Post on 08-Apr-2018
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ANALYSIS OF
VARIENCE(ANOVA)
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ANOVA????
Statistical technique for determining
the degree of difference or similarity
between two or more groups ofdata.
It is based on the
comparison of the average value of a
common component.
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WHY ANOVA?????
When the number of samples is more
than two, for comparing their means,
this approach is convenient as it is :Time saving
Reducing type 1 error
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GENERAL
ASSUMPTIONS
Independence of cases
Normality
Homoscedasticity
Errors are independent
Random selection
Statistics: the
mathematical
theory of
ignorance
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TYPES(BASED ON NUMBER OF
INDEPENDENT VARIABLES)
One way
Two way
Multi variate or n-way ANOVA
USAToday has
come out with a
new survey apparently, 3 out
of every 4 people
make up 75% of
the population
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ONE WAY ANOVA
Examines whether multiple means differ.
ASSUMPTIONS:
Subjects are sampled randomly.
Groups are independent.
Population variances are homogenous.
Population distribution is normal inshape.
Null hypothesis.
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EXAMPLE:
A research study was conducted to
examine the clinical efficacy of a newantidepressant.
Depressed patients were randomly
assigned to one of three groups:
a placebo group, a group that received a
low dose of the drug, and a group that
received a moderate dose of the drug.
After four weeks of treatment, thepatients completed the Beck Depression
Inventory.
The higher the score, the more depressed
the patient. The data are presented below.
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PLACEBO LOW DOSE MODERATE
DOSE
38 22 14
47 19 26
39 8 11
25 23 18
42 31 5
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HYPOTHESIS:
SOURCE SS df MS F
BETWEE
N
1484.93333 2 742.466666 11.26
WITHIN 790.8 12 65.9
TOTAL 2275.73333 14
H0: There will be no difference in depression levelsbetween the three groups.
H1: There will be difference in depression levels
between the three groups.
team 3
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TWO WAY ANOVA
This allows for a second independentvariable and addresses
interaction
ASSUMPTIONS:
y Groups are sampled randomly.
y Groups are independent.
y Population variances are homogenous.
y Population distribution of the DV is
normal in shape.
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y n's are equal and greater than 1
(typically at least 5).
y The null hypothesis.
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EXAMPLE:
Five doctors each test five treatments for a
certain disease and observe the number
of days each patient takes to recover. The
results are given in the following table.
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1 10 14 23 18 20
2 11 15 24 17 21
3 9 12 20 16 19
4 8 13 17 17 20
Doctor
s
Treatments
1 2 3 4 5
5 12 15 19 15 22
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H0A: There is no significant difference between the doctors.
H0B:There is no significant difference between thetreatments.
SOURCE SS df MSS F
A(Doctors) 25.84 4 6.46 2.99
B(Treatments
)
406.64 4 101.66 47.06
Error 34.56 16 2.16
Total 467.04 24
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WEARE DIFFERENT
ONEWAY ANOVA TWOWAY ANOVA
used to verify the data
collected from different sources
converge on a common mean
based on single category of
defining characteristics.
It deals with only one factor
such as group or treatment
generates one F-value
used to verify the data
collected from different sources
converge on a common mean
based on two categories of
defining characteristics.
It deals with two or more
treatment means
generates three F-values
Fett's Law: Never replicate a
successful experiment.
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WHEREAMIUSED????
MARKETING:
Product testing, copy testing and concept testing.
Manipulation of certain variables like promotion,ad copy, display at PoP and observe changes in
other variables like sales, consumer preference,
behavior or attitude etc.
Whenever, a variable in marketing mix ischanged , we can determine its effect.
How do advertising levels interact with price
levels to influence a brands sale.
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R & D IN BIO-TECH RELATED FIRMS:
To study the effect of a drug with different
stimulus in a particular species.
Investigation on the degree of microbialcontamination on coins collected from three
different premises.
Precipitation behaviour studies
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Statistics is the art of never
having to say you're wrong.
Variance is what any two
statisticians are at." -
C.J.Bradfield