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N.P.Bali; P.N.Gupta; Dr C.P.Gandhi Laxmi Publications PDF

11

F-Test and Analysis of Variance

ANOVA

11.1. ANALYSIS OF VARIANCE

We have studied t-test which is used to test the significance of the difference between two sample means. But, if the number of means is more than two, then t-test is not applicable.

Hence, if we have a large number of means and we have to test the hypothesis that

(1) Means are homogeneous or not

(2) Means differ significantly or not

(3) Independency of errors

The techniques known as �Analysis of Variance� developed by �Fisher� is useful.

11.2. TECHNIQUES OF ANOVA (ANALYSIS OF VARIANCE)

There are two types of techniques for the analysis of variance :

(1) One way classification

(2) Two way classification.

We now discuss the above classification in details.

11.3. ONE WAY CLASSIFICATION

Consider a set of N values of the variable x arranged into h rows and k columns so that

N = hk. Assume the null hypothesis.

H0 : µ1 = µ2 = µ3 = µ4 etc., i.e., there is no significant difference between the sample means

H1 : µ1 ≠ µ2 ≠ µ3 ≠ µ4 etc., i.e., there is a significant difference between the sample means.

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