statistic introduction

8/9/2019 Statistic Introduction

1/68


2/68

WE RESEARCHERSUSE STATISTICS THE

WAY A DRUNKARDUSES A LAMP POST,

MORE FOR SUPPORT

THAN

ILLUMINATION.

WE RESEARCHERSUSE STATISTICS THE

WAY A DRUNKARD

USES A LAMP POST,

MORE FOR SUPPORT

THANILLUMINATION.


3/68

StatisticsStatistics

The branch of mathematicsThe branch of mathematics

that deals with thethat deals with the

collectioncollection,,organizationorganization,,

analysisanalysis, and, andinterpretationinterpretation

of numerical data.of numerical data.


4/68


is especiallyis especially

useful in drawinguseful in drawing

general conclusionsgeneral conclusions

about a set of dataabout a set of data

from a sample of the data.from a sample of the data.


5/68

DATADATASINGULARSINGULAR ----------DATUM.DATUM.

PLURALPLURAL ----------------DATA.DATA.

WE MAY DEFINE DATAASWE MAY DEFINE DATAASNUMBERSAND THERE ISNUMBERSAND THERE ISTWO KINDS OF NUMBERSTWO KINDS OF NUMBERS

THAT WE USE INTHAT WE USE INSTATISTICS THE RESULTS OFSTATISTICS THE RESULTS OF: COUNTINGAND: COUNTINGAND

MEASUREMENTSMEASUREMENTS..


6/68

variablevariable

ANYASPECT OF ANANYASPECT OF ANINDIVIDUAL THAT ISINDIVIDUAL THAT IS

MEASURED, LIKEMEASURED, LIKEBLOOD PRESURE,BLOOD PRESURE,

AGE,AGE,

SEX etc.SEX etc.


7/68

Variables divide intoVariables divide into

different typesdifferent types

QUALITATIVEQUALITATIVE

(CATEGORICAL)(CATEGORICAL)

QUANTITATIVEQUANTITATIVE(NUMERICAL)(NUMERICAL)


8/68

ReadRead

not to contradictnot to contradictand confute,and confute,

not to believenot to believe

and take for granted,and take for granted,

not to find talk and discourse,not to find talk and discourse,

but to weigh and consider.but to weigh and consider.

Sir Francis BaconSir Francis Bacon


9/68

WHAT MAKE STATISTICS UNIQUE?WHAT MAKE STATISTICS UNIQUE?

ITSABILITY TOITSABILITY TO

QUANTIFYQUANTIFYUNCERTAINTYUNCERTAINTY,,

TO MAKE ITTO MAKE ITPRECISEPRECISE..


10/68


11/68

A more positive example in statistics isA more positive example in statistics isthethe SALK POLIO VACCINESALK POLIO VACCINE in 1954in 1954

vaccine trials were performed on somevaccine trials were performed on some400,000 children, with strict controls to400,000 children, with strict controls toeliminate biased results.eliminate biased results.

Good statistical analysisGood statistical analysis ofof thetheresults firmly established theresults firmly established the

vaccines effectiveness,vaccines effectiveness,and to dayand to day

POLIO is almost unknown.POLIO is almost unknown.


12/68

To accomplishtheirfeats of mathematicalTo accomplishtheirfeats of mathematicalLEGERDEMAIN (STATISTICIANS)LEGERDEMAIN (STATISTICIANS)

RELY ON THREE RELATED DISCIPLINE:RELY ON THREE RELATED DISCIPLINE:

Data analysisData analysisThe gathering, display, and summaryThe gathering, display, and summary

of dataof data

ProbabilityProbabilityThe law of chanceThe law of chance

Statistical InferenceStatistical InferenceThe science of drawing statisticalThe science of drawing statistical

conclusions from specific data, using aconclusions from specific data, using a

knowledge of probability.knowledge of probability.


13/68

Objectives ofthiscourseObjectives ofthiscourse

At the end of the course the studentsAt the end of the course the studentswill be able towill be able to

1.1. organize dataorganize data2.2. summarize datasummarize data

3.3. reach decision aboutreach decision about

a large body of dataa large body of data

by examiningby examining

only small part of the data.only small part of the data.


14/68

Objective number 1 and 2Objective number 1 and 2

we will discuss inwe will discuss in

DESCRIPTIVE STATISTICS.DESCRIPTIVE STATISTICS.

Objective number 3Objective number 3

we will discusswe will discuss

INFERENCIALSTATISTICSINFERENCIALSTATISTICS


15/68

What is biostatisticsWhat is biostatistics


16/68


17/68

TheThe statisticsstatistics partpart

involvesinvolves

CCollectionollection,,

OrganizationOrganization,, AAnalysisnalysis,,

andand

interpretationinterpretation

of numerical dataof numerical data


18/68

BiostatisticsBiostatisticsis the applicationis the application

ofofstatisticsstatistics

to a wide range of topics into a wide range of topics inbiologybiology. It has particular. It has particularapplications toapplications to medicinemedicine

andand

toto agricultureagriculture..


