition. Intense pain, exceptional sports performance, and high stock prices are likely to be followed by more subdued conditions eventually due to natural fluctuation. Failure to recognize this fact can lead to wrong conclusions about causation. For example, someone might suffer from back pain now and then but nothing seems to solve the problem completely. During a period of very intense pain, the patient decided to try alternative therapy like putting a magnetic patch on his back. He felt less pain afterward and concluded that the patch worked. But this could just be the result of regression. If he sought treatment when the pain was very intense, it is quite possible that the pain has already reached its peak and would lessen in any case as part of the natural cycle. Inferring that the patch was effective ignored a relevant alternative explanation. Similarly, sometimes we are lucky in the sense that things go very well, and other times we are unlucky and everything seems to go wrong. This is just an inevitable fact of life. But if we read too much into it, we might think we need to do something to improve our luck, and look for solutions where none is needed, such as using crystals to boost our karma. Of course, it is important to reflect on ourselves when things are not working well since it could be due to personal failings such as not working hard enough. What is needed is a careful and objective evaluation of the situation.
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Copyright © 2011 by John Wiley & S
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VIII CONTENTS 9 Valid and sound arg
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X PREFACE • This book has a compa
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2 INTRODUCTION Which is more import
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4 INTRODUCTION knowing the rules of
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6 INTRODUCTION 1. The first questio
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8 INTRODUCTION • Open-mindedness:
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12 THINKING AND WRITING CLEARLY Con
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14 THINKING AND WRITING CLEARLY own
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16 THINKING AND WRITING CLEARLY •
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18 THINKING AND WRITING CLEARLY Tip
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20 THINKING AND WRITING CLEARLY g)
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22 DEFINITIONS • The referent of
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24 DEFINITIONS is too wide because
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26 DEFINITIONS sophisticated sense.
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28 DEFINITIONS 3.5.2 Definition by
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30 DEFINITIONS 3.2 Evaluate these d
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34 NECESSARY AND SUFFICIENT CONDITI
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42 LINGUISTIC PITFALLS ambiguous. A
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44 LINGUISTIC PITFALLS change of di
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46 LINGUISTIC PITFALLS BILLY : All
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48 LINGUISTIC PITFALLS absolve anyb
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50 LINGUISTIC PITFALLS 5.4 GOBBLEDY
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52 LINGUISTIC PITFALLS c) Our cooki
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54 TRUTH false, but we would never
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56 TRUTH matter of linguistic conve
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58 TRUTH i) If Rebecca is Shannon's
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60 BASIC LOGIC 7.1.1 Consistency A
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62 BASIC LOGIC Q, or equivalently,
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64 BASIC LOGIC "or both", or "but n
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66 BASIC LOGIC • PiffQ. • P whe
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70 IDENTIFYING ARGUMENTS of opinion
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72 IDENTIFYING ARGUMENTS it easier
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76 VALID AND SOUND ARGUMENTS This s
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78 VALID AND SOUND ARGUMENTS genera
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80 VALID AND SOUND ARGUMENTS 9.2.5
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82 VALID AND SOUND ARGUMENTS If P t
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84 VALID AND SOUND ARGUMENTS 9.4 SO
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88 INDUCTIVE REASONING highly confi
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90 INDUCTIVE REASONING elusion give
