research hypothesis.ppt

Hypothesis

1. Course Instructor
Dr. Rupasi Tiwari
Pr. Scientist and Incharge ATIC
ICAR-Indian Veterinary Research Institute
Izatnagar, UP-243122, India

2. HYPOTHESIS:
Aftertheproblemhasbeenformulated,thehypothesisisderived
fromtheproblem.
•Itisatentativeanswertotheresearchquestionoran
educatedguessoftheresearchoutcome.
•Ahypothesisisaconjecturalstatementoftherelation
betweentwoormorevariables.
•Itisatentativeanswertotheresearchquestionoran
educatedguessoftheresearchoutcome.
•
•Itindicatestheexpectationsoftheresearcherregarding
certainvariables.
•Itisthemostspecificwayinwhichananswertoaproblem
canbestated.

3. HYPOTHESIS:
greek-hypotithenai
meaning"toputunder"or"tosuppose.
A hypothesis is a logical supposition, a
reasonable guess, an educated
conjecture.
A hypothesis states what we are
looking for and it is a proposition
which can be put to a test to
determine it’s validity.

4. Definitions :
Ahypothesismaybepreciselydefinedasa
tentativepropositionsuggestedasasolution
toaproblemorasanexplanationofsome
phenomenon.(Ary,JacobsandRazavieh,
1984)
Ahypothesisisaconjecturalstatementofthe
relationbetweentwoormorevariables.
(Kerlinger,1956)
Hypothesisisaformalstatementthat
presentstheexpectedrelationshipbetween
anindependentanddependentvariable.
(Creswell,1994)

5. Definitions :
Ahypothesisisatentativegeneralization,the
validityofwhichremainstobetested.Initsmost
elementarystage,thehypothesismaybeany
hunchguess,imaginativeideawhichbecomesthe
basisforactionforactionorinvestigation.
(Lundberg,G.A.)
Hypothesisasapropositionstatinginatestable
formtherelationshipbetweentwoormore
variables,andaconjecturalstatementofthe
relationshipbetweentwoormorevariables.
Onyeogi(2000)
Hypothesisisastatementpostulatingapossible
relationshipbetweentwoormorephenomenaor
variables.Mouton's(1990)

6. Hypothesis
It is tentative statement: May be generalization about social
phenomena. The generalization is unknown, the validity of
the statement is unknown, it is never correct or wrong. You
may either support the statement or refute it.
It is sometimes called a hunch, guess or an intuition it
indicates that with your own intuition hypothesis can be
formulated.
◦Intution= comes from with in that’s likely to happen
◦Hunch= a floating idea
◦Guess=Anticipation
It is a preposition. You propose it based on something
Hypothesis aims at explaining casual relationships. It is in
fact an indispensable tool of the research process and
enables one to restrict and streamline one‘s search for the
ultimate solution to the research problem under investigation.

7. Salient differences between research
problem and hypothesis
ResearchProblem Hypothesis
Problemisaquestionandisnot
testable
Hypothesescanbetested
Itistheoriginofhypothesis Itisderivedfromproblem
Itistheproblemofresearch Itisthesuggestedsolution
Relationbetweenvariablesin
problemstatements
Relationbetweenvariablesin
hypotheses
IsArelatedtoB? IfA,thenB.
HowareAandBrelatedtoC? IfA&BthenC.
HowisArelatedtoBunder
conditionsCandD?
IfA,thenBunderconditionsCand
D.

8. Sources:
Professional journals
Creative thinking
Conversation and discussion with peer & senior
researchers.
Deduction from theories
Experience of researcher himself
Review of literature
Pilot studies
Based on chance-intuition
Findings of another study
One's own experience.
Study and review of research literature pertaining to
the problem..Books, journals, theses directories,
encyclopedia etc..

