testing of hypothesis i

8/3/2019 Testing of Hypothesis I

http://slidepdf.com/reader/full/testing-of-hypothesis-i 1/30

(Parametric or Standard Tests of Hypothesis)

5/1/20121

Testing of Hypothesis I

Rehna. V. J



Hypothesis

5/1/20122

Main function is to suggest newexperiments & observations

Decision makers test hypothesis on the

basis of available information and thentake decisions on the basis of suchtesting

Hypothesis testing enables us to makeprobability statements about populationparameters

The hypothesis may not be provedabsolutely, but in practice it is accepted



What is a Hypothesis?

5/1/20123

Hypothesis means a mere assumption orsome supposition to be proved or disproved

But for a researcher, hypothesis is a formal

question that he intends to resolve. A hypothesis may be defined as a proposition

or a set of proposition set forth as anexplanation for the occurrence of some

specified group of phenomena either assertedmerely as a provisional conjuncture to guidesome investigation or accepted as highlyprobable in the light of established facts



Example of a hypothesis capable of beingexperimentally verified and tested

5/1/20124

“Students who receive counseling will show agreater increase in creativity than students notreceiving counseling”

“Automobile A is performing as well asautomobile B”

We may conclude that a hypothesis states whatwe are looking for and it is a proposition which

can be put to test to determine its value.



Characteristics of Hypothesis

5/1/20125

Hypothesis must posses the following characteristics:

A hypothesis must be clear and precise. If not, the

inferences drawn on its basis cannot be taken asreliable

Hypothesis should be capable of being tested Hypothesis should state relationship between

variables

Hypothesis should be limited in scope and must be

specific. A researcher must remember that narrowerhypothesis are generally more testable and he shoulddevelop such hypothesis

Hypothesis should be stated as far as possible in

simple terms so that it is easily understandable by



Characteristics of Hypothesis

5/1/20126

Hypothesis must posses the followingcharacteristics:

Hypothesis should be possible to be tested

within a reasonable time. One cannot spenda lifetime collecting data to test it.

Hypothesis must explain the facts that giverise to the need for explanation.

Thus hypothesis must actually explain whatit claims to explain i.e. it should haveempirical reference.



Basic concepts concerning testing of

hypothesis.

5/1/20127

Null hypothesis or alternative hypothesis

The level of significance. Decision rule or test of hypothesis.

Type I and Type II errors.

Two-tailed and one-tailed test.



Basic concepts concerning testing ofhypothesis.

5/1/20128

Null hypothesis or alternative hypothesis:

If we are to compare method A with methodB about its superiority and if we proceed on

the assumption that both methods areequally good, thenA = B

This assumption is termed as the null

hypothesis. If method A is superior or if method B is

inferior then we are stating what is termedas alternative hypothesis.

The null hypothesis is symbolized as Ho and




5/1/20129

The null hypothesis and alternativehypothesis are chosen before the sample isdrawn.

In choice of null hypothesis, the followingconsiderations are usually kept in view : Alternative hypothesis is usually the one which

one wishes to prove and the null hypothesis is theone which one wishes to disprove.

The rejection of a certain hypothesis when it isactually true involves great risk.

Null hypothesis should be always be specific. Itshould not state an approximate value.




5/1/201210

Decision rule or test of hypothesis: Given a null hypothesis Ho and alternative

hypothesis Ha, we make a rule known asdecision rule according to which we accept Ho

(reject Ha) or reject Ho (i.e. accept Ha).

For example, if Ho is that a certain lot is goodagainst Ha, means there are very few defectiveitems in Ho.

If the lot is not good, it means there are toomany defective items in it.

Then we must decide the number of items to be

tested and the criterion for accepting orrejecting the hypothesis.




5/1/201211

Type I and Type II errors: There are two basic types of errors which we

make in the context of testing of hypothesis.

We may reject Ho when Ho is true – Type I

error. We may accept Ho, when Ho is not true – Type

II error.

Type I error means rejection of hypothesis

which should have been accepted and Type IIerror means accepting the hypothesis whichshould have been rejected.

Type I error is denoted by α (alpha error) andalso called the level of significance of test.

Type II error is denoted by ß (beta error).




