Adjusting the data

There is another way to think of the residuals from the full model. They can be obtained by:

These adjustments sequentially reduce the total sum of squares by SSBlocks and SSFactor so, after both adjustments, the total sum of squares becomes SSResid.

Adding a term for the blocks can be thought of as adjusting the values to remove the block effect.


Acupuncture and Codeine for dental pain relief

An anaesthetist conducted an experiment to assess the effects of codeine and acupuncture for relieving dental pain. The experiment used 32 subjects who were grouped into blocks of 4 according to an initial assessment of their tolerance to pain.

The horizontal lines are initially the differences between the observations and the overall mean. Their sum of squares is the total sum of squares.

The vertical lines in each block show the block means. Click Remove block effect to add a constant to all the values in each block making its block mean equal to the overall mean. The reduction in the total sum of squares is equal to the block sum of squares, so the sum of squares of the horizontal lines is now the sum of the factor and residual sums of squares.

Finally click Group by treatments to rearrange the observations by treatment. The treatment means differ so click Remove treatment effect to adjust them to be all equal to the overall mean. The horizontal lines are now the residuals from the randomised block model and their sum of squares is the residual sum of squares from the full model with both block and factor terms.