Answer:
2 a) When employing a Randomized Block design, two variables exist: one as the blocking variable, and the other as the treatment variable. In this case, the type of shoe serves as the treatment variable, while the classification of runners functions as the blocking variable. Blocking groups subjects with similar characteristics together. Here, professional and recreational runners are distinct. The purpose of blocking is to minimize variability within groups, resulting in less variability within blocks compared to between blocks. Subsequently, runners in each block will be randomly assigned either of the shoes.
b) Randomization involves assigning participants to specific treatments so each one has an equal opportunity to be assigned either shoe A or B. This process is conducted using random number generation, linking assignments to those numbers. The central aim of randomization is to remove biases. If participants are permitted to select their shoes, they may opt for their preferred choice based on previous experiences or a predominant preference within the group, thus undermining the study's purpose. For instance, if a group from a certain region favors type A. Implementing randomization ensures a mix, with about half receiving type A and the other half type B, hence mitigating personal bias. Therefore, both randomization and blocking are vital in a randomized block design to reduce response bias.
Step-by-step explanation:
