
 
 
 
 
 
 
 
 
 
 
player does not think batting slumps or hitting streaks are real? Basketballfans, players, coaches, and sports commentators speak of the so-calledhot hand, a trend of above-average shooting accuracy.
These beliefs are widely held because trends in athletic performanceseem so obvious. However, rigorous statistical analysis of player perfor-mance! indicates that the hot hand phenomenon is an illusion. The fanshave been duped by their intuition. This erroneous belief stems from afaulty notion about how random phenomena ought to behave." Commonsense would have us believe that streaks (a sequence of strike-outs, or asequence of successful shots, and so forth) should not occur in a randomprocess. Rather, intuition incorrectly tells us that random processesshould display something resembling an alternating pattern of positiveand negative outcomes.
The truth is that sports trends are, by and large a cognitive illusion.What appears to be a batting slump or a hitting streak is often nothingmore than a run of similar outcomes, a phenomenon that is quite commonin random processes. A valid trend is a streak of longer duration thanthose that are ordinary in random data. That is to say, a real trend is astreak of sufficient length that it would be rare in a random process.
Gilovich points out that “although a player's performance does notdisplay longer streaks than those allowed by chance, it does not mean thatthe player’s performance is chance determined. It is not. Whether a given8G METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
shot is hit or missed is determined by a host of non-chance factors, fore-most among them being the skill of the offensive and defensive players in-volved. However, one factor that does not influence or predict theoutcome is the player’s recent hit rate.”!*
To understand why sports fans, athletes, and chart analysts fall preyto the illusion of trends and patterns in data that may in fact be randomwe must delve a bit deeper into the nature of intuitive judgment.
THE INTUITIVE JUDGMENT AND THE ROLEOF HEURISTICS
 
