Monday, January 14, 2013

ANOVA - Analysis Of Variance


The Analysis Of Variance, popularly known as the ANOVA, can be used in cases where there are more than two groups.

When we have only two samples we can use the t-test to compare the means of the samples but it might become unreliable in case of more than two samples. If we only compare two means, then the t-test (independent samples) will give the same results as the ANOVA.

It is used to compare the means of more than two samples. This can be understood better with the help of an example.


EXAMPLE: Suppose we want to test the effect of five different exercises. For this, we recruit 20 men and assign one type of exercise to 4 men (5 groups). Their weights are recorded after a few weeks.
We may find out whether the effect of these exercises on them is significantly different or not and this may be done by comparing the weights of the 5 groups of 4 men each.
The example above is a case of one-way balanced ANOVA.
It has been termed as one-way as there is only one category whose effect has been studied and balanced as the same number of men has been assigned on each exercise. Thus the basic idea is to test whether the samples are all alike or not.
There are four basic assumptions used in ANOVA.
= the expected values of the errors are zero
= the variances of all errors are equal to each other
= the errors are independent

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