Analysis of VArience

8/7/2019 Analysis of VArience

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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

Analysis of VArience

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