9. Generation of research
hypothesis:
Initial ideas
(undeveloped
)
Literature
review
Initial
observation
s
Problem
statement
Research
hypothesis
Operational
definitions of
constructs

10. Importance :
Itformsthestartingpointofinvestigation.
Itmakesobservationandexperimentpossible.
Itgivespointstoenquiryandhelpsin
decidingthedirectioninwhichtoproceed.
Ithelpsinselectingpertinentfacts.
Itoffersexplanationsfortherelationships
betweenthosevariablesthatcanbe
empiricallytested.
Itfurnishesproofthattheresearcherhas
sufficientbackgroundknowledgetoenable
him/hertomakesuggestionsinorderto
extendexistingknowledge.
Itguidestheresearch.

11. Importance
Itprovidestheinvestigatorwitharelationalstatementthatis
directlytestableinaresearchstudy.
Thehypothesishelpsaninvestigatortocollecttherightkindsof
dataneededfortheinvestigation.
Itprovidesaframeworkforreportingconclusionsofthestudy.
Itensurestheoptimaluseofresearcher‘svaluabletimeand
otherscarceresourcesbylimitingthescopeoftheinquiry.
Ittransformsresearchquestionsintotestablepropositions.
Itsuggeststhemostappropriatemethodsandtoolsforthe
analysisofdata.
Infact,conclusionsaredirectresponsetothehypothesis
formulatedforthestudyasconfirmedordiscontinuedbydata
analysis.

12. Characteristics of Hypothesis

13. 1. Simple, understandable
terms
Asimplehypothesiscontainsonepredictorandoneoutcome
variable,e.g.positivefamilyhistoryofschizophreniaincreases
theriskofdevelopingtheconditioninfirst-degreerelatives.
Herethesinglepredictorvariableispositivefamilyhistoryof
schizophreniaandtheoutcomevariableisschizophrenia.
Acomplexhypothesiscontainsmorethanonepredictor
variableormorethanoneoutcomevariable,e.g.,apositive
familyhistoryandstressfullifeeventsareassociatedwithan
increasedincidenceofAlzheimer’sdisease.
Herethereare2predictorvariables,i.e.,positivefamilyhistory
andstressfullifeevents,whileoneoutcomevariable,i.e.,
Alzheimer’sdisease.
Complexhypothesislikethiscannotbeeasilytestedwitha
singlestatisticaltestandshouldalwaysbeseparatedinto2or
moresimplehypotheses.

14. 2. It should be specific
Aspecifichypothesisleavesnoambiguityaboutthesubjects
andvariables,orabouthowthetestofstatisticalsignificance
willbeapplied.
Itusesconciseoperationaldefinitionsthatsummarizethe
natureandsourceofthesubjectsandtheapproachto
measuringvariables(Historyofmedicationwithtranquilizers,
asmeasuredbyreviewofmedicalstorerecordsand
physicians’prescriptionsinthepastyear,ismorecommonin
patientswhoattemptedsuicidesthanincontrolshospitalized
forotherconditions).
Thisisalong-windedsentence,butitexplicitlystatesthe
natureofpredictorandoutcomevariables,howtheywillbe
measuredandtheresearchhypothesis.Oftenthesedetails
maybeincludedinthestudyproposalandmaynotbestated
intheresearchhypothesis.However,theyshouldbeclearin
themindoftheinvestigatorwhileconceptualizingthestudy.

15. 3. Hypothesis should be
stated in advance
Thehypothesismustbestatedinwritingduringthe
proposalstate.
Thiswillhelptokeeptheresearcheffortfocused
ontheprimaryobjectiveandcreateastronger
basisforinterpretingthestudy’sresultsas
comparedtoahypothesisthatemergesasaresult
ofinspectingthedata.
Thehabitofposthochypothesistesting(common
amongresearchers)isnothingbutusingthird-
degreemethodsonthedata(datadredging),to
yieldatleastsomethingsignificant.
Thisleadstooverratingtheoccasionalchance
associationsinthestudy.

