Literature on Heuristics Hlbba

8/13/2019 Literature on Heuristics Hlbba

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A Sample of the Literature on

Heuristics* and BiasesA LECTURE TO TYBBA HONOURS STUDENTS

OF BKMIBA BY DR MUNISH Y ALAGH

HL COLLEGE CAMPUS, 30thJANUARY 2014.


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What is this lecture about?

This lecture is a Sample of the Literatureon Heuristics* and Biases(Shortcuts in

Thinking* and Biases Related To Them)-

the law of smal l numbers (and i ts

related heur ist ic: representat iveness )

and errors in statistical thinking related to

it demystified.

What is all this? I will present this slideagain in the end and ask you to explain it.


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The law of small numbers

demystified

A study of the incidence of kidney cancer inCounties of United States.

Kidney Cancer is lowest in counties which

are mostly rural and sparsely populated and

located in traditionally Republican States.

You probably ignored the Republican Part.

Did you focus on the Rural Part?

Did you think that rural lifestyle leads to lowkidney cancer? Probably.


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Now comes the surprise!

The counties in the United States whichhave the highest incidence of kidneycancer also tend to be in mostly rural,sparsely populated counties and

Republican States! Maybe the poverty of the rural lifestyle

caused this!

Something is wrong here! Rural Lifestylecannot explain both high and lowincidence of kidney cancer!


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What is the solution to this riddle?-

lets begin to think.

Well, what could be the solution to thisriddle?, Lets atleast begin the process ofexploration.

Infact, the key factor is not that the

counties were rural or predominantlyRepublican, it is that rural counties havesmall populations.

More about this explanation later*, firstlets investigate certain features of thisconondrum.


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The Problem is In fact: Errors in

Statistical Reasoning-

From whatever I told you above you musthave thought O My God! Here, we have -

another average lecture on some

academic topic, but the lecture I am about

to give you is not academic at all, infact it

is a lecture whose basis is on the difficult

relationship between our mind and

statistics.

Wh h h h


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What was the shortcut that your

mind got trapped in at the beginning

of this story?

We automatically and effortlessly identifycausal connections between events,sometimes even when the connection is

spurious. What was the shortcut that your mind got

into? When told about the high incidencecounties, you immediately assume that

these counties are different from othercounties for a reason, that there must be acause that explains this difference.


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Our Mind and Statistics.

Our mind, specially the intuitive part ofour mind is inept when faced with merely

statistical facts, which change the

probability of outcomes but do not cause

them to happen. How can we justify the

above? Here we go-

As I had promised earlier there is an

explanation to this story of KidneyCancer. What is it?


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The Explanation:

Imagine the population of the UnitedStates as marbles in a giant urn. Somemarbles are marked KC, for kidneycancer. You draw samples of marbles and

populate each county in turn. RuralSamples are smaller than other samples.Extreme Outcomes (very high and/or verylow cancer rates) are most likely to be

found in sparsely populated counties. Thisis all there is to the story.


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Going Deeper into the Explanation.

Imagine a large urn filled with marbles. Halfthe marbles are red, half are white. Next,

draw 4 marbles from the urn, record the

number of red balls in the sample, throw the

balls back into the urn, and then do it again,many times. If you summarize the results,

you will find that the outcome "2 red, 2 white"

occurs (almost exactly) 6 times as often as

the outcome "4 red" or "4 white." This

relationship is a mathematical fact.


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A related statistical fact

A related statistical fact is relevant to thecancer example. From the same urn,

Jack draws 4 marbles on each trial, Jill

draws 7. They both record each time they

observe a homogeneous sampleall

white or all red. If they go on long enough,

Jack will observe such extreme outcomes

more often than Jillby a factor of 8.


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Just an accident of sampling

The small population of a county neithercauses nor prevents cancer; it merely

allows the incidence of cancer to be much

higher (or much lower than in the larger-

population. The deeper truth is that there is

nothing to explain. The incidence of cancer

is not truly lower or higher than normal in a

countv with a small population it justappears to be so in a particular year

because of an accident of sampling.


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Law of large and small numbers

large samples- deserve more trust than smaller samples.

you may find that the following statements apply to you:

"sparsely populated" did not immediately stand out asrelevant when you read the kidney cancer story.

You were at least mildly surprised by the size of the difference between samples

of 4 and samples of 7.

The following two statements mean exactly the same thing:

Large samples are more precise than small samples.

Small samples yield extreme results more often than large samples do.

The first statement has a clear ring of truth, but until the second versionmakes intuitive sense, you have not truly understood the first.

The bottom line: yes, you did know that the results of large samples are moreprecise, but you may now realize that you did not know it very well.


