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What is the purpose of the randomized block design?
Solution
VerifiedIn Oneway ANOVA, the assignment of treatments to test units are random. With this, some treatments may overrepresent these units while others may underrepresent them, all without certainty.
However, unlike the Oneway ANOVA, the purpose of the Randomized Block Design of ANOVA (Analysis of Variance) is to minimize the amount of variation in error by first arranging the test units or subjects into similar blocks before the assignment of the treatment.
Moreover, we want to test whether the population means of the group are equal. The null and alternative hypotheses can be expressed in terms of the equality of the population means for all of the treatments.
In symbols:
$H_0: \mu_1 = \mu_2 = \cdot \cdot \cdot = \mu_i$
$H_1: \mu_i \ne \mu_j \text{, where } i \ne j$
 $\mu_1$ is the population mean of the first group, $\mu_2$ is the population mean of the second group, and so on until the ith group.
In words:

Null Hypothesis: The population means are the same

Alternative Hypothesis: The population means are not all the same. (At least two of the groups have different population means)
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