16. Other Characteristics
4.Itshouldhaveelucidatingpowerandshouldbeableto
furnishanacceptableexplanationofthephenomenon.
5.Itmustbecapableofempiricaltesting
6.Itshouldbeconsistentwithrelevantobjectivesofresearch
andmustbestatedinamannerwhichprovidesdirectionfor
theresearch.
7.A Hypothesis must be conceptually clear -concepts should
be clearly defined -the definitions should be commonly
accepted -the definitions should be easily communicable
8.The hypothesis should have empirical reference -Variables
in the hypothesis should be empirical realities -If they are
not it would not be possible to make the observation and
ultimately the test

17. Other Characteristics
A hypothesis should be related to available
techniques of research-Either the techniques are
already available or -The researcher should be in
a position to develop suitable techniques
The hypothesis should be related to a body of
theory -Hypothesis has to be supported by
theoretical argumentation -It should depend on the
existing body of knowledge. In this way the study
could benefit from the existing knowledge and later
on through testing the hypothesis could contribute
to the reservoir of knowledge

18. Some examples of hypothesis
The productivity and production level in the poultry farms is
poor due to unawareness about improved methods.
There exists in the country improved methods of poultry
production which, if used by the producers would increase
their profit.
Farmers have not adopted new methods because they are
unaware of their existence.
Farmers are unable to obtain new technologies due to
financial limitations.
Special credit sources are necessary if farmers are to adopt
improved methods of production
Farmers are unable to obtain credit which limit their ability to
finance changes in production methods.
Eggpricestabilizationprogrammecouldinducefarmersto
adoptimprovedmethodsofproduction.

19. Categorizing Hypotheses
Can be categorized in different ways
1. Based on their formulation
: Null Hypotheses and Alternate Hypotheses
2. Based on direction:
Directional and Non-directional Hypothesis
3. Based on their derivation
Inductive and Deductive Hypotheses

20. Categorizing Hypotheses
(Cont…)
1. Null Hypotheses and Alternate Hypotheses
Nullhypothesisalwayspredictsthatnodifferences
betweenthegroupsbeingstudied(e.g.,
experimentalvs.controlgroup)ornorelationship
betweenthevariablesbeingstudied
Bycontrast,thealternatehypothesisalways
predictsthattherewillbeadifferencebetweenthe
groupsbeingstudied(orarelationshipbetweenthe
variablesbeingstudied)

21. Null Hypothesis
•Itisaconcisewaytoexpressthetestingofobtained
dataagainstchanceexpectations.
•Thenullhypothesisisapropositionthatstipulatesthat
therewouldbenorelationshipordifferencebetween
thevariablesbeingstudiedandthatanysuch
relationshipordifferenceiffoundtoexistdoesso
accidentallyorasaresultofchance.
•Thisisreverseofresearchhypothesis.
•NullHypothesisisusedagainstresearchhypothesis
withawaytoapproveitorrejectit.
•Itisahypothesisofnodifference.Nullmeanzero,
whenahypothesisisstatednegatively.

22. Null Hypothesis
•Theobjectiveofthehypothesisistoavoidthepersonalbiasof
theinvestigatorinthematterofcollectionofdata.
•Anullhypothesisisusedtocollectadditionalsupportforthe
knownhypothesis.
•Thestandarderrorisameansoftestingthenullhypothesis.It
expressesthenullhypothesissinceitisameasureofexpected
chancefluctuationaroundthemeanzero.
•Itisveryusefultoolintestingthesignificanceofdifference.Inits
simplestformthehypothesisassertsthatthereisnoreal
differenceinthesampleandthepopulationintheparticular
matterunderconsideration.
Forexampleanullhypothesis:“Thereisnodifferenceinthemilk
hygieneamongthefarmsoflivestockownerswhohaveundergone
thecleanmilkproductiontrainingsthanthosewhohavenotattended
suchtrainings”

