br - anova

8/14/2019 BR - ANOVA

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Submitted to:Mrs. SHALINI GUPTA MAMSubmitted by:-

Deepak Kumar Relhan

8/14/2019 BR - ANOVA


A sincere thanks to Shalini mam for her sincereguidance and support throughout the preparation of this presentation.

8/14/2019 BR - ANOVA


Parameters on which a researcher

select the appropriate statisticaltests Purpose of using a test

Measurement scales involved Number of samples involved

Inter-relationship of samples

Many number of variables involved

8/14/2019 BR - ANOVA


8/14/2019 BR - ANOVA


Conditions to use t-test Small sample size(<30)

When population variance is not known

8/14/2019 BR - ANOVA


Conditions to use z-test Large samples(>30)

When population variance is known.

8/14/2019 BR - ANOVA


Analysis of variance(ANOVA) Useful technique in researches in the field of

economics , biology , education , psychology ,sociology, buisness/industry etc.

It is used when multiple sample cases are involved.

It is important in the context of all those situations when we want to compare more than 2 populations

e.g. gasoline mileage of 4 automobiles, yield of cropfrom several varieties of seeds etc.

8/14/2019 BR - ANOVA


HISTORY Professor R.A. Fisher was the first man to use the term

variance, and he developed a very elaborate theory concerning ANOVA , explaining its usefulness inpractical field.

Later on Professor Snecdecor and many otherscontributed to the development of this technique.

Also known as F-TEST.

8/14/2019 BR - ANOVA


USES OF ANOVA Used in such a problem where a researcher wants to

test for the significance of the differences betweenmore than two sample means.

Each sample is drawn in a random manner fromnormal population. Also the sample statistics tend toreflect the chracteristics of the population.

The population from which the samples are taken haveidentical means and variances.

8/14/2019 BR - ANOVA


How to apply ANOVA There are two methods of using ANOVA

1)One – way ANOVA

2)Two– way ANOVA

8/14/2019 BR - ANOVA


One –

way ANOVA Data are classified according to one criterion.

HO:u1 =u2=u3= uk i.e. the arithmetic means of the

population from which the k samples arerandomly drawn ,are equal to one another.

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STEPS of One –

way ANOVA1)Take the total of the values of individual items in all

the samples and call it T

2) Work out the correction factor3)Find total SS

4)Obtain SS between

5) Find SS within

6)Find MS Between

7)Find MS within

8) Find F ratio

8/14/2019 BR - ANOVA


Two-way ANOVA We attempt to study the effect of two factors in the

same experiment.

In this the data are classified on the basis of twofactors e.g. the agricultural output may be classified onthe basis of different varieties of seeds and also on thebasis of different varieties of fertilizers used, a buisnessfirm may have its data classified on the basis of different salesman and also on the basis of sales indifferent regions.

8/14/2019 BR - ANOVA


STEPS OF Two- Way ANOVA 1) Use coding device

2)take the total of all values of individual items in all

the samples and call it T 3) find correction factor

correction factor =TxT/n

4)find total SS

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5)find SS between columns

6)find SS between rows

7) find MS between columns 8)find MS between rows

9)find F ratio of between columns

10)find F ratio of between rows

11) find residual or error=total SS-(SS between columns+ SS between rows)

br - anova

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