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92 INDUCTIVE REASONING tive strengt
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96 ARGUMENT MAPPING Every person is
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98 ARGUMENT MAPPING of arguments ex
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100 ARGUMENT MAPPING elusion. Separ
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Page 116 and 117: 104 ARGUMENT MAPPING a) High school
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Page 120 and 121: 108 ARGUMENT ANALYSIS ing. It will
Page 122 and 123: 110 ARGUMENT ANALYSIS As an example
Page 124 and 125: 112 ARGUMENT ANALYSIS b) We should
Page 126 and 127: 114 SCIENTIFIC REASONING or perhaps
Page 128 and 129: 116 SCIENTIFIC REASONING crease our
Page 130 and 131: 118 SCIENTIFIC REASONING the planet
Page 132 and 133: 120 SCIENTIFIC REASONING dollars in
Page 134 and 135: 122 SCIENTIFIC REASONING report. Ho
Page 136 and 137: 124 SCIENTIFIC REASONING 13.3 Some
Page 138 and 139: 126 MILLS METHODS 14.1 THE METHOD O
Page 140 and 141: 128 MILLS METHODS 14.3 THE JOINT ME
Page 142 and 143: 130 MILLS METHODS feet is not among
Page 144 and 145: 132 MILLS METHODS d) Situation Cand
Page 146 and 147: 134 REASONING ABOUT CAUSATION Simil
Page 148 and 149: 136 REASONING ABOUT CAUSATION suffe
Page 150 and 151: 138 REASONING ABOUT CAUSATION immor
Page 152 and 153: 140 REASONING ABOUT CAUSATION i) Te
Page 154 and 155: 142 DIAGRAMS OF CAUSAL PROCESSES an
Page 156 and 157: 144 DIAGRAMS OF CAUSAL PROCESSES co
Page 158 and 159: 146 STATISTICS AND PROBABILITY 17.1
Page 160 and 161: 148 STATISTICS AND PROBABILITY •
Page 162 and 163: 150 STATISTICS AND PROBABILITY A mi
Page 166 and 167: 154 STATISTICS AND PROBABILITY 17.4
Page 168 and 169: 156 STATISTICS AND PROBABILITY 4,12
Page 172 and 173: 160 THINKING ABOUT VALUES It is the
Page 174 and 175: 162 THINKING ABOUT VALUES Once thes
Page 176 and 177: 164 THINKING ABOUT VALUES is flat o
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Page 180 and 181: 168 THINKING ABOUT VALUES Similarly
Page 182 and 183: 170 THINKING ABOUT VALUES 18.2 M Ou
Page 186 and 187: 174 FALLACIES One further clarifica
Page 188 and 189: 176 FALLACIES All circular argument
Page 190 and 191: 178 FALLACIES 19.4.1 Irrelevant res
Page 192 and 193: 180 FALLACIES the question. Murder,
Page 194 and 195: 182 FALLACIES • Non sequitur: Non
Page 196 and 197: 184 FALLACIES g) All my Facebook fr
Page 198 and 199: 186 COGNITIVE BIASES These question
Page 200 and 201: 188 COGNITIVE BIASES • Subjects w
Page 202 and 203: 190 COGNITIVE BIASES more likely to
Page 204 and 205: 192 COGNITIVE BIASES - Avoid framin
Page 208 and 209: 196 ANALOGICAL REASONING a big appe
Page 210 and 211: 198 ANALOGICAL REASONING Furthermor
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202 MAKING RATIONAL DECISIONS 22.1
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204 MAKING RATIONAL DECISIONS So if
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206 MAKING RATIONAL DECISIONS the s
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208 MAKING RATIONAL DECISIONS succe
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210 MAKING RATIONAL DECISIONS about
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212 MAKING RATIONAL DECISIONS EXERC
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216 WHAT IS CREATIVITY? The observa
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218 WHAT IS CREATIVITY? Step 1 : Pr
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220 WHAT IS CREATIVITY? remedy our
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224 CREATIVE THINKING HABITS made o
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226 CREATIVE THINKING HABITS materi
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228 CREATIVE THINKING HABITS orate
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230 CREATIVE THINKING HABITS Ellis
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234 SOLUTIONS TO EXERCISES any of t
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236 SOLUTIONS TO EXERCISES SOLUTION
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242 SOLUTIONS TO EXERCISES 1 l.l.h
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244 SOLUTIONS TO EXERCISES 12.1.f T
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246 SOLUTIONS TO EXERCISES 13.4 One
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250 SOLUTIONS TO EXERCISES 17.3.d T
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252 SOLUTIONS TO EXERCISES 19.2.e F
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Bibliography Ackerman, J., Nocera,
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258 BIBLIOGRAPHY McRae, C, Cherin,
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260 BIBLIOGRAPHY Wolf, G. (1996). S
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262 INDEX consequentialist reasonin
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