Description
PPT on Hypothesis testing and Chi Square testing in statistics. It also covers F-Test.
Kurukshetra university
postgraduate regional
centre,jind….
1
Hypothesis testing..
Presented by:
Prachii garg
Roll no.6
2
Meaning
• It is a claim or a belief about an unknown
population parameter.
• It is a well-defined procedure which help
us to decide objectively whether to accept
or reject the hypothesis based on the
information available from the sample.
In other words, in attempting to
arrive at decisions about the
population on the basis of sample
information, it is necessary to make
assumption about population
parameters involved. Such an
assumption is called hypothesis
testing
Example
A judge assumes that a person
charged with a crime is innocent and
subject this assumption
(hypothesis) to a verification by
reviewing the evidence and hearing
testimony before reaching to a
verdict.
Types of Hypothesis
• There are two types of hypothesis-
• 1)Null Hypothesis
• It represents the claim or a statement made
about the value or range of values of the
population parameter. H stands for hypothesis
and ‘o’ implies that is no difference between
sample statistic and parameter value.
Symbolically, it is
• represented by- `
o o
H µ µ = :
( )
o
H
2) Alternative Hypothesis-
• Generally referred by
• Opposite of null hypothesis.
• When null hypothesis Is true, this is
false and vice versa
• It is the claim made against the value of
the particular population parameter
1
H
o
o
o
H
H
H
µ µ
µ µ
µ µ
>
<
=
:
:
:
1
1
1
Procedure of testing a hypothesis:-
• Set up null and alternate hypothesis
• Set up a suitable set of statistical test
• Set up a suitable level of significance
• Doing necessary calculations
• Set the decision rule
Level of significance
This refers to the degree of significance
with which we accept or reject a particular
hypothesis. In most cases, such a
confidence is fixed at 5%level,which
implies that our decision would be correct
to the extent of 95%
Level of
significan
ce
.10 .05 .01 .005
Critical
value of Z
(one tail
test)
1.28 1.645 2.33 2.58
Critical
value of Z
(two tail
test)
1.645 1.96 2.58 2.81
( ) o
F - TEST………………
• F- Test is based upon f-distribution & is
used to compare the variance of two
independent Samples.This test is used in
context of ANOVA for judging the
significance of more than two sample
means at one & same Iime.Its also used to
judge the significance of multiple
corelation coefficients.
• Test statistic,F, is calculated & compared
with its probable value for accepting or
rejecting the null hypothesis.
Hypothesis testing based on F-
distribution
• A hypothesis test for comparing the variance of
two independent population with the help of
variance of two small samples
• F-test is done to test whether the two
independent population variance differ
significantly or not.
( ) ( )
2
2
2
2
2
1
2
1
) ( ) (
o
o
s
s
F =
( )
( )
1
,
1
2
1
2
1
1
÷
÷ ¿
=
n
x x
s here
( )
( )
1
,
2
2
2
2
2
2
÷
÷ ¿
=
n
x x
s and
) . . . (
. 2 1
mean are x and x
CHI-SQUARE TEST…….
Chi square symbolically written as ?
2
is a
statistical measure used in context of
sampling analysis for comparing a variance to
a theoretical variance.The CHI-SQUARE
test is applicable in large number of
problems.
CHI-SQUARE HELPS
THE RESEARCHER IN..
a. Testing the goodness of fit.
b. Testing the significance of association
between two attributes.
c. Testing the homogeneity or significance
of population variance.
Formula……….
for testing the goodness of fit or to judge
significance of associations between
attributes.chi square can be calculated
as….......
?
2
=
• where, O
ij
=observed freq.of cell in i cell &
E
ij
= expected freq.
CONDITIONS FOR
APPLICATIONS OF CHI-SQUARE
TEST…….
?Observations recorded & used shud be
collected on a random basis.
?All items in sample must be independent.
?No group should contain very few
items,say less than 10.
?The overall number of items must also be
reasonably large say atleast 50.
?The constraints must be linear.
