👁 Analysis of Variance

• The ANOVA is a powerful statistical tool for tests of significance.
• The test of significance based on t-distribution is an adequate procedure only for testing the significance of the difference between two sample means. In a situation when we have more than two samples to consider at a time, an alternative procedure is needed for testing the hypothesis that all the samples have been drawn from the same population.
• For example, if three fertilizers are to be compared to find their efficacy, this could be done by a field experiment, in which each fertilizer is applied to 10 plots and then the 30 plots are later harvested with the crop yield being calculated for each plot. Now we have 3 groups of ten figures and we wish to know if there are any differences between these groups. The answer to this problem is provided by the technique of ANOVA.
• The term ANOVA was introduced by Prof. R.A. Fisher in 1920’s to deal with problem in the analysis of agronomical data.
• It is statistical technique of partitioning the total variation into component variations and computing them by F-test.
• Variation is inherent in nature. The total variation in any set of numerical data is due to a number of causes which is classified by ANOVA as
  • Assignable causes
  • Chance causes (error)
• The variation due to assignable causes can be detected and measured whereas the variation due to chance causes is beyond the control of humans and cannot be traced separately.
• ANOVA: The ANOVA is a simple arithmetical process of sorting out the components of variation in a given data.
• Minimum degree of freedom for error in ANOVA is 12.
• Types of ANOVA: There are two types:
  • One-way classification
  • Two-way classification

Application

👉🏻 The analysis of variance (ANOVA) technique is used for comparing the means of more than two populations.

Assumptions of ANOVA

• The observations are independent
• Parent population from which observations are taken is normal
• Various treatment and environmental effects are additive in nature
• The experimental errors are distributed normally with mean zero and variance σ².