Randomized Complete Block Design (RCBD) vs Completely Randomized Design (CRD)
The fuel economy analyses were performed both with and without the block factors are provided in Figure 3. Although the conclusion has not been changed from the completely randomized design without the block factor, the experimental error reduction was huge. The error sum of square (SS) is reduced to 67.96 from 264.4. The mean square for the experimental error was reduced to 0.79 from 3.04 ((3.04-.79)/3.04=74% reduction). The systematic known variation due to the climate conditions, which is blocked in the randomized complete block design providing a better justification as compared to the completely randomized design. In fact, it would be wrong to use the completely randomized design when a known nuisance factor is adding variations in the response. Blocking the known nuisance factor not only reduces the experimental error, but also widen the statistical findings over the range of the nuisance factor. Blocking the nuisance factors also improves the signal to noise ratio by reducing the noise (error in this case). Completely randomized design (CRD) can only account for unknown and uncontrolled variations (which are also known as “lurking” nuisance factors). Complete randomization will minimize the effects from the lurking factors as they cannot be blocked simply because we don’t know them. However, systematic source of variations can be controlled by blocking using the randomized block design.
Figure 3. Randomized Complete Block Design (RCBD) vs Completely Randomized Design (CRD)