19/68

StatisticsStatistics calculationscalculations

are an importantare an important

part of data analysis,part of data analysis,

butbut interpreting datainterpreting dataalsoalso

requiresrequiresa great deal of judgmenta great deal of judgment


20/68

UnderstandingUnderstanding

the statistical calculationsthe statistical calculations

is only a small partis only a small part

ofof1.1. evaluating clinicalevaluating clinical

2.2. pharmaceuticalpharmaceutical

3.3. biological research.biological research.


21/68

WhyWhyis it hardis it hard

to learnto learn

statistics?statistics?


22/68

Theterminology is deceptiveTheterminology is deceptive

You have to understand :You have to understand :

1.1. SignificantSignificant

2.2. ErrorError3.3. HypothesisHypothesis

4.4. Null hypothesisNull hypothesis5.5. Confidence intervalConfidence interval


23/68

Level of significantLevel of significant

p valuep value

PopulationPopulation

SampleSample

Paired and unpairedPaired and unpaired

samplessamples


24/68

RememberRememberThe phraseThe phrase

statistically significantstatistically significant

isisseductiveseductive

andand

isis

oftenoften misinterpretedmisinterpreted..


25/68


isisat the interfaceat the interface

ofofmathematicsmathematics

andandsciencescience


26/68

HoweverHoweverYou can learnYou can learn

toto useuse

statistical teststatistical test

and interpretand interpretthe resultsthe results

eveneven

if you dont fully understandif you dont fully understand

how they work.how they work.


27/68

Inductiv

e reasoningInductiv

e reasoning


28/68

often describedoften describedasas

"going from the specific"going from the specificto the general."to the general."

ANDANDIt is based onIt is based on


29/68

observingobserving

specific instancesspecific instancesof a certain qualityof a certain quality

in individual membersin individual members

of a group ofof a group of

1.1. peoplepeople

2.2. animals oranimals or

3.3. eventsevents


30/68

notingnoting

the individual membersthe individual members

in whichin which

a certain qualitya certain quality

occursoccurs

belong to a certain groupbelong to a certain group


31/68

generalizinggeneralizing

to the conclusionto the conclusion

thatthat

other membersother members

of that groupof that group

have the same quality.have the same quality.


32/68

For exampleFor example

if you were to go to a cat show,if you were to go to a cat show,you would see many breedsyou would see many breeds

of cats with tails.of cats with tails.

After walking up and down,After walking up and down,

you might begin to noticeyou might begin to notice

a pattern,a pattern,and your reasoningand your reasoning

might go something like this:might go something like this:


33/68

Siamese cats have tails.Siamese cats have tails.

Persian cats have tails.Persian cats have tails.

Himalayan cats have tails.Himalayan cats have tails.

Russian Blues have tails.Russian Blues have tails.American Tabbies have tails.American Tabbies have tails.


34/68

Aftera while, you would probablyAftera while, you would probably

cometo theconclusioncometo theconclusion --

All catsAll cats

have tailshave tails


35/68

The problem with thisThe problem with this

conclusion isconclusion isthat it isn't true.that it isn't true.

TheThe manxmanxis one breed of catis one breed of cat

that has no tail.that has no tail.


36/68

So the conclusionSo the conclusion

ofof

an inductive argumentan inductive argumentcan be shown to be wrongcan be shown to be wrong

if only one instanceif only one instance

does not fitdoes not fit

the general pattern.the general pattern.


37/68

TheTheManxManx isaisabreedbreed ofcats withanaturallyofcats withanaturally

occurringoccurring mutationmutation oftheofthespinespine..


38/68

ForthisreasonForthisreasonthe result ofthe result of

anan inductive argumentinductive argument

is never consideredis never considered

to be TRUE or FALSEto be TRUE or FALSE

insteadinstead

we refer to the conclusions reachedwe refer to the conclusions reachedthroughthrough

inductive reasoninginductive reasoning

asas

MORE ORLESSRELIABLE.MORE ORLESSRELIABLE.


39/68

Before proceeding,thinkaboutthisBefore proceeding,thinkaboutthis

question:question:

What would make theWhat would make theconclusion from an inductiveconclusion from an inductive

argument MORE reliable?argument MORE reliable?


40/68

Ininductivereasoning,Ininductivereasoning,

the morethe more specificspecific instancesinstances

you observe,you observe,

the more reliablethe more reliable

your conclusion.your conclusion.


41/68

BecauseBecause

the conclusion fromthe conclusion from

an inductive argumentan inductive argument

cannot be consideredcannot be considered

true or falsetrue or falsethe conclusion must be qualified.the conclusion must be qualified.


42/68

TheconclusionTheconclusion

from your observations about catsfrom your observations about catsand their tails might be qualifiedand their tails might be qualified

in one of the following ways:in one of the following ways:


43/68


44/68

A conclusionA conclusion

that isthat is

more or lessmore or less

reliablereliableThe more specific instancesThe more specific instances

observedobserved

the more reliable the conclusion.the more reliable the conclusion.


