Hypothesis Testing and Tests of Significance

HYPOTHESIS TESTING AND TESTS OF SIGNIFICANCE

HYPOTHESIS• “Hypothesis is a proposition or a set of proposition,

explaining the occurrence of a specified group of phenomena, either to conjecture a provisional guide for an investigation or as the highly probable in the light of established facts.”

PURPOSE OF HYPOTHESIS• Defining relationship between variables• Variable- changing quantities in a study• Independent variable• Dependent variable• Controlled variable

COMPONENTS OF HYPOTHESIS• Subject Group

• Treatment or exposure

• Outcome measure

• Control group

SOURCES OF HYPOTHESIS• Environment • Current popular beliefs• Analogies• Findings of other studies• Cases- exception to a theory• Personal experiences• Body of theory

FORMULATION OF HYPOTHESIS

• Quantitative study-Testable proposition deduced from the theory

Independent and dependent variables- separated and measured separately

INDUCTIVE METHOD used

• Qualitative study-Use of words- what, how.

Questions under continual review and reformulation

DEDUCTIVE METHOD used

DIFFICULTIES IN FORMULATION

• Lack of clear theoretical background

• Lack of logical background

• Lack of knowledge of scientific methods

STEPS TO REMOVE DIFFICULTIES

• Complete and perfect knowledge of the basic principles of social science or related science

• Hypothesis – brief and timely

• Grow as research proceeds furthur

CHARACTERISTICS OF GOOD HYPOTHESIS

• Based on the information- review of literature

• Include – independent and dependent variables

• Conceptually clear

• Point towards line of action or research design

• Empirical referents

• Consistent with data

HYPOTHESIS TESTING

PRE-REQUIREMENTS

1) Hypothesis should be testable-reasonable time

2) Variables- measurable

3) Establish decision rules/ level of significance

4) Type of sampling distribution

5) Parameters- select a real social situation i.e. a

reasonable testing ground for hypothesis

BASIC CONCEPTS

1. Null Hypothesis and Alternative Hypothesis

2. Significance Levels

3. Decision rule or Test of Hypothesis

4. Type I Error and Type II Error

5. One- tailed and Two- tailed tests

6. Degrees of Freedom

NULL HYPOTHESIS & ALTERNATIVE

HYPOTHESIS

• NULL HYPOTHESIS- statement of no change or no

difference or no relationship

• ALTERNATIVE HYPOTHESIS- negative or logical

opposite of null hypothesis

SIGNIFICANCE LEVEL

DECISION RULE OR TEST OF

HYPOTHESIS

• According to this rule that we accept or reject –

hypothesis.

TYPE I & TYPE II ERROR

DECISION

ACCEPT H0 REJECT H0

CORRECT

DECISION

TYPE I ERROR

TYPE II ERROR

CORRECT

DECISION

H0 (TRUE)

H0 (FALSE)

ONE- TAILED TEST & TWO- TAILED

TEST

DEGREES OF FREEDOM

• Number of values or observations independent from

each other.

• The values can be chosen freely

• Degrees of freedom in a sample distribution- (n-1)

• The strength of prediction of population parameter

from a statistic is increased when number of degrees

of freedom is increased

PROCEDURE- HYPOTHESIS TESTING

State H0 and Ha

Specify the level of significance

Decide the correct sampling distribution

Calculate the probability of divergence of sample from H0

Is it = to or smaller than the significance value.

(one tailed and two tailed test

NOYES

REJECT H0 ACCEPT H0

Committing Type I error Committing Type II error

TESTS OF SIGNIFICANCE

• PARAMETRIC TESTS –depends on the parameter

or parametric characteristics

Values are independent

Normally distributed

Equal variances- population

Measured @ interval level hence use of arithmetic

operation

• NON- PARAMETRIC TESTS- when conditions of

parametric are not met.

Size of sample- small

Normality of distribution- doubtful

Measurement- ordinal or nominal form

PARAMETRIC TESTS

• z- test – for large samples

• t- test- for small samples

• f- test- for significance of difference in population

variance.

NON- PARAMETRIC TESTS

CHI-SQUARE

• Degrees of freedom- (r-1) (c-1) in case of table values.

• TEST OF GOODNESS OF FIT

• TEST OF INDEPENDENCE

• TEST THE SIGNIFICANCE OF POPULATION VARIANCE

TEST OF POPULATION VARIANCE-

PARAMETRIC TEST• Illustration 1

• Can we say that the variance of the distribution of weight of all students from which the above sample of 10 students was drawn is equal to 20 kgs? Test this at 5 per cent and 1 percent level of significance

Sl.no 1 2 3 4 5 6 7 8 9 10

Weight(kg)

38 40

45

53 47 43 55 48 52 49

• Illustration 2

• Two hundred digits were chosen at random from a set of tables. The frequencies were as follows :

Use chi-square test to assess the correctness of hypothesis if the digits were distributed in equal numbers in the tables from which they were chosen.

Digit 0 1 2 3 4 5 6 7 8 9

Frequency 18 19 23 21 16 25

22

20

21 15

• Illustration 3• The following values of x2 from different

experiments carried out to examine the effectiveness of a recently invented medicine for checking malaria are obtained:

• What conclusion would you draw about the effectiveness of the new medicine on the basis of 5 experiments taken together

Experiment No:

x2 Degrees of Freedom

12345

2.53.24.13.74.5

11111

• Illustration 4

• Two research studies were carried out on classifying people in income groups on the basis of sampling studies. The result was as follows:

• Prove that the sampling techniques of at least one research study is defective

RESEARCH STUDIES

INCOME GROUPSTOTALPOOR MIDDLE RICH

AB

160140

30120

1040

200300

TOTAL 300 150 50 500