Improving accuracy of estimating the factor effect

Both increasing the number of blocks and increasing the number of measurements made in each block increase the accuracy of estimating the factor effect in an experiment where the factor levels are varied at block level.

Increasing the number of measurements per block

The more measurements that are obtained from each block, the less variable the block means and hence the more accurate the estimate of the factor effect. However there is a limit to the improvement that is possible if the number of blocks is not increased.

The denominator of the F-ratio for testing the factor effect is the between-blocks mean sum of squares and its degrees of freedom limit the power of the test for the factor effect.

Increasing the number of blocks

Increasing the number of blocks used in the experiment has a more direct influence on accuracy. With enough blocks, the factor effect can be estimated to any accuracy, irrespective of the number of measurements per block.

A balance

The balance between these two ways of improving accuracy depends on the variability of measurements within the blocks. If this high, it is worth taking more measurements within each block. This is usually cheaper than increasing the number of blocks.

On the other hand, if the measurements are consistent within each block, it is better to increase the number of blocks that are used.

We have not given detailed guidelines here, but have indicated the design trade-off between these two ways of increasing the size of an experiment.