hypothesis testing research methodology

8/13/2019 Hypothesis Testing research methodology

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TYBMS Prof. Hemant Kombrabail

TESTING OF HYPOTHESES(Parametric or Standard Tests of Hypotheses)

Hypothesis is usually considered as the principal instrument in research. Its main function

is to suest ne! e"periments and obser#ations. In fact$ many e"periments arc carried out

!ith the deliberate ob%ect of testin hypotheses. &ecision'maers often face situations!herein they are interested in testin hypotheses on the basis of a#ailable information

and then tae decisions on the basis of such testin. In social science$ !here directno!lede of population parameter(s) is rare$ hypothesis testin is the often'used stratey

for decidin !hether a sample data offer such support for a hypothesis that eneraliation

can be made. Thus$ hypothesis testin enables us to mae probability statements about

population parameters). The hypothesis may not be pro#ed absolutely$ but in practice it isaccepted if it has !ithstood a critical testin. Before !e e"plain ho! hypotheses arc

tested throuh different tests meant for the purpose$ it !ill be appropriate to e"plain

clearly the meanin of a hypothesis and the related concepts for better understandin ofthe hypothesis testin techni*ues.

MEANING OF HYPOTHESIS

+rdinarily$ !hen one tals about hypothesis$ one simply means a mere assumption or

some supposition to be pro#ed or dispro#ed. But for a researcher hypothesis is a formal*uestion that he intends to resol#e. Thus a hypothesis may be defined as ,a proposition or

a set of propositions set forth as an e"planation for the occurrence of some specified

roup of phenomena either asserted merely as a pro#isional con%ecture to uide somein#estiation or accepted as hihly probable in the liht of established facts-. uite often

a research hypothesis is a predicti#e statement$ capable of bein tested by scientific

methods$ that relates an independent #ariable to some dependent #ariable. /or e"ample$consider statements lie the follo!in ones0

1Students !ho recei#e counselin !ill sho! a reater increase in creati#ity than students

not recei#in counselin1 or 1the automobileAis performin as !ell as automobileB.These are hypotheses capable of bein ob%ecti#ely #erified and tested. Thus$ !e may

conclude that a hypothesis states !hat !e are looin for and it is a proposition that can

be put to a test to determine its #alidity.

CHARACTERISTICS OF HYPOTHESIS

2 hypothesis must possess the follo!in characteristics0(i) Hypothesis should be clear and precise. If the hypothesis is not clear and precise$

the inferences dra!n on its basis cannot be taen as reliable.

(ii) Hypothesis should be capable of bein tested. In a s!amp of un'testablehypotheses$ many a time the research prorams ha#e boed do!n. 3esearcher may

do some prior study in order to mae hypothesis a testable one. 2 hypothesis 1is

testable if other deductions can be made from it !hich$ in turn$ can be confirmed or

dispro#ed by obser#ation.1(iii) Hypothesis should state relationship bet!een #ariables$ if it happens to be a

relational hypothesis

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(i#) Hypothesis should be limited in scope and must be specific. 2 researcher must

remember that narro!er hypotheses are enerally more testable and he should

de#elop such hypotheses(#) 3esearchers should state hypothesis as far as possible in most simple terms so that

the same is easily understandable by all concerned. But one must remember that

simplicity of hypothesis has nothin to do !ith its sinificance(#i) Hypothesis should be consistent !ith most no!n facts i e.$ it must be consistent

!ith a substantial body of established facts. In other !ords$ it should be one !hich

%udes accept as bein the most liely(#ii) Hypothesis should be amenable to testin !ithin a reasonable time.+ne should not

use e#en an e"cellent hypothesis$ if the same cannot be tested in reasonable time for

one cannot spend a life'time collectin data to test it

(#iii) Hypothesis must e"plain the facts that a#e rise to the need for e"planation. Thismeans that by usin the hypothesis plus other no!n and accepted eneraliations$

one should be able to deduce the oriinal problem condition. Thus hypothesis must

actually e"plain !hat it claims to e"plain5 it should ha#e empirical reference.

