Why Randomized Complete Block Design is so Popular?

If the fuel economy study is conducted in practical driving conditions that include so many variables, including traffic congestions, busy city driving, high-way driving, variation of speed, etc. will affect the fuel economy. These variables, if not controlled, the study findings will be completely useless. Let’s look at the data set in Table 2 that is collected in real-life driving conditions. Instead of the climate conditions blocking with all other conditions fixed, this time the vehicle was run in real-life driving conditions (city vs highway, etc.)

Table 2. Justification for a Randomized Complete Block Design

The analyses were performed both using (1) the randomized complete block design including blocking the driving condition and (2) completely randomized design without blocking any nuisance factors. The analysis results are providing in Figure 4. Even though the fuel types are still observed to be significant with respect to the fuel economy, the experimental error without blocking the driving conditions is observed to unimaginable. Without blocking the known systematic variations, the analysis conclusions will be useless. If the nuisance factors like these are not considered, they may increase the experimental error to a level making the factor of interest insignificant. For example, the data set 2 in Table 3 is analyzed using both randomized complete block design (RCBD) and the completely randomized design (CRD). Analysis results in Figure 5 show the comparison between the RCBD and CRD analysis. The fuel type is observed to be insignificant in CRD analysis, while RCBD analysis shows that the fuel type is significant due to the reduction in experimental error.

Figure 4. RCBD vs CRD Analysis Output

Table 3. Justification for a Randomized Complete Block Design Data Set 2

The analysis results for the data set 2 is provided in Figure 5.

Figure 5. RCBD vs CRD Analysis Output Data Set 2