“To simplify, there are basically two types of thought processes: automaticand controlled.”’” “Intuition is automatic. It is our capacity for directknowledge, for immediate insight without observation or reason.”"* It isperception-like, rapid, and effortless, notes Princeton University psychol-ogist Daniel Kahneman. In contrast, “deliberate or controlled thinkingis reasoning-like, critical, and analytic.”"® The prototype of controlledthought is scientific reasoning. The prototype of intuition is the brilliantmedical diagnostician who always seems to sniff the underlying disease.Subjective technicians rely primarily on intuition, and they do so to theirdetriment.
Human intelligence has limits. We can only pay attention to anextremely small fraction of the information that comes to us throughour sensory organs. Moreover, the mind is not well suited to complextasks such as estimating probabilities and making decisions in a logi-cally and probabilistically correct manner in situations characterizedby uncertainty.
To cope, we must simplify. We reduce the complexities of estimatingand decision making by resorting to a variety of quick and dirty rules ofreasoning known as judgment heuristics. They focus our attention on alimited portion of the total information picture and utilize relatively sim-ple forms of information processing and reasoning to arrive at conclu-sions quickly. All of this is done without awareness or exertion. We makeintuitive judgments as automatically and effortlessly as we recognizesomeone’s face, a task for which the mind is very well suited.
We acquire judgment heuristics from life experience. The termheuristic refers to the notion of discovery by trial and error, and this ishow these rules of thought are acquired. Moreover, they slip into usage sosubtly that we are unaware of how or when we learned them. And weadopt them because, in general, they work. However, they work imper-fectly and when they fail our judgment suffers.The Illusory Validity of Subjective Technical Analysis 37
The good news is that heuristic judgment tends to err in a consistentmanner. In other words, the judgments are biased—they tend to be wrongin the same way over and over again.'”° This consistency makes it possibleto predict the conditions under which heuristic judgments will fail andhow they will fail—whether the deviation from true value will be a posi-tive or a negative one.
In general, heuristic judgments tend to err in situations characterizedby uncertainty.'"' Financial markets are highly uncertain, so intuitive judg-ments in this arena are likely to be biased. The specific bias that afflictssubjective technicians is the propensity to see trends and patterns in datawhere such structures are not truly present. In other words, there is a sys-tematic tendency to perceive order where only random behavior exists.This may explain why chartists are unable to distinguish real charts frompseudocharts produced from random data.
In the words of Professor Burton Malkiel, “Randomness is a difficultnotion for people to accept. When events come in clusters and streaks,people look for explanations and patterns. They refuse to believe thatsuch patterns—which frequently occur in random data—could equally bederived from tossing a coin. So it is in the stock market as well.”!? Malkeiltakes the extreme position that the market is random. I do not share thisconviction but agree that people misperceive order in data that is random.For this reason visual inspection of price charts cannot be trusted.
The illusion of trends and patterns in data that is truly random may beattributable to the failure of a specific judgment heuristic called reason-ing by representativeness. That is to say, a faulty application of the gener-ally useful representativeness rule biases us toward the perception oforder where it does not exist.
Heuristic Bias and the Availability Heuristic
To recap, heuristics help us make complex decisions rapidly in spite ofthe limitations of human intelligence, but they can cause those decisionsto be biased. The notion of heuristic bias is easily explained by consider-ing the availability heuristic.
We rely on the availability heuristic to estimate the likelihood of fu-ture events. It is based on the reasonable notion that the more easily wecan bring to mind a particular class of events, the more likely it is thatsuch events will occur in the future. Events that are easily brought tomind are said to be cognitively available. For example, plane crashes area class of events with high cognitive availability.
The availability heuristic makes a certain amount of sense. The abilityto recall a class of events is indeed related to how frequently they have oc-curred in the past, and it is also true that events that have happened fre-8B METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
quently in the past are generally more likely to occur in the future. This isin keeping with one theory of probability that asserts that the future likeli-hood of an event is related to its historical frequency.' Taken as a class,thunderstorms have been more frequent in the past than asteroid impacts,and they do indeed have a higher future likelihood.