BASIC CONCEPTS CONCERNING TESTING OF HYPOTHESES

Basic concepts in the conte"t of testin of hypotheses need to be e"plained.

(a) Null hypothesis and alternatie hypothesis:In the conte"t of statistical analysis$ !e

often tal about null hypothesis and alternati#e hypothesis. If !e are to compare method

A!ith method Babout its superiority and if !e proceed on the assumption that bothmethods are e*ually ood$ then this assumption is termed as the null hypothesis. 2s

aainst this$ !e may thin that the method Ais superior or the methodBis inferior$ !e

are then statin !hat is termed as alternati#e hypothesis. The null hypothesis is enerallysymbolied as H6and the alternati#e hypothesis as Ha. Suppose !e !ant to test the

hypothesis that the population mean (.) is e*ual to the hypothesied mean (H6)=466.Then !e !ould say that the null hypothesis is that the population mean is e*ual to the

hypothesied mean 466 and symbolically !e can e"press as0

H60 7H67 466

If our sample results do not support this null hypothesis$ !e should conclude that

somethin else is true. 8hat !e conclude re%ectin the null hypothesis is no!n as

alternati#e hypothesis. In other !ords$ the set of alternati#es to the null hypothesis is

referred to as the alternati#e hypothesis. If !e acceptH0$ then !e are re%ectinHaand if

!e re%ect H0,then !e are acceptinHa./or H60 7H67466$ !e may consider threepossible alternati#e hypotheses as follo!s0

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cent ris of re%ectin the null hypothesis !hen it (Ho) happens to be true. Thus the

sinificance le#el is the ma"imum #alue of the probability of re%ectin H6!hen it is true

and is usually determined in ad#ance before testin the hypothesis.

(c) $e#ision rule or test o! hypothesis0 =i#en a hypothesis Ho and an alternati#e

hypothesis Ha$ !e mae a rule !hich is no!n as decision rule accordin to !hich !eaccept H6(i.e.$ re%ect Ha)or re%ect Ho(i.e.$ accept Ha). /or instance$ if H6is that a certain

lot is ood (there are #ery fe! defecti#e items in it) aainst Ha that the lot is not ood

(there are too many defecti#e items in it)5 then !e must decide the number of items to betested and the criterion for acceptin or re%ectin the hypothesis. 8e miht test 46 items

in the lot and plan our decision sayin that if there are none or only 4 defecti#e item

amon the 46$ !e !ill accept Hoother!ise !e !ill re%ect Ho(or accept Ha).This sort of

basis is no!n as decision rule.

(d) Type I and Type II errors: In the conte"t of testin of hypotheses$ there are

basically t!o types of errors !e can mae. 8e may re%ect H6!hen H6is true and !e may

accept H6!hen in fact H6is not true. The former is no!n as Type I error and the latteras Type II error. In other !ords$ Type I error means re%ection of hypothesis that should

ha#e been accepted and Type II error means acceptin the hypothesis$ !hich should ha#e

been re%ected. Type I error is denoted by (alpha) no!n as a error$ also called the le#el

of sinificance of test5 and Type II error'is denoted by (beta) no!n as 'error. In a

tabular form the said t!o errors can be presented as follo!s0

The probability of Type I error is usually determined in ad#ance and is understood as the

le#el of sinificance of testin the hypothesis. If type I error is fi"ed at ? percent$ itmeans that there are about ? chances in 466 that !e !ill re%ectH0!hen H6is true.8e

can control Type I error %ust by fi"in it at a lo!er le#el. /or instance$ if !e fi" it at 4 per

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cent$ !e !ill say that the ma"imum probability of committin Type I error !ould only be

6.64.

