Assumptions and Objective of ANOVA

Assumptions of  ANOVA

1.      Observations and errors are independently distribbuted.

2.      Observations and errors conferm to normal distribution with equal variance.

3.      Treatments and environmental effects are additive

Objective of  ANOVA

1.     It identifies the couses of variation and sort out corresponding components of  variation with associated degrees of freedom.

2.     It provides test of significance based on F-distribution.

Models for ANOVA

Models for ANOVA

There are three types of models used in the analysis of variance,thus are.

  1.Fixed-effects models or Model 1

The fixed-effects model of analysis of variance applies to situations in which the experimenter applies one or more treatments to the subjects of the experiment to see if the response variable values change. This allows the experimenter to estimate the ranges of response variable values that the treatment would generate in the population as a whole.

  2.Random-effects models or Model 2

Random effects models are used when the treatments are not fixed. This occurs when the various factor levels are sampled from a larger population. Because the levels themselves are random variables, some assumptions and the method of contrasting the treatments differ from ANOVA model 1.

  3.Mixed-effects models or Model 3

A mixed-effects model contains experimental factors of both fixed and random-effects types, with appropriately different interpretations and analysis for the two types.

Analysis of variance (ANOVA)

Analysis of variance (ANOVA)

In statistics, analysis of variance (ANOVA) is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation.

In other words, 

Analysis of variance (ANOVA) is the process of partitioning and decomposing total variation contained in the data into various independent components, each of which is attributed to an identifiable cause or sources of variation and a further component due to chance factor.