What is analysis of variance How does the variance of a data

What is analysis of variance? How does the variance of a data set relate to the regression of that same data set?

Solution

Analysis of the variance (ANOVA) is a powerful statistical tool in testing of hypothesis. It is useful to compare more than two groups, thus it is an alternative to t-test. ANOVA is based on F-statistic.

Assumptions:

1. All the observations are independent.

2. Effects are additive in nature (can add assignable cause of variation and chanced cause of variation)

3. Eij ~ N(0, sigma(e)^2)   {Residuals follows normal with mean 0 and variance sigma(e)^2}

Types of ANOVA:

1:ANOVA one-way classification:

The technique of analysing the data in only one-direction (either through experimental units or through treatments (groups)).

The total variation can be expressed as sum of two non-negative components.

2:ANOVA two-way classification:

The technique of analysing the data in two purpendicular directions (blocks and treatments).

The total variation can be expressed as sum of three non-negative components.

3:ANOVA three-way classification:

The technique of analysing the data in three direction (rows, columns, and treatments).

The total variation can be expressed as sum of four non-negative components.