But !ith a fi"ed sample sie$ n,!hen !e try to reduce Type I error$ the probability ofcommittin Type II error increases. Both types of errors cannot be reduced

simultaneously. There is a trade'off bet!een these t!o types of errors$ !hich means that

the probability of main one type of error can only be reduced if !e are !illin toincrease the probability of main the other type of error. To deal !ith this trade'off in

business situations$ decision'maers decide the appropriate le#el of Type I error by

e"aminin the costs or penalties attached to both types of errors. If Type I error in#ol#esthe time and trouble of re!orin a batch of chemicals that should ha#e been accepted$

!hereas Type II error means tain a chance that an entire roup of users of this

chemical compound !ill be poisoned$ then in such a situation one should prefer a Type I

error to a Type II error. 2s a result one must set #ery hih le#el for Type I error in one:stestin techni*ue of a i#en hypothesis. Hence$ in the testin of hypothesis$ one must

mae all possible effort to strie an ade*uate balance bet!een Type I and Type II errors.

(e) T%o tailed and One&tailed tests: In the conte"t of hypothesis testin$ these t!o

terms are *uite important and must be clearly understood. 2 t!o'tailed test re%ects thenull hypothesis if$ say$ the sample mean is sinificantly hiher or lo!er than thehypothesied #alue of the mean of the population. Such a test is appropriate !hen the null

hypothesis is some specified #alue and the alternati#e hypothesis is a #alue not e*ual to

the specified #alue of the null hypothesis. Symbolically$ the t!o'tailed test is appropriate

!hen !e ha#e H60 7 H6and Ha0 H6!hich may mean


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/iure a

Mathematically !e can state0

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2cceptance 3eion 20 E F E'4.CD

3e%ection 3eion 30 E F E 4.CD

/iure b

Mathematically!e can state0

2cceptance 3eion 20 F('4.DA?

3e%ection 3eion 30 F ' 4.DA?

If our 7 466 and if our sample mean de#iates sinificantly from 466 in the lo!er

direction$ !e shall re%ect H6$ other!ise !e shall accept H6 at a certain le#el of

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sinificance. If the sinificance le#el in the i#en case is ept at ?@$ then the re%ection

reion !ill be e*ual to 6.6? of area in the left tail as has been sho!n in the abo#e cur#e.

In case ourH60 7 H6and Ha0 H6 !e are then interested in !hat is no!n as one'

tailed test (riht tail) and the re%ection reion !ill be on the riht tail of the cur#e as

sho!n belo!0

Mathematically !e can state0

2cceptance 3eion 20 F'4.DA?3e%ection 3eion 30 F4.DA?

If our 7 466 and if our sample mean de#iates sinificantly from 466 in the up!ard

direction$ !e shall re%ect H6other!ise !e shall accept the same If in the i#en case the

sinificance le#el is ept at ?@ then the re%ection reion !ill be e*ual to 6 6? of area inthe riht'tail as has been sho!n in the abo#e cur#e


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It should al!ays be remembered that acceptin H6on the basis of sample information

does not constitute the proof that H6 is true. 8e only mean that there is no statisticale#idence to re%ect it$ but !e are certainly not sayin that H 6is true (althouh !e beha#e

as ifH6is true)

PROCE$)RE FOR HYPOTHESIS TESTING

To test a hypothesis means to tell (on the basis of the data the researcher has collected)!hether or not the hypothesis seems to be #alid. In hypothesis testin the main *uestion

is0 !hether to accept the null hypothesis or not to accept the null hypothesis> Procedure

for hypothesis testin refers to all those steps that !e undertae for main a choice

bet!een the t!o actions i.e.$ re%ection and acceptance of a null hypothesis

The #arious steps in#ol#ed in hypothesis testin are stated belo!0

(i) Ma*in" a !or+al state+ent,The step consists in main a formal statement of the

null hypothesis (H6) and also of the alternati#e hypothesis (H a) This means thathypotheses should be clearly stated$ considerin the nature of the research problem

/or instance$ Mr. Mohan of the i#il Jnineerin &epartment !ants to test the loadbearin capacity of an old bride !hich must be more than 46 tons In that case he

can state his hypotheses as under0


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(d) !hether the hypothesis is directional or non'directional (2 directional hypothesis

is one !hich predicts the direction of the difference bet!een$ say$ means). In

brief$ the le#el of sinificance must be ade*uate in the conte"t of the purpose andnature of en*uiry.

