Question

What is the purpose of using a blocking variable in a two-way ANOVA?

Answer 1

The purpose of using a blocking variable is to reduce variability in the data. In two-way ANOVA, we try to group the data in such a way that the elements in a group are likely to homogeneous. Since most of the experimental output is heterogeneous which cause much variation in the data. So, in order to reduce the total variability, we use blocking such that units within the block are homogeneous and units between the block are heterogeneous.

Let us consider an example: Let we have a data of 30 students of class 10. There are 3 ways to study like 10 students study by self, 10 students take Tuition & 10 students to attend school to study from the class teacher. These three-ways of study are treatment. Let us consider that there are 3 sections in class 10 as A, B, C & D. If we analyze this experiment by using one-way analysis, we will get much variability in their score in an exam because it is generally assumed that the students of section A are intelligent as compared to B, students of section B is intelligent as compared to C and so on. So, in order to reduce the variability in this experiment, we will use blocking. Blocking can be done according to the section of the class.