Thanks…………
17
doc_282593890.pptx
PPT on Hypothesis testing and Chi Square testing in statistics. It also covers F-Test.
Kurukshetra university
postgraduate regional
centre,jind….
1
Hypothesis testing..
Presented by:
Prachii garg
Roll no.6
2
Meaning
• It is a claim or a belief about an unknown
population parameter.
• It is a well-defined procedure which help
us to decide objectively whether to accept
or reject the hypothesis based on the
information available from the sample.
In other words, in attempting to
arrive at decisions about the
population on the basis of sample
information, it is necessary to make
assumption about population
parameters involved. Such an
assumption is called hypothesis
testing
Example
A judge assumes that a person
charged with a crime is innocent and
subject this assumption
(hypothesis) to a verification by
reviewing the evidence and hearing
testimony before reaching to a
verdict.
Types of Hypothesis
• There are two types of hypothesis-
• 1)Null Hypothesis
• It represents the claim or a statement made
about the value or range of values of the
population parameter. H stands for hypothesis
and ‘o’ implies that is no difference between
sample statistic and parameter value.
Symbolically, it is
• represented by- `
o o
H µ µ = :
( )
o
H
2) Alternative Hypothesis-
• Generally referred by
• Opposite of null hypothesis.
• When null hypothesis Is true, this is
false and vice versa
• It is the claim made against the value of
the particular population parameter
1
H
o
o
o
H
H
H
µ µ
µ µ
µ µ
>
<
=
:
:
:
1
1
1
Procedure of testing a hypothesis:-
• Set up null and alternate hypothesis
• Set up a suitable set of statistical test
• Set up a suitable level of significance
• Doing necessary calculations
• Set the decision rule
Level of significance
This refers to the degree of significance
with which we accept or reject a particular
hypothesis. In most cases, such a
confidence is fixed at 5%level,which
implies that our decision would be correct
to the extent of 95%
Level of
significan
ce
.10 .05 .01 .005
Critical
value of Z
(one tail
test)
1.28 1.645 2.33 2.58
Critical
value of Z
(two tail
test)
1.645 1.96 2.58 2.81
( ) o
F - TEST………………
• F- Test is based upon f-distribution & is
used to compare the variance of two
independent Samples.This test is used in
context of ANOVA for judging the
significance of more than two sample
means at one & same Iime.Its also used to
judge the significance of multiple
corelation coefficients.
• Test statistic,F, is calculated & compared
with its probable value for accepting or
rejecting the null hypothesis.
Hypothesis testing based on F-
distribution
• A hypothesis test for comparing the variance of
two independent population with the help of
variance of two small samples
• F-test is done to test whether the two
independent population variance differ
significantly or not.
( ) ( )
2
2
2
2
2
1
2
1
) ( ) (
o
o
s
s
F =
( )
( )
1
,
1
2
1
2
1
1
÷
÷ ¿
=
n
x x
s here
( )
( )
1
,
2
2
2
2
2
2
÷
÷ ¿
=
n
x x
s and
) . . . (
. 2 1
mean are x and x
CHI-SQUARE TEST…….
Chi square symbolically written as ?
2
is a
statistical measure used in context of
sampling analysis for comparing a variance to
a theoretical variance.The CHI-SQUARE
test is applicable in large number of
problems.
CHI-SQUARE HELPS
THE RESEARCHER IN..
a. Testing the goodness of fit.
b. Testing the significance of association
between two attributes.
c. Testing the homogeneity or significance
of population variance.
Formula……….
for testing the goodness of fit or to judge
significance of associations between
attributes.chi square can be calculated
as….......
?
2
=
• where, O
ij
=observed freq.of cell in i cell &
E
ij
= expected freq.
CONDITIONS FOR
APPLICATIONS OF CHI-SQUARE
TEST…….
?Observations recorded & used shud be
collected on a random basis.
?All items in sample must be independent.
?No group should contain very few
items,say less than 10.
?The overall number of items must also be
reasonably large say atleast 50.
?The constraints must be linear.
Thanks…………
17
doc_282593890.pptx