23. Example:
H
0 : There is no difference in the
academic performance of high school
students who participate in
extracurricular activities and those
who do not participate in such
activities.
H
1:The academic performance of high
school students is related to their
participation in extracurricular
activities.
(non directional )

24. Research Hypothesis
•ThisiscalledWorkingHypothesisorSpecificHypothesis.
•Anyhypothesiswhichiscomplementarytothenullhypothesisis
calledanalternativehypothesisandisusuallydenotedbyH1.
•Suchhypothesisarethestatementaboutrealityofthingsand
theirrealitiesarederivedfromtheoriesandthesepertainto
socialphenomena.
•Thesespecifytheresearcher‘sexpectationofhis/herempirical
test.
•Theseindicatethatarelationshipordifferenceexistsbetween
twovariablesorgroupsandgoesfurthertostatethenatureor
directionofthatrelationshipordifferences.Thesearethe
hypothesiswhichcanbeconfirmatoryornon-confirmatoryyou
havetotestit.
•Thesecouldbeoftwotypes:Directionalandnondirectional.

25. Categorizing Hypotheses
(Cont…)
Alternate Hypothesis can further be classified as
2. Directional Hypothesis and Non-directional
Hypothesis
Simplybasedonthewordingofthehypotheseswecantell
thedifferencebetweendirectionalandnon-directional
Ifthehypothesissimplypredictsthattherewillbeadifference
betweenthetwogroups,thenitisanon-directional
hypothesis.
Itisnon-directionalbecauseitpredictsthattherewillbea
differencebutdoesnotspecifyhowthegroupswilldiffer.
If,however,thehypothesisusesso-calledcomparisonterms,
suchas“greater,”“less,”“better,”or“worse,”thenitisa
directionalhypothesis.
Itisdirectionalbecauseitpredictsthattherewillbea
differencebetweenthetwogroupsanditspecifieshowthe
twogroupswillperform.

26. Directional /Non Directional
Hypothesis
•Forexample:IfAisvalid,Bfollows...orIfyoushoutintheclassthe
teacherwillpunishyouorTrainingswhereintheteacherismoreofa
facilitatorandfriendlyleadstohigherlearningamongthetraineesthan
thosewhereintheteacherisnotfriendly.
•Thesesamehypothesiscanbestatedinanondirectionalmanner.
•Therewillbeasignificantdifferencebetweenthelearninglevelsof
traineeswhohaveattendedtrainingswithafriendlyteacherandthose
whohaveattendedtrainingswithanotsofriendlyone.
•Anotherhypothesiscouldbethat“Milkhygieneinthefarmsoflivestock
ownerswhohaveundergonethecleanmilkproductiontrainingsis
differentthanthosewhohavenotattendedsuchtrainings”

27. Example
Directional :
specifies the direction of expected
findings
Eg: Students with high IQ will exhibit
more anxiety than students with low IQ”
Non-directional:
no definite direction of the expected
findings is specified.
Eg: There is a difference in the anxiety
level of the children of high IQ and those
of low IQ.”

28. Categorizing Hypotheses
(Cont…)
Inductive and Deductive
Hypotheses(TheoryBuildingandTheoryTesting)
classifiedintermsofhowtheywerederived:-
Inductivehypothesis-ageneralizationbasedon
observation-
Observation-Pattern-Hypothesis-Theory
Deductive hypothesis -derived from theory
Theory-Hypothesis-Observation-Confirmation

29. Deductive and Inductive
procedure
Deductive Inductive
1.Deductivereasoninghappens
whenaresearcherworksfrom
themoregeneralinformationto
themorespecific.
2.Sometimesthisiscalledthe“top-
down”approach.Becausethe
researcherstartsatthetopwitha
verybroadspectrum of
informationandtheyworktheir
waydowntoaspecific
conclusion.
3.Forinstance,aresearchermight
beginwithatheoryabouthisor
hertopicofinterest.Fromthere,
heorshewouldnarrowthatdown
intomorespecifichypotheses
thatcanbetested
1.Inductivereasoningworksthe
oppositeway,movingfrom
specificobservationsto
broadergeneralizationsand
theories.
2.Thisissometimescalleda
“bottomup”approach.
3.Theresearcherbeginswith
specificobservationsand
measures,beginstothen
detect patterns and
regularities,formulatesome
tentativehypotheses to
explore,andfinallyendsup
developingsome general
conclusionsortheories.