The problem with the availability heuristic is that there are factorsthat can enhance an event's cognitive availability that have nothing to dowith its historical frequency and are, therefore, irrelevant to estimatingits future likelihood. Consequently, our judgments of likelihood aresometimes falsely inflated by the intrusion of these irrelevant factors.Two factors that have no relevance to an event's likelihood but that do in-crease its cognitive availability are recency and vividness. That is to say,how recently'“ an event of the type in question took place and how vividthe event was both impact how easily we can bring such events to mind.Consider plane crashes as a class of events. A plane crash that just oc-curred is both vivid and recent. As a result, in the period right after awell-publicized plane crash many people tend to overestimate the likeli-hood of future plane crashes and are inordinately fearful of flying. Notethe bias in the judgment is one of overestimating a probability. The avail-ability heuristic never causes us to underestimate an event’s likelihood.The error is always one of overestimating the probability.
The Representativeness Heuristic:Reasoning by Similarity
The representativeness heuristic, which was first identified by Tverskyand Kahneman! is of particular relevance to subjective TA. We use thisrule to make intuitive classification judgments. In other words, it is usedto estimate the probability that a particular object, for example the dogbefore me, belongs to a particular class of objects, for example the classof poodles. The underlying premise of the representativeness heuristic isthat each member of a class should display the key common attributesthat define the class. It is quite reasonable to expect that objects from thesame class should possess a similar set of characteristics. In arriving at ajudgment by representativeness about whether a given object belongs to aparticular class, we unconsciously consider the degree of similarity ormatch between the attributes of the object and the set of attributes pre-sumed to be representative of that class. This is why this heuristic is re-ferred as a reasoning by representativeness.
In this section and the next, I will argue that visual chart analysis is in-herently flawed because of a bias toward the perception of order and pat-tern even in data that is truly random. I will contend that this bias is due toa misapplication of the representativeness heuristic. In other words, aThe Illusory Validity of Subjective Technical Analysis 389
bias stemming from a faulty application of the representativeness heuris-tic can explain why subjective technicians fall prey to an illusion of orderin charts that were, in fact, produced by a random process.
To explain how chartists make this mistake, which is rather subtle, wewill take a brief detour by considering a more easily understood case ofheuristic bias caused by representativeness reasoning.
As mentioned earlier, reasoning by representativeness is premised onthe notion that a class of objects or events can be represented by a classstereotype—a typical example that possesses the class’s key distinguish-ing characteristics. Often this line of reasoning works well. However, itfails when an object’s most noticeable features are not reliable indicatorsof the object’s class. In other words, when the characteristics that mostdraw our attention are not relevant in judging the object’s class" reason-ing by representativeness tends to fail. Unfortunately, intuitive judgmenttends to be based on the most obvious features of an object or event re-gardless of whether these features are truly useful indicators of its class.
Reasoning by representativeness estimates the probability than anobject belongs to a given class by considering the degree of match be-tween the object’s most salient attributes and the most salient attributesof the class stereotype. The greater the number of matching attributes,the higher the adjudged probability that the object is indeed a member ofthe class in question. “Modern psychologists hypothesize that our con-cepts of categories (classes) like bank tellers, feminists, microcomput-ers, skunks, and all kinds of things are represented cognitively as lists ofattributes that we believe are defining characteristics of those entities.”!”This is illustrated in Figure 2.19. In many instances this fast and frugalclassification rule gives accurate results. People would not use such arule it if it did not.
Let’s consider an example where the application of the representa-tiveness rule leads to an erroneous judgment about an object’s class.Imagine that you have just taken your seat on a commercial airline flightand you become concerned that a person (the object) seated next to youmay be a terrorist (the class). Your apprehension is aroused because theperson has the following obvious characteristics: man of apparently Mid-dle Eastern origin, mustache, 25-30 years of age, wearing a turban, read-ing the Koran, and appearing nervous. Your conclusion that the man mayvery well belong to the class of terrorists occurred quite spontaneouslybecause his obvious characteristics are similar to a set of characteristicsthat was also possessed by (i.e., is representative of) the terrorists whoconducted the attacks of September 11, 2001. Your inference was basedon the representativeness heuristic. Now consider how you would havereacted if the passenger were a young Middle Eastern man but was wear-ing blue jeans and a tee-shirt with an obscene logo, had on a New York90 > METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
UncertainClass
 
