Hypothesis Testing and Tests of Significance
Transcript of 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