30. Deductive and Inductive
procedure
Deductive
The hypotheses are then narrowed
down even further when
observations are collected to test
the hypotheses.
This ultimately leads the researcher
to be able to test the hypotheses
with specific data, leading to a
confirmation (or not) of the original
theory and arriving at a conclusion.

31. Deductive and Inductive
procedure
Deductive Inductive
An example of deductive reasoning
can be seen in this set of
statements:
Every day, I leave for work in my
car at eight o’clock.
Every day, the drive to work takes
45 minutes I arrive to work on time.
Therefore, if I leave for work at
eight o’clock today, I will be on
time.
An example of inductive reasoning
can be seen in this set of
statements:
Today, I left for work at eight o’clock
and I arrived on time.
Therefore, every day that I leave
the house at eight o’clock, I will
arrive to work on time.

32. Deductive and Inductive
procedure
Theory Theory
↓ ↑
Hypothesis Hypothesis
↓ ↑
Observation Pattern
↓ ↑
Confirmation Observation
Deduction Reasoning Induction Reasoning
Inductive reasoning is open-ended and
exploratory especially at the beginning.
Newton reached to "Law of Gravitation"
from "apple and his head” observation").
In a conclusion, when we use Induction
we observe a number of specific
instances and from them infer a general
principle or law.
Deductivereasoningis
narrowinnatureandis
concernedwithtestingor
confirminghypothesis.

33. Problems in Formulating
Hypothesis
Therearesometimesprobleminformulation
hypothesis.Thismaybedueto:
•Clearabsenceoftheoreticalframework
•Lackofabilityofresearcher
•ResearchTechniques:Researcherisnot
familiarwiththeresearchtechniqueornot
wellacquaintedtotheavailableresearch
techniques.

34. Basics of hypothesis testing:
•Hypothesis testing or significance testing is
a method for testing a claim or hypothesis
about a parameter in a population, using
data measured in a sample.
•It involves:
•Formulation of hypothesis
•setting up a criterion for decision
•determining the test statstic
•making the decision

35. Example
Ahypothesis(forexample,Tamiflu[oseltamivir],drugofchoicein
H1N1influenza,isassociatedwithanincreasedincidenceofacute
psychoticmanifestations)iseithertrueorfalseintherealworld.
Becausetheinvestigatorcannotstudyallpeoplewhoareatrisk,he
musttestthehypothesisinasampleofthattargetpopulation.
Nomatterhowmanydataaresearchercollects,hecannever
absolutelyprove(ordisprove)hishypothesis.
Therewillalwaysbeaneedtodrawinferencesaboutphenomenain
thepopulationfromeventsobservedinthesample(Hulleyetal.,
2001).
Insomeways,theinvestigator’sproblemissimilartothatfacedbya
judgejudgingadefendant
Theabsolutetruthwhetherthedefendantcommittedthecrime
cannotbedetermined.
Instead,thejudgebeginsbypresuminginnocence—thedefendant
didnotcommitthecrime.