  
 
   
Stereotypical Class Member
 
Class
FIGURE 2.19 Classification by number of matching attributes.
Yankee baseball cap instead of a turban, was reading a copy of Playboyinstead of the Koran, and was listening to rock music on an iPod whileblowing chewing-gum bubbles. You would not have been worried. Intu-itive judgments of class rest on the assumption that the most obviouscharacteristics of an individual are reliable indicators of that individ-ual’s class.
Judgments based on representativeness can err because they fail totake into account statistical and/or logical elements of a situation that aretruly relevant to an accurate judgment about its class. The probabilisti-cally correct way of estimating the class of an event or object is calledBayes’ theorem,'® which is derived from the axioms of probability theory.If it were applied to the airline passenger suspected of being a terrorist, itwould take into account such things as the proportion of terrorists in theworld (i.e., the base rate of the class of terrorists), the proportion of peo-ple in the world that possess the set of observed characteristics (i.e., thebase rate of the pattern), and the proportion of terrorists that have thispattern of characteristics (i.e., the conditional probability that these char-acteristics are present given that the individual is in fact a terrorist). Whenthese values are plugged into the equation that expresses Bayes’ theoremwe obtain the conditional probability that the person is a terrorist, giventhat they possess the pattern of characteristics.The Illusory Validity of Subjective Technical Analysis 91
Because intuition operates on the basis of representativeness, ratherthan Bayes’ law, we tend to commit an error called the base rate fallacy.This is the failure to consider the base rate statistics characterizing a situ-ation. Terrorists, fortunately, are very rare (i.e., have a very low base rate).Thus, among the entire set of people who possess the same salient charac-teristics as the terrorists of 9/11/01, the fraction that are actually terroristsis extremely small. Perhaps only one person in a million with these traitsis actually a terrorist. This fact is highly relevant to judging the likelihoodthat the person seated next to us is dangerous. However, we tend to ne-glect base-rate statistics because intuitive judgment is focused on the at-tention-grabbing features of a situation or object rather than relevant factssuch as a base-rate.
An example of fallacious reasoning by representativeness was dis-played by market analysts who predicted that a deflationary depressionwould follow the stock market crash of October 1987. They were capti-vated by the very noticeable similarity between the behavior of the stockmarket in 1929, which did lead to a deflationary depression, and its behav-ior in 1987. Both witnessed market crashes. This glaring similarity tookanalysts’ attention away from significant dissimilarities between 1987 and1929. In other words, 1987 and 1929 were different with respect to factorsthat do have some predictive information with respect to deflationary col-lapses. An examination of market crashes over the last 100 years showsthat a price crash is not a reliable predictor of a deflationary depression.
Another error associated with representative reasoning is called theconjunction fallacy, a failure to take into account a basic law of logictelling us that a proper subset must contain a smaller number of objectsthan the larger set to which it belongs. The set horses is a proper subset ofthe larger set, animals. It follows that horses must be fewer in numberthan animals in general, which includes horses, bluebirds, aardvarks, andso forth. However, when people rely on the representativeness rule, theyseem to ignore this law of logic and commit the conjunction" fallacy. Inone experiment conducted by Tversky and Kahneman,'® subjects werepresented with the following description:
Linda is 31 years old, single, outspoken, and very bright. She ma-Jored in philosophy. As a student, she was deeply concerned with is-sues of discrimination and social justice, and also participated inantinuclear demonstrations. Which possibility is most likely? (1)Linda is a bank teller, or (2) Linda is a bank teller AND is active inthe feminist movement.
Astoundingly, 85 percent of the subjects responded that it was morelikely that Linda was a bank teller AND active in the feminist movement92 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
than that Linda was simply a bank teller. This conclusion ignores the logi-cal relationship between a set and a proper subset. Subjects became sofixated on the fact that Linda possessed a set of salient characteristics thatmatched an intuitive stereotype of a feminist, that they committed theconjunction fallacy. Clearly, the set of women who are both bank tellersand active in the feminist movement is a subset of a larger category whichcontains all female bank tellers including those who are feminists andthose who are not. Other studies confirmed these findings and led Tverskyand Kahneman to conclude that people’s probability judgments are biasedby the addition of salient detail. Even though each additional detail de-scribing an object reduces the probability that such an object exists,'*!when people reason by representativeness, additional detail increases thenumber of characteristics that match a class stereotype, thus increasingan intuitive estimate of probability. The conjunction fallacy is illustratedin Figure 2.20.
The conjunction fallacy can have disastrous consequences when itseeps into jury verdicts. For example, consider which of two possibilitieswould seem more likely'”:
1. The defendant left the scene of the crime.
2. The defendant left the scene of the crime for fear of being accused ofmurder.
        
