Analysis of Variance

ANALYSIS OF VARIANCE

1. Introduction:

The analysis of variance is a powerful statistical tool for tests of significance. The term "Analysis of Variance" was introduced by Prof. R.A. Fisher in 1920's to deal with problem in the analysis of agronomical data. Variation is inherent in nature. The total variation in any set of numerical data is due to a number of causes which may be classified as (i) Assignable causes, and (ii) Chance causes.

The variation due to assignable causes can be detected and measured whereas the variation due to chance is beyond the control of human hand and cannot be traced separately.

2. Definition:

Analysis of variance (ANOVA) is the separation of variance ascribable to one group of causes from the variance ascribable to other groups.

It is nothing but an arithmetical procedure, used to express the total variation of data, as the sum of its non-negative components.

3. Assumptions:

For the validity of the F-test in ANOVA, the following assumptions are made: [A.U. CBT A/M 2011]

(i) The observations are independent

(ii) Parent population from which observations are taken is normal and

(iii) Various treatment and environmental effects are additive, in nature.

S.S.C - Sum of Squares between Columns

T.S.S - Total Sum of Squares

S.S.T - Sum of Squares due to Treatments

M.S. - Mean Sum of Squares

S.S.E - Error Sum of Squares (or) Within Sum of Squares

R.S.S - Row Sum of Squares

C.F - Correction Factor

C.D - Critical Difference

S.S.R -  Sum of Squares between Rows

M.S.C - Mean Sum of Squares (between Columns)

M.S.E - Mean Sum of Squares (within Columns)

M.S.R -  Mean Sum of Squares (between Rows)

N - Number of Observations

N₁ - Number of elements in each column

N₂ - Number of elements in each row

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