36. Example Contd….
Thejudgemustdecidewhetherthereissufficientevidenceto
rejectthepresumedinnocenceofthedefendant;thestandard
isknownasbeyondareasonabledoubt.
Ajudgecanerr,however,byconvictingadefendantwhois
innocent,orbyfailingtoconvictonewhoisactuallyguilty.
Insimilarfashion,theinvestigatorstartsbypresumingthenull
hypothesis,ornoassociationbetweenthepredictorand
outcomevariablesinthepopulation.
Basedonthedatacollectedinhissample,theinvestigator
usesstatisticalteststodeterminewhetherthereissufficient
evidencetorejectthenullhypothesisinfavorofthe
alternativehypothesisthatthereisanassociationinthe
population.
Thestandardforthesetestsisshownasthelevelof
statisticalsignificance.

37. Hypothesis testing
Hypothesistestingisoftenreferredtoas
significancetesting.
Atestofsignificanceisconductedby
comparingthevaluesofastatistics
computedfromasamplewithvalues
predictedbythesamplingdistributionunder
theassumptionthatthenullhypothesisis
true.
Testsaremadeatessentiallyarbitrary
levelsofsignificance,usuallythe5percent
orthe1percentlevel.

38. Level of Significance
Foradifferencetobetakenasstatistically
significantornot,theprobabilitythatthegiven
differencecouldhavearisen―bychancemustbe
ascertained.
Beforetheinvestigatormakesajudgmentof
significanceornon-significance,somecritical
point(s)mustbedesignatedalongtheprobability
scalewhichwillservetoseparatethesetwo
judgmentcategories.
Forconvenience,researchershavechosen
severalarbitrarystandardscalledlevelof
significanceofwhichthe0.05and0.01levelsare
mostoftenused.
Theconfidencewithwhicharesearcherrejectsor
acceptsanullhypothesisdependsuponthelevel

39. Level of Significance
Suchlevelofsignificancemusthavebeensetbeforeshe
collectshis/herdata.Itisnotagoodpracticetoshiftfroma
highertoalowerlevelafterdatahavebeencollected.The
0.01levelofsignificanceismoreexactingthan0.05level.
Themaximumprobabilityatwhichwewouldbewillingtorisk
atype-1errorisknownasthelevelofsignificance.
Ingeneral5%and1%aretakenaslevelofsignificance,
therebyindicatingthatonanaveragewemaygowrong5out
of100casesand1outof100casesrespectively.
Tosay5%levelofsignificance,thereis95%confidencein
theresultwithamarginoferror5%.

40. Types of Errors
Hypothesis testing involves risks because answers are
provided in terms of probability.
Nobody is absolutely sure that the observed differences or
relationships between two variables are not due to chance.
The probability value (p-value) is an indication of the odds
against the results of the study occurring by chance.
There is the chance that the results obtained might have
been influenced by force other than the ones provided for in
the study.
Therefore, the Null hypothesis may be rejected when it
should in reality be accepted.
Alternatively, the Null hypothesis may not be rejected when
in reality it should have been rejected.

41. Types of Errors
Type I Errors
These errors are made when the researcher rejects a Null
hypothesis by making a difference or relationship significant,
although no true difference or relationship exists. In other words,
Type I error is committed by rejecting Null hypothesis when it is true,
thereby making a non-significant difference or relationship to appear
to be significant. The probability of rejecting a hypothesis(Ho) when
it is true. (also called level of significance/critical region) is Type I
error.
Type II error: These errors are made when a researcher accepts a
Null hypothesis by making a difference or relationship not significant,
when a true difference or relationship actually exists. In other Words,
Type II error is committed by accepting Null hypothesis when it is not
true, thereby making a significant difference or relationship to appear
to be non-significant. The probability of accepting a hypothesis(Ho)
when it is false is Type –II error

42. Example of Type-I error
Forexample,inaclinicaltrialofanewdrug,thenull
hypothesismightbethatthenewdrugisnobetter,on
average,thanthecurrentdrug;i.e.H0:thereisnodifference
betweenthetwodrugsonaverage.AtypeIerrorwouldoccur
ifweconcludedthatthetwodrugsproduceddifferenteffects
wheninfacttherewasnodifference
AtypeIerrorisoftenconsideredtobemoreserious,and
thereforemoreimportanttoavoid,thanatypeIIerror.
Thehypothesistestprocedureisthereforeadjustedsothat
thereisaguaranteed'low'probabilityofrejectingthenull
hypothesiswrongly;thisprobabilityisnever0.
ThisprobabilityofatypeIerrorcanbepreciselycomputedas
P(typeIerror)=significancelevel=

