Anova table

The three components that add to total sum of squares are usually laid out in an analysis of variance table (or simply anova table).

The anova table adds a few extra columns:

Degrees of freedom
They also add up to the value in the Total row, (n − 1).
Mean sums of squares
These are the sums of squares divided by their degrees of freedom.
F-ratios
For the blocks and treatments, the F-ratio divides the mean sum of squares by the mean residual sum of squares.

Tests

The F-ratio for differences between the treatments compares the variability explained by the treatments to the residual (unexplained) variation. The larger the F-ratio, the stronger the evidence for a difference between treatments. A formal hypothesis test is based on the F-ratio and its p-value is the probability of getting as big an F-ratio as that recorded if all treatment means were equal. It is interpreted in the same way as all other p-values.

p-value > 0.1
No evidence of a difference between treatments
0.1 < p-value < 0.05
Very mild evidence of a difference between treatments
0.05 < p-value < 0.01
Moderately strong evidence of a difference between treatments
p-value < 0.01
Strong evidence of a difference between treatments

A p-value can also be found to test whether there are differences between the blocks, but this is usually of less interest.

In practice, computer software will produce the anova table for you, so you only need to interpret the p-value associated with the treatments.

Examples