Business Problems & ANOVA Analysis

Solution Preview

1. Could you please help me with four examples of ANOVA analysis that would be used in the business world? What types of business problems would use ANOVA in research issues, problems or opportunities to use ANOVA in figuring out business issues?

What a great question!

Since it is important to understand the ANOVA (one-way, one-way for repeated measures, factorial, and mixed-design) and the types of data that the ANOVAs are used to analyze, let's do that first prior to looking at some some examples to consider.

Although there are different types of ANOVAs based on the number of groups and the associated number of group means to compare, in general, the ANOVA is used to compare the treatment means of more than two groups on more than one level of the independent variable (as opposed to using the t-or z- test to compare two treatment means on one level of the independent variable (IV) e.g., influence factors (IV) on buying behavior (DV). It is also used to compare means of tow or more group means on two or more level s of the independent variable

So, as mentioned above, there are several types of ANOVA depending on the number of treatments and the way they are applied to the subjects in the experiment:

(1) One-way ANOVA is used to test for differences among two or more independent groups. Typically, however, the One-way ANOVA is