43. Example of Type-II errors
Forexample,inaclinicaltrialofanewdrug,thenull
hypothesismightbethatthenewdrugisnobetter,on
average,thanthecurrentdrug;i.e.H0:thereisnodifference
betweenthetwodrugsonaverage.
AtypeIIerrorwouldoccurifitwasconcludedthatthetwo
drugsproducedthesameeffect,i.e.thereisnodifference
betweenthetwodrugsonaverage,wheninfactthey
produceddifferentones.
AtypeIIerrorisfrequentlyduetosamplesizesbeingtoo
small.
TheprobabilityofatypeIIerrorisgenerallyunknown,butis
symbolisedbyandwrittenP(typeIIerror)=

44. Errors
Decision
AcceptHo RejectHo
Ho(True) Correct
Decision
TypeIerror(α
error)
Ho(False) TypeIIerror(β
error)
Correct
Decision

45. Ways to Reduce Type-I and II
errors
Wheneverthesignificanceisdoubtfuloruncertain,thebest
waytoguideagainstbothtypesoferroneousinferenceisto
demandorseekmoreevidence.Additionaldata,repetitionof
theexperimentandbettercontrolswilloftenmakepossiblea
correctjudgment.
SettingahighlevelofsignificancetendstopreventTypeI
errorsbutencouragetheappearanceofTypeIIerrors.The
advisegivenisthattheresearchermustdecideonwhichkind
ofwronginferencehe/shewouldratheravoid,asapparently
he/shecanpreventonetypeoferroronlyattheriskof
makingtheothermorelikely.
Themostgenerallyacceptablepracticeistosetlevelof
significanceofatleast0.01inmostexperimentalresearch,
thatis,toriskTypeIIerrorsbypreventingthoseofTypeI.
However,ithasbeenexpressedthat0.05levelofsignificance
isoftensatisfactory,especiallyonpreliminarywork.

46. Power of Test
The power of a statistical hypothesis test measures
the test's ability to reject the null hypothesis when it
is actually false -that is, to make a correct
decision.
In other words, the power of a hypothesis test is
the probability of not committing a type II error. It is
calculated by subtracting the probability of a type II
error from 1, usually expressed as: Power = 1 -
P(type II error) =
The maximum power a test can have is 1, the
minimum is 0.
Ideally we want a test to have high power, close to
1.

47. Test Statistic
A test statistic is a quantity calculated
from our sample of data. Its value is
used to decide whether or not the null
hypothesis should be rejected in our
hypothesis test.
The choice of a test statistic will
depend on the assumed probability
model and the hypotheses under
question.

48. Critical Value(s)
The critical value(s) for a hypothesis
test is a threshold to which the value
of the test statistic in a sample is
compared to determine whether or not
the null hypothesis is rejected.
The critical value for any hypothesis
test depends on the significance level
at which the test is carried out, and
whether the test is one-sided or two-
sided.

49. Critical Region
ThecriticalregionCR,orrejectionregionRR,isa
setofvaluesoftheteststatisticforwhichthenull
hypothesisisrejectedinahypothesistest.
Thatis,thesamplespacefortheteststatisticis
partitionedintotworegions;oneregion(thecritical
region)willleadustorejectthenullhypothesisH0,
theotherwillnot.
So,iftheobservedvalueoftheteststatisticisa
memberofthecriticalregion,weconclude"Reject
H0";ifitisnotamemberofthecriticalregionthen
weconclude"DonotrejectH0".

