Week 8 - Assignment

Week 8 - Assignment

Chapter # 14

Question No. 01

Answer

A simple One Way ANOVA analysis is used to test the significance of the difference between the averages of two or more groups, provided that there is one independent variable only. On the other hand, a factorial ANOVA analysis can be used to test the significance of the difference between averages of two or more groups while analyzing two or more Independent variables.

Using a factorial ANOVA analysis, experimental designs of the notation 2 x 3 x 4 can be evaluated with ease, where 2, 3, and 4 represent the number of levels present for each of the three Independent variables. The number of Independent variables in such notations is represented by the number of numerical figures present in the notation. For example in the mentioned notation, 2 represents the first variable with two distinct levels, 3 represents the second independent variable which has three levels, whereas, 4 symbolizes the third variable which has four levels (Dobler, 2002).

Briefly explained, a simple ANOVA or one-way ANOVA is used to test only one factor or an Independent variable. However, in instances, when two or more than two independent variables need to be analyzed, a Factorial ANOVA analysis is utilized, as it helps in testing the effect of these variables on the difference between the dependent variable. For such analysis a factorial design is formulated in which each level belonging to a particular factor is paired up with each level belonging to every other factor. In such an analysis, each combination of the various levels of factors is demonstrated in the design. This kind of a design is often portrayed in the form of a table.

A factorial design is usually referred in terms of the number of factors or the number of levels present within a variable. Therefore, a one way ANOVA refers to a design that has only one factor, while a two way ANOVA has two factors, whereas, a three way ANOVA is one, that has three factors, etc. A 4 x 5 experimental design represents a two way ANOVA with four levels of the first variable and five levels of the second variable. A 6 x 7 x 4 ANOVA is a three way ANOVA with six levels of the first variable, seven of the second, and four of the third.

The formulation of such experimental designs helps in the ...