# Randomized Complete Block Design

The fuel type study in the Completely Randomized Design in the previous module only uses the fuel type factor without considering any additional factors. As vehicles are used in many climate conditions. Assume that the fuel economy study would like to widen its finding for two climate conditions (e.g., hot and cold climate). We can only randomly assign fuel types to experimental vehicles within a climate, while the climates are not possible to randomize. Therefore, the climate conditions can be run as the block factor and the fuel type is the factor of interest. The data for the fuel economy study with the block factor is provided in Table 1.

Table 1. Randomized Complete Block Design Fuel Economy Study Data

# The Four Steps

### Randomized Complete Block Design Example

The procedure for the four steps design and analysis of experiments does not change from the completely randomized design. As the interest in both the completely randomized design (CRD) and randomized complete block design (RCBD) is the treatment effect, the four steps process of hypothesis testing or the design experiments stays the same.

### Step #2. Method

Randomized Complete Block Design of Experiments. The analyses were performed using Minitab version 19.

### Step #3. Analysis and Results

The fuel economy study analysis using the randomized complete block design (RCBD) is provided in Figure 1.

According the ANOVA output, we reject the null hypothesis because the p-value (0.000) is smaller than the level of significance (0.05).

Figure 1. Randomized Complete Block Design (RCBD) vs Completely Randomized Design (CRD)

### Step #4. Contextual Conclusion

Statistically, the fuel types are significantly different with respect to the fuel economy in miles per gallon. [rewrite the accepted hypothesis. The alternative hypothesis was accepted in this case.]

# Post-hoc analysis

When the ANOVA results are observed to be significant (i.e., rejecting the null hypothesis), post-hoc pairwise comparisons are performed to determine the best or worst treatment with respect to the response (e.g., fuel economy in this example). The pairwise comparison result is provided in Figure 2. Fuel Type 1 is observed to be significantly better in producing a better fuel economy at 32.37 miles per gallon. Same results were observed when it was run as the completely randomized design.

Figure 2. Fisher LSD Pairwise Comparison Result RCBD