5/1/201212

Two-tailed & one-tailed tests

• A two-tailed test rejects thenull hypothesis if the sample

mean is significantly higher orlower than the hypothesizedvalue of the mean of thepopulation

•Thus in a two-tailed test,there are two rejectionregions, one on each tail ofthe curve




5/1/201213

Two-tailed & one-tailed tests

• There are situations whenonly one-tailed test is

considered appropriate

•A one-tailed test would beused when we are to test

whether the population meanis either lower than or higherthan some hypothesizedvalue



Procedure for hypothesis testing

5/1/201214

To test a hypothesis means to tellwhether the hypothesis is valid or not(on the basis of the data collected by the

researcher) In hypothesis testing, the main question

is whether to accept the null hypothesis

or not Procedure for hypothesis testing refers

to all those steps that we undertake for

making a choice between the two.




5/1/201215

The various steps involved in hypothesistesting are:

Making a formal statement.

Selecting a significance level.Deciding the distribution to use.

Selecting a random sample and computingan appropriate value.

Calculation of the probability.

Comparing the probability.




5/1/201216

Making a formal statement :

Hypothesis should be clearly stated

considering the nature of the researchproblem.

It also indicates whether we should use a

one – tailed test or a two - tailed test.




5/1/201217

Selecting a significance level:The hypothesis are tested on a

predetermined level of significance and it

should be specified. In practice, either 5% or 1% level is

adopted for the purpose.

The factors that affect the level of

significance are : The magnitude of the difference between

sample means

Size of the sample

The variability of measurements within samples




5/1/201218

Deciding the distribution to use:The next step in hypothesis testing is to

determine the appropriate sampling

distribution.The choice generally remains between

normal distribution and the t- distribution.

The rules for selecting the correctdistribution are similar to those in thecontext of estimation.




5/1/201219

Selecting a random sample andcomputing an appropriate value:Draw a sample to furnish empirical data.

Here we select random sample(s) andcompute an appropriate value from thesample data concerning the test statisticutilizing the relevant distribution.




5/1/201220

Calculation of the probability :

The next step is to calculate the probabilitythat the sample result would diverge aswidely as it has from expectations, if thenull hypothesis is in fact true.




5/1/201221

Comparing the probability :The last step is to compare the probability

thus calculated with the specified value of

α, the significance level. If the calculated probability is equal to or

smaller than the α value in case of one – tailed test(and α /2 in case of two - tailed

test), then reject the null hypothesis (i.e.accept the alternative hypothesis)

If the calculated probability is greater thanα, then accept the null hypothesis.

Fl di f h th i t ti



Flow diagram for hypothesis testing

5/1/201222



Tests of Hypothesis

5/1/201223

Hypothsis testing helps to decide on whatbasis of a sample data, whether thehypothesis about a population is likely to betrue or false

Tests of hypothesis is also called as test ofsignificance

Classified as:

Paramatric Tests or Standard tests ofHypothesis

Non-parametric Tests or Disribution-free test

of hypothesis



Parametric Tests

5/1/201224

Parametric tests usually assume certainproperties of the parent population from whichwe draw samples

Assumptions like, sample size is large,assumptions about the population parameterslike mean, variance, etc must hold goodbefore parametric tests can be used

But there are some situations where theresearcher does not want to make suchassumptions. In such cases we use statisticalmethods for testing hypothesis, which are

called non-parametric tests because such



Important parametric tests

5/1/201225

z-test

t-test

λ 2-test

f-test

All these tests are based on the

assumption of normality, i.e source of datais considered to be normally distributed



z-test

5/1/201226

Based on the normal probability distribution

Used for the judging of the significance ofseveral statistical measures, particularly themean

Most frequently used test in research studies

Generally used for comparing the mean of asample to some hypothesized mean for thepopulation in case of large sample



t-test

5/1/201227

Based on t-distribution

An appropriate test for judging thesignificance of a sample mean in case of

small samples, when population variance isnot known

In case two samples are related, we usepaired t-test (or difference t-test) for judgingthe significance of the mean of differencebetween the two related samples



λ2-test

5/1/201228

Based on chi-square distribution

Parametric test used for comparing asample variance to a theoreticalpopulation variance



f -test

5/1/201229

Based on F-distribution

Parametric test used for compare thevariance of two independent samples



Thank You

5/1/201230

testing of hypothesis i

Documents