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ANOVA is a study about the variances of two or more series. It was merely used in Agricultural Research. But now the technique finds useful applications in the field of both natural and social sciences.

If the component variances do not differ significantly it is concluded that the effects of all the factors are equal.

- Populations from which samples have been drawn are normally distributed.
- Populations from which samples have been drawn have same variance.
- The observations are non correlated random variables.
- Any observation is the sum of the effect of the factors influencing it
- The observations in the sample are randomly selected from the population.
- The random errors are normally distributed with mean 0 and variance $\sigma^{2}$.

The term treatment is used because of the early applications of analysis of variance involved agricultural experiments in which different plots of farmland were treated with different fertilizers, seed types, insecticides etc. It is also known as single factor ANOVA. The following is the procedure for carrying out analysis of variance in one way classification: -

- The null hypothesis is taken as "all population means are equal"
- Compute the mean square between the samples MSC and MSE
- Calculate the F ratio
- Obtain the F table value with k – 1 and N – k degrees of freedom.
- If the calculated F value is less than the table value, we accept the hypothesis that the samples are equal.

- The null hypothesis is taken; as "all means of the columns are equal" Also another null hypothesis is "all means of the rows are equal".
- Compute the mean square between the samples MSC, MSE and MSR
- Calculate the F ratios
- Obtain the F table values.
- If the calculated F values are less than the table value, we accept the hypothesis that the samples are equal.

Sources of Variation | Sum of squares | Degree of freedom | Mean squares |
F ratio | P- value |

Between samples |
SSC | k - 1 | MSC | ||

Within samples | SSE | N – k | MSE | ||

Total | SST | N - 1 |

Similarly, A specimen of an ANOVA table in two way classification is given below.

Sources of Variation |
Sum of squares | Degree of freedom |
Mean squares | F ratio |
P- value |

Between columns | SSC | c - 1 | MSC | ||

Between rows | SSR | r - 1 | MSR | ||

Residual | SSE | (c – 1) $\times$ (r – 1) |
MSE | ||

Total | SST | N - 1 |

F = $\frac{Unexplained\ variance}{explained\ variance}$