45/68


46/68

Inductive Reasoningallows you to learnallows you to learn

something newsomething new

about the world.about the world.

Deductive Reasoningallows you to apply whatallows you to apply what

you have learned.you have learned.


47/68


48/68

The first premiseThe first premise

("All men are mortal.")("All men are mortal.")

is the resultis the result

ofof

inductive reasoning.inductive reasoning.


49/68

The second premiseThe second premiseidentifiesidentifies

a specific membera specific member

of that group (Abdullah).of that group (Abdullah).


50/68


51/68

In order for the conclusionIn order for the conclusion

ofof

a deductive reasoning processa deductive reasoning process

to be true,to be true,

all of its premisesall of its premises

must be true.must be true.

..


52/68

Most peopleMost people

would agreewould agree

thatthat

the first premise giventhe first premise given

is true.is true.


53/68

Most peopleMost people

would also agreewould also agree

thatthat

the second premisethe second premise

given is truegiven is true


54/68

IF both of the premises are true,IF both of the premises are true,

thenthenthe conclusion must also be truethe conclusion must also be true

if and only if it follows necessarilyif and only if it follows necessarily

fromfromthe informationthe information

given in the premises.given in the premises.


55/68

SupposeSuppose

we return to our observationswe return to our observations

about catsabout cats

and their tailsand their tails

and the conclusionand the conclusionwe arrived atwe arrived at

by usingby using

inductive reasoning:inductive reasoning:


56/68

Most cats haveMost cats have

tails.tails.

Remember that thisRemember that this

conclusion had to beconclusion had to bequalified.qualified.

Ra is a cat.Ra is a cat. I could show you pictures.I could show you pictures.

Ra has a tail.Ra has a tail. Therefore,Therefore,

this conclusionthis conclusion

follow necessarily?follow necessarily?


57/68

A trick question:A trick question:

When it rains, the streets get wet.When it rains, the streets get wet.

The streets are wet.The streets are wet.

Therefore,Therefore,

it has been raining.it has been raining.

Is the conclusion valid?Is the conclusion valid?

Why or why not?Why or why not?


58/68

Theconclusionto thattrickTheconclusionto thattrick

questionis NOT valid:questionis NOT valid:

When it rains, the streets getWhen it rains, the streets getwet.wet.

The streets are wet.The streets are wet.

Therefore, it has been raining.Therefore, it has been raining.


59/68

The conclusion of a deductiveThe conclusion of a deductive

argument must follow necessarilyargument must follow necessarilyfrom the argument's premises;from the argument's premises;however, the first premise in thishowever, the first premise in thisargument is a conditional statement.argument is a conditional statement.

(It gives a condition under which(It gives a condition under whichsomething becomes true.) Thesomething becomes true.) Thestatement can be restated like this:statement can be restated like this:


60/68

IF it rains,IF it rains,

THENTHEN

the streets get wet.the streets get wet.


61/68

The problem withtheconclusionThe problem withtheconclusion

from theaboveargumentfrom theaboveargument

isthatthereare otherconditionsisthatthereare otherconditionswhich may causethestreetsto get wet:which may causethestreetsto get wet:


62/68

snow, sleet or other forms ofsnow, sleet or other forms ofprecipitation besides rainprecipitation besides rain

fire hydrants being openedfire hydrants being opened

people washing their cars in the streetspeople washing their cars in the streets

floodingflooding


63/68


64/68

Giving the second part of aGiving the second part of aconditional statementconditional statement

(the THEN part),(the THEN part),results inresults in

an invalid argument.an invalid argument.


65/68

Anotherway of looking atthisAnotherway of looking atthis

problem isto thinkinterms ofproblem isto thinkinterms of

our firstargumentour firstargument(about Abdullah):(about Abdullah):


66/68

Step in ProcessStep in Process SocratesSocratesArgumentArgument

Rain ArgumentRain Argument

Identify a sharedIdentify a sharedquality of the set:quality of the set:

All men areAll men aremortalmortal

All rainy daysAll rainy dayscause the streetscause the streetsto get wet.to get wet.

Identify a memberIdentify a memberof the set:of the set:

Abdullah is a manAbdullah is a man It is raining today.It is raining today.

Valid conclusion:Valid conclusion: Abdullah isAbdullah ismortal.mortal.

The streets areThe streets arewet.wet.


67/68

All men are mortal.All men are mortal.

Abdullah is mortal.Abdullah is mortal.

Therefore,Therefore,Abdullah is a man.Abdullah is a man.


68/68

Thisconclusion doesnot followThisconclusion doesnot follow necessarilynecessarily

from the premisesfrom the premises

becausebecause

Abdullahcould beAbdullahcould be

acat,acat,

a mule,a mule,a dog,a dog,

orany other living thing.orany other living thing.

statistic introduction

Documents