(iii) $e#idin" the distri-ution to use,2fter decidin the le#el of sinificance$ the ne"tstep in hypothesis testin is to determine the appropriate samplin distribution The

choice enerally remains bet!een normal distribution and the t'distribution. The

rules for selectin the correct distribution are similar to those that !e ha#e statedearlier in the conte"t of estimation.

(i#) Sele#tin" a rando+ sa+ple and #o+putin" an appropriate alue, 2nother step is

to select a random sample(s) and compute an appropriate #alue from the sample dataconcernin the test statistic utiliin the rele#ant distribution. In other !ords$ dra! a

sample to furnish empirical data.

(#) Cal#ulation o! the pro-a-ility,+ne has then to calculate the probability that thesample result !ould di#ere as !idely as it has from e"pectations$ if the null

hypothesis !ere in fact true

(#i) Co+parin" the Pro-a-ility,Yet another step consists in comparin the probability

thus calculated !ith the specified #alue for $ the sinificance le#el If the calculated

probability is e*ual to or smaller than the #alue in case of one'tailed test (and 9

in case of t!o'tailed test)$ then re%ect the null hypothesis (i e$ accept the alternati#e

hypothesis)$ but if the calculated probability is reater$ then accept the null

hypothesis. In case !e re%ect H6,8e run a ris of (at most the le#el of sinificance)

committin an error of TypeI$but if !e accept H6,then !e run some ris (the sie of

!hich cannot be specified as lon as the H6 happens to be #aue rather than specific)of committin an error of Type II.

F.O/ $IAGRAM FOR HYPOTHESIS TESTING

The abo#e stated eneral procedure for hypothesis testin can also be depicted in the

form of a flo!'chart for better understandin as sho!n belo!0

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Tests o! Hypotheses

Hypothesis testin helps to decide on the basis of a sample data$ !hether a hypothesis

about the population is liely to be true or false. Statisticians ha#e de#eloped se#eral testsof hypotheses (also no!n as the tests of sinificance) for the purpose of testin of

hypotheses !hich can be classified as0

(a) Parametric tests or standard tests of hypotheses(b)


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can also be used for %udin the sinificance of the coefficients of simple and partial

correlations The rele#ant test statistic$ t$ is calculated from the sample data and then

compared !ith its probable #alue based on t'distribution (to be read from the table thati#es probable #alues of t for different le#els of sinificance for different derees of

freedom) at a specified le#el of sinificance for concernin derees of freedom for

acceptin or re%ectin the null hypothesis. It may be noted that t'test applies only in caseof small sample(s) !hen population #ariance is unno!n.

052 4&test or Chi&s6uare test9 ' testis based on chi's*uare distribution and as a parametric test is used for comparin

a sample #ariance to a theoretical population #ariance. 2s a non'parametric test$ it 1canbe used to determine if cateorical data sho!s dependency or if t!o classifications are

independent. It can also be used to mae comparisons bet!een theoretical populations

and actual data !hen cateories arc used.1 Thus$ the chi's*uare test is applicable in larenumber of problems. The test is$ in fact$ a techni*ue throuh the use of !hich it is

possible for all researchers to (i) test the oodness of fit (ii) test the sinificance of

association bet!een t!o attributes$ and (iii) test the homoeneity or the sinificance ofpopulation #ariance.

072 F&test8

/'test is based on /'distribution and is used to compare the #ariance of the t!o

independent samples. This test is also used in the conte"t of analysis of #ariance(2

hypothesis testing research methodology

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