Analysis of Variance

Abstract

Often an experimental scientist consults a statistician when he cannot get the inference that he had expected to get from his experimental data. Usually in such cases the statistician is unable to analyse the data property due to the fact that the experiment was not planned properly, in the sense, that the experiment was not planned keeping in mind the particular analysis to be done later. We had seen that for applying any particular statistical test a number of conditions are to be satisfied by the data. For example suppose that the department of education wants to compare two methods of teaching. Suppose that two classes of students are exposed to the two methods of teaching. The effect of teaching is a hypothetical quantity which cannot be measured directly. Hence the marks obtained by the students may be taken as an indication of the effect of teaching. But the difference in the average marks in the two classes cannot be taken as a measure of the difference in the effects of teaching, because there are a number of other factors, such as the intelligence of the students, their previous acquaintance with the methods of teaching, etc., which contributed towards the average marks But if the experiment is planned in such a way that all the extraneous factors (factors other than the methods of teaching) are controlled, then the difference in the average marks can be taken as an indication of the difference in the effects of the two methods of teaching.