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Sampling Variation

you wish to confirm the hypothesis that thevocabulary of the average six-year-old girlis larger than the vocabulary of an averageboy of the same age. The hypothesis is truein the population; Girls and boys vary agreat deal, however, and by the luck of thedraw you could select a sample in whichthe difference is inconclusive, or even onein which boys actually score higher. Using asufficiently large sample is the only way toreduce the risk. Researchers who pick toosmall a sample leave themselves at themercy of sampling


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Content versus reliability

In a poll of 300 seniors 60% support thePresident

summarize in exactly three words,

you would choose The elderly support

the President.'' These words provide thegist of the story. Your summary would bethe same if the sample size had beendifferent. Of course, a completely absurd

number of sample size, small or big,would draw your attention.


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Halo Effect

believing that small samples closelyresemble the population from which they are

drawn implies: we are prone to exaggerate

the consistency and coherence of what we

see, The exaggerated faith of researchers inwhat can be learned from a few observations

is closely related to the halo effect, the

sense we often get that we know and

understand a person about whom weactually know very little.

Th h b f


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There has to be a reason for

everything

Take the sex of six babies born in sequence at a hospital. Thesequence of boys and girls is obviously random; the eventsare independent of each other, and the number of boys andgirls who were born in the hospital in the last few hours hasno effect whatsoever on the sex of the next. However we willnot consider the fact that if in the sequence all events areindependent and outcome boy and girl are approximately

equally likely, then any possible sequence of six births is aslikely as any other. We are pattern seekers, believers in acoherent world, in which regularities (such as a sequence ofsix girls) appear as a result of someone's intention. Lionsmay appear on the plain at random times, but it would besafer to notice and respond to an apparent increase in the

rate of appearance of prides of lions, even if it is actually dueto the fluctuations of a random process.


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Search for certainty, search for

causality- a waste of time.

War broke out in 1973. Squadrons flying from thesame base, one of which had lost four planeswhile the other had lost none. An inquiry wasinitiated. There was no prior reason to believethat one of the squadrons was more effectivethan the other, and no operational differences

were found, but of course the lives of the pilotsdiffered in many random ways, including, howoften they went home between missions..Rationally the command should accept that thedifferent outcomes were due to blind luck, a

random search for a non obvious cause washopeless.


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Finding Patterns in Sports

The assumed hot hand in sports is veryusual, if in basketball a player sinks three

or four baskets in a row, defense starts

guarding him more, his players start

passing more to him, even his coachthinks he has a temporary hot hand, we

are too quick to perceive order and

causality in randomness.

In a small sample there will be


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In a small sample there will be

more extreme results. A research study showed that more small schools

had done well, so the Gates foundation startedfunding small schools and a causal story caneasily be linked to this saying that attention tostudents is more in small schools, actually largerschools empirically, if anything, do better possibly

because of greater curriculum options . And soUnfortunately the causal analysis is wrong, theactual fact is which could have been pointed outhad the Gates foundation taken statisticsseriously is that more small schools had also

done badly. Clearly on average small schools arenot better just more variable.


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Journal Articles

In further reading

1) if you read the article I have given you

Belief in the law of small numbers.Tversky, Amos;Kahneman, Daniel, Psychological Bulletin, Vol76(2), Aug 1971, 105-110.

This article gives many examples which showthat the fact that extreme outcomes result fromsmall samples more often than large samples is astatistical fact and can lead to a bias or statisticalerror in misinterpreting, what is a result of sample

size, as a factor related to the content of thestory. Unfortunately we focus more on contentthan reliability.


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Journal Articles

In further reading 1) if you read the article I have given you

On the psychology of prediction.Kahneman,Daniel; Tversky, Amos Psychological Review, Vol80(4), Jul 1973, 237-251.

You will find examples of how people see patternswhere none exist. People judge even extremeand rare outcomes as more probable if thecontent of the story indicates that a particular

outcome is more representative, even if thatoutcome is extreme or rare. This is the heuristicof representativeness.


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Journal Articles

In further reading

1) if you read the article I have given you How to Make CognitiveIllusions Disappear: Beyond Heuristics and Biases, Gerd Gigerenzer,European Review of Social Psychology,Volume 2, Issue 1, 1991

Special Issue: European Review of Social Psychology.

You will find that this statistical error of not considering thesample size and focussing on the content of the story, itself

has limitations, as the author explains: by considering a moredetailed view of statistics ie by considering, for example:relative frequency rather than single frequency case, andalso, whether or not the observation was randomly selectedor self selected itself; this kind of a nuanced technical view ofstatistics could possibly remove this statistical error itself.

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What was this lecture about?-

Explain below statement-

This lecture is a Sample of the Literature

on Heuristics* and Biases(Shortcuts in

Thinking* and Biases Related To Them)-the law of smal l numbers (and i ts

related heur ist ic: representat iveness)

and errors in statistical thinking related to

it demystified.

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Literature on Heuristics Hlbba