Bank TellersWho AreFeminists
FIGURE 2.20 The conjunction fallacy.The Illusory Validity of Subjective Technical Analysis 93
The second hypothesis involves a conjunction of “left the scene” and“fear of accusation.” Because the second alternative is a subset of the first,it is by definition less probable. Clearly, there are reasons for someone’sleaving a crime scene other than fear of being accused, like going to pickup the dry cleaning. However, the additional detail of the second hypothe-sis lends a ring of plausibility because it increases a sense of match to ac-tions that would be representative of a guilty party.
THE REPRESENTATIVENESS HEURISTIC AND THEILLUSION TRENDS AND PATTERNS IN CHARTS:REAL AND FAKE
 
So far the representativeness heuristic has been discussed with respect toits use in classifying objects. In fact, the heuristic is also involved in amore abstract type of classification judgment that is central to the prac-tice of subjective TA: judging that a sample of data evidences trends andpatterns and is, therefore, worthy of further analysis or alternatively thatthe data is a random hodge-podge not worthy of further analysis.
Bear in mind the judgment about whether a data set appears randomor nonrandom is not made with conscious awareness or intention. It oc-curs as automatically and unconsciously as the judgment involved in rec-ognizing the face of a friend. All heuristic judgments, including reasoningby representativeness, occur automatically and without conscious aware-ness. As a result, when a chartist concludes that a sample of price historycontains authentic patterns and trends (i.e., that the data is nonrandom)and is, therefore, worthy of analysis, it is not a matter of controlled think-ing. That is to say, the chartist does not consciously pose the question:“Does this data appear as if it contains exploitable order and structure.”
Although heuristic judgments slip into our thinking unnoticed, theycan have a profound influence on our beliefs. The problem is that heuris-tic thinking fails to take into account important features of the data thatare relevant to determining if it does contain authentic patterns andtrends that might be exploited with further analysis.
In a previous section, I asked you to create an artificial price history(random-walk chart) by flipping a coin 300 times. If you did not do sothen, I urge you to do so now. Not only will it make this section moremeaningful, it may permanently change the way you look at charts. Toquote Martha Stewart, “that’s a good thing.”
If this was your first exposure to data generated by a random process,you may be surprised by how nonrandom it looks. You may not have ex-pected to see formations that look like chart patterns (head-and-shoulders,94 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
double top, etc.). The question we must consider is this: Why does this se-quence, which we know to be random in origin, give the appearance ofhaving authentic patterns and trends. Or, said differently, why does datagenerated by a purely random process appear as if it were generated bya process governed by rules, which, if discovered, would make predic-tion possible?
Your chart may have looked something like Figure 2.21.
The bottom line is this: That which appears to be nonrandom is notnecessarily nonrandom. My contention is that the perception of trendsand patterns in randomly generated data occurs because of a faulty appli-cation of the representativeness heuristic. Specifically, the heuristic cre-ates a faulty intuitive notion of how random data is supposed to look. Thatis to say, it produces a false stereotype of randomness. Thus, when weview data that does not appear to match this false stereotype, we automat-ically and erroneously conclude that the data is nonrandom. From thisflawed conclusion, it is a short leap to the equally false perception of pat-terns and the equally false notion that the patterns contain predictiveinformation.
One consequence of representativeness-based reasoning is the ex-pectation that an effect should resemble its cause. This is often reason-able. The Earth (big cause) is responsible for gravity (big effect), while amere pebble in our shoe causes only a minor annoyance. However, therule that an effect should resemble its cause does not always hold. The1918 flu pandemic, a big effect, was caused by a creature of submicro-scopic proportions.
How does this relate to charts of asset prices? A set of data on a chartcan be seen as an effect of a process, the activity of a financial market.The process is the cause whereas the data is the effect. A chart of our
Price
Time
FIGURE 2.21 Data from a random process that appears ordered.The Illusory Validity of Subjective Technical Analysis 95
body’s hourly temperature over a 24-hour period is an effect caused by aprocess that happens to be our body’s metabolism.
Because representativeness-based thinking operates involuntarily be-neath conscious awareness, when we view the chart of an asset’s pricehistory, we tend to draw an automatic conclusion about the nature of theprocess that generated the chart. Perhaps, if stock charts looked some-thing like the trace in Figure 2.22, the pioneers of TA would have been lesslikely to see exploitable structure, and the practice of TA would neverhave been born. This data is supposed to approximate an intuitive stereo-type of randomness: haphazard, disorderly, and without any hint of trend.
On the basis of the representativeness heuristic, we presume that if aprocess (the cause) is random, its effect (the data) should also appear ran-dom. As a consequence of this assumption, any sample of data that devi-ates from the presumed stereotype of randomness, because it manifestssome sense of pattern or trend, is concluded to be the product of a non-random process. Stock charts give the appearance of having been gener-ated by a nonrandom process. In other words they match an intuitivenotion of order and predictability. Bear in mind that financial markets mayindeed be nonrandom to some degree and hence be amenable to predic-tion. However, that is not the issue here. Rather the issue is can non-random structure that is amenable to prediction be detected by visualinspection and intuitive appraisal?
As mentioned previously, the deficiencies of reasoning by representa-tiveness are due to an excessive focus on obvious appearances and the si-multaneous disregard of important statistical and logical features. As willbe explained in Chapter 4, one of the most important features of a sampleof data, from the standpoint of data analysis, is the number of observationscomprising the sample. Valid conclusions about a sample of data musttake the number of observations into account. Moreover, the statistical
Price
Time
FIGURE 2.22 Intuitive stereotype of random data: haphazard, disordered,nontrending.96 — METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
characteristics of a large number of observations are required to accu-rately represent the true nature of the process that generated the data(e.g., random or nonrandom). Conversely, small samples of data oftenconvey the illusion of patterns and trends because the statistical charac-teristics of a small sample of data can be wildly unrepresentative of thedata generating process.
I contend that the belief that visual chart analysis is a valid method fordetecting trends and patterns is based on a flawed chain of thinking thatgoes something like this:
1. On the basis of the representativeness heuristic, it is erroneouslythought that data generated by a random process should look ran-dom—a formless haphazard flip-flop without any hint of patterns, or-ganized shapes or trends.
2. This stereotype is erroneously assumed to manifest in all samples ofrandom data, irrespective of the number of observations comprisingthe sample.
3. Asmall sample of data is examined and it appears not to match the in-tuitive stereotype of randomness.
4. The data is thus deemed to be the product of a nonrandom process.
a
Nonrandom processes are amenable to prediction, hence it would bereasonable to look for patterns and trends in the data to make predic-tions.
This is illustrated in Figure 2.23.
The principal flaw in this chain of reasoning is the failure to considerthe matter of sample size (step 2 of the preceding list). The presumptionthat a sample of data can accurately reflect the nature of the data generat-ing process, irrespective of the number of observations comprising thesample, violates an important principle of formal data analysis, the Law ofLarge Numbers. Reasoning by representativeness fails to respect the Lawof Large Numbers. In other words, it commits the crime of small numbersor sample size neglect. The penalty is automatic membership in The Foolsof Randomness!* club.
The Law of Large Numbers and the Crimeof Sample Size Neglect
The Law of Large Numbers tells us that sample size is of paramount im-portance because it determines the confidence we can have in inferencesbased on a sample of data. Also known as the Law of Averages, the Law ofLarge Numbers tells us that only samples comprised of large numbers ofThe Illusory Validity of Subjective Technical Analysis 97
Does The Data Contain Predictable Order?Yes: Data sample does not match intuitive stereotype of randomness
 
RandomProcess
 
 
 
 
 
?
    
