# Anova Table

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The Anova Table is a table which summarizes the results of all the calculations that were done when carrying out the ANOVA procedure.

We carry out the ANOVA (Analysis of Variance) test to check whether the means of three or more populations are all equal or not. The null hypothesis states that all the means are equal whereas, the alternative hypothesis states that all the means are not equal to each other.

### Example of Anova table for one way ANOVA procedure:

As we can see in the above example, the Anova table consists of the following pieces of information:

1. Degrees of Freedom – Between groups (due to treatment) and within groups (due to error)
2. Sum of squares – Between groups (due to treatment) and within groups (due to error)
3. Mean Sum of Squares – This is obtained by dividing the sum of squares by the respective degrees of freedom.
4. The F statistic which is obtained using the formula, \text{F statistic }= \frac{\text{Mean sum of squares due to treatment}}{\text{Mean sum of squares due to error }}
5. The p-value which helps us to decide whether to accept or reject the null hypothesis.

### Interpretation of Anova Table:

We look at the p-value obtained in the table. If the p-value is less than the level of significance \alpha, then we reject the null hypothesis and conclude that all the means are not equal.

If the p-value is greater than the level of significance \alpha, then we accept the null hypothesis and conclude that all the means are equal.

### Two way Anova Table:

A two way Anova table is similar to the one way table except for the fact that it contains another additional row for the sum of squares and mean sum of squares due to blocks.

It consists of two p values – one for deciding if there is any significant difference due to treatment and the other to decide if there is any significant difference due to blocks.

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