INTRODUCTION - 0093Da/Analysis-of-Variance GitHub Wiki

ANOVA is a collection of statistical models used to analyze the differences among group means and their associated procedures (such as "variation" among and between groups) developed by statistician and evolutionary biologist Ronald Fisher. ANOVA provides a statistical test of whether or not the means of several groups are equal, and therefore generalizes the t-test to more than two groups.In the ANOVA setting, the observed variance in a particular variable is partitioned into components attributable to different sources of variation. For testing three or more means (groups or variables) for statistical significance ANOVAs are useful. It is conceptually similar to multiple two-sample t-tests, but is less conservative (results in less type I error) and is therefore suited to a wide range of practical problems. ANOVA are commonly used in three ways: one-way ANOVA, two-way ANOVA and N-way Multivariate ANOVA. There explanation is given below:

One-Way

when comparison is done on the basis of one factor i.e., independent variable for more than two groups, than this is called as one way ANOVA. For example, it is used if a manufacturing company wants to compare the productivity of three or more employees based on working hours. This is called one way ANOVA.

Two-Way

when comparison is done on the basis of two factors i.e., 2 independent variables then it said to be two way (Factorial) ANOVA. For example, based on the working hours and working conditions, if a company wants to compare employee productivity, it can do that through two way ANOVA. Two-way ANOVA can be used to see the effect of one of the factors after controlling for the other, or it can be used to see the interaction between the two factors.

N-Way ANOVA

When the comparison is purely based on factors, then it said to be n-way ANOVA. For example, in productivity measurement if a company takes all the factors for productivity measurement, then it is said to be n-way ANOVA.

Classical ANOVA for balanced data does three things at once:

• As exploratory data analysis, an ANOVA is an organization of an additive data decomposition, and its sums of squares indicate the variance of each component of the decomposition (or, equivalently, each set of terms of a linear model).
• Comparisons of mean squares, along with an F-test ... allow testing of a nested sequence of models.
• Closely related to the ANOVA is a linear model fit with coefficient estimates and standard errors.

In short, ANOVA is a statistical tool used in several ways to develop and confirm an explanation for the observed data.The terminology of ANOVA is largely from the statistical design of experiments. ANOVA is the synthesis of several ideas and it is used for multiple purposes.It is computationally elegant and relatively robust against violations of its assumptions. ANOVA provides industrial strength (multiple sample comparison) statistical analysis.It has been adapted to the analysis of a variety of experimental designs.