 
 
Stereotype _RacdomData
Data Sample
 
 
 
 
 
Non-RandomProcess
 
 
FIGURE 2.23 Data is presumed to be amenable to prediction because it doesnot match an intuitive stereotype of randomness.
 
observations reliably and accurately reflect the characteristics of theprocess that generated the sample. Or, said differently, only large samplescan inform us about the characteristics of the population from which thesample came. Thus, the larger the number of coin tosses, the more closelythe proportion of heads in the sample will reflect an essential truth aboutfair coins: the probability of heads is 0.50. The bottom line is we can havegreater confidence in what we learn from large samples than from smallones. The Law of Large Numbers will be discussed in greater depth in con-nection with statistics in Chapter 4. For the present discussion, what isimportant is the connection between the Law of Large Numbers and theappearance of illusory patterns and trends in small samples of data.
Small samples can be misleading because they can manifest charac-teristics that are very different from the true characteristics of the processthat generated the sample. This explains why a small segment of a pseudo-stock chart—one that was actually generated by a random process—givesthe appearance of authentic patterns and trends. Of course, by design,such a chart cannot have real trends and patterns. Thus, a reliable conclu-sion about whether a sample of data was the result of a random or non-random process cannot be obtained from a small sample. This is depictedby Figures 2.24 and 2.25. When the parts (small samples) of the chart looknonrandom, an illusion of nonrandomness is created in the entire chart,when they are put together.
Coin-toss experiments illustrate how small samples can produce mis-leading impressions. The obvious statistical characteristic of this random98 — METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
 
 
Random Process
ei Pl
Small Sample Small Sample Small SampleIllusory Uptrend Illusory H&S Pattern Illusory Downtrend
 
 
 
 
 
 
 
 
 
 
FIGURE 2.24 The illusion of trends and patterns in small samples—data gener-ated by a random process.
process is that there are two equally likely outcomes. This is the basis foran expectation that the proportion of heads is 0.50. This intuition is in-deed correct when the number of tosses is large. In a sample of 100,000tosses, the proportion of heads will be extremely close to 0.50. If one wereto repeat this experiment many times, the proportion of heads would al-ways be very close to 0.50. In fact, it would be unlikely to fall outside therange of 0.497-0.503.!%4
The problem is intuition pays no attention to sample size or the Lawof Large Numbers. So we also expect 0.50 heads to appear in all samples.Although it is true that the expected proportion of heads in any sample isalways 0.50, even for just two tosses, the proportion of heads that will ac-
Price poverty
      
  
IllusoryH&SPattern
           
Illusory Down-Trend
   
Illusory Up-TrendTime
FIGURE 2.25 If small parts of a chart look orderly, the whole chart assumes anonrandom look.The Illusory Validity of Subjective Technical Analysis 99
tually appear in a given small sample can depart significantly from 0.50. Inten tosses, for example, three heads (0.30) or seven heads (0.70) can eas-ily happen. In a sample of 100,000 tosses, 0.30 heads (30,000) or 0.70(70,000) would be virtually impossible with a fair coin.
Another faulty intuition about random processes is that outcomesshould alternate (up/down, head/tail) more than they really do. When peo-ple are asked to imagine what a sequence of coin tosses would be like,they tend to imagine sequences that show far more head /tail alternationthan would really occur in a random sequence.'® In reality, randomprocess displays less alternation and longer streaks of similar outcomes(up, up, up) than is widely believed. Therefore, when a set of data doesnot match the false expectation of an alternating sequence, it gives rise tothe illusion of a trend. For example, it seems intuitively correct that a cointoss would be more likely to produce the sequence H,T,H,T,H,T than thesequence H,H,H,H,H,H. However, both sequences are, in fact, equallyprobable,'** so we come away with the erroneous impression that the for-mer sequence suggests a random process whereas the latter suggests aprocess that displays a trend.
Because random sequences actually alternate less and streak moreth