50. Two tailed or one tailed test
Thecriticalregionmayberepresentedbyaportionofthearea
underthenormalcurveintwoways:-
Twotailedtest:Thetestofhypothesiswhichisusedoncritical
regionrepresentedbyboththetailsunderthenormalcurveiscalled
twotailedtest.Atwotailedtestappliedincaseswhereitis
consideredeitherapositiveornegativedifferencebetweenthe
samplemeanandthepopulationmeanistendingtowardsrejecting
ofthenullhypothesis.
Onetailedtest:Ifthecriticalregionisrepresentedbyonlyonetail
thetestiscalledonetailedtest.Theonetailedtestisappliedincase
whereitisconsideredthatthepopulationmeanisatleastaslarge
assomespecifiedvalueofthemeanoratleastassmallassome
specifiedvalueofthemean.Intheformercaserighttailtestis
appliedandthelattercaselefttailtestisapplied.

51. Tests of significance:
Two tailed tests:
Non directional tests, or two-tailedtests,
are hypothesis tests where the
alternative hypothesis is stated as not
equal to (≠).
Eg:H0: m = 558
Mean test scores are equal to 558 in the
population.
H1: m ≠ 558
Mean test scores are not equal to 558 in
the population.

52. For two-tailed tests, the alpha is split
in half and placed in each tail of a
standard normal distribution.
This decides the rejection region.
Rejection areas
Fail to reject H
0
Reject H
0 Reject H
0

53. One tailed test:
Directional tests, or one-tailed tests,
are hypothesis tests where the
alternative hypothesis is stated as
greater than (>) or less than (<) a
value stated in the null hypothesis .
Eg: H0: m = 558
H1: m > 558

54. For one-tailed tests, the alpha level is
placed in a single tail of a distribution.
The rejection region will lie on either
side.
Rejection area
Rejection area

55. Significance Level
Thesignificancelevelofastatisticalhypothesis
testisafixedprobabilityofwronglyrejectingthe
nullhypothesisH0,ifitisinfacttrue.
ItistheprobabilityofatypeIerrorandissetbythe
investigatorinrelationtotheconsequencesofsuch
anerror.Thatis,wewanttomakethesignificance
levelassmallaspossibleinordertoprotectthe
nullhypothesisandtoprevent,asfaraspossible,
theinvestigatorfrominadvertentlymakingfalse
claims.
Thesignificancelevelisusuallydenotedby
SignificanceLevel=P(typeIerror)=Alpha
Usually,thesignificancelevelischosentobe0.05
(orequivalently,5%).

56. p-value
Theprobabilityvalue(p-value)ofastatisticalhypothesistest
istheprobabilityofgettingavalueoftheteststatisticas
extremeasormoreextremethanthatobservedbychance
alone,ifthenullhypothesisH0,istrue.
Itistheprobabilityofwronglyrejectingthenullhypothesisifit
isinfacttrue.
Itisequaltothesignificancelevelofthetestforwhichwe
wouldonlyjustrejectthenullhypothesis.Thep-valueis
comparedwiththeactualsignificancelevelofourtestand,if
itissmaller,theresultissignificant.Thatis,ifthenull
hypothesisweretoberejectedatthe5%signficancelevel,
thiswouldbereportedas"p<0.05".
Smallp-valuessuggestthatthenullhypothesisisunlikelyto
betrue.Thesmalleritis,themoreconvincingistherejection
ofthenullhypothesis.Itindicatesthestrengthofevidencefor
say,rejectingthenullhypothesisH0,ratherthansimply
concluding"RejectH0'or"DonotrejectH0".

57. Negative Findings
Even if hypotheses are not confirmed, they
have power.(Kerlinger, 1956)
Negative findings are as important as positive
ones, since they cut down ignorance and
sometimes point up fruitful hypotheses and
lines of investigation.
It acts as a guiding factor for future research
in that field.
Hypothesis cannot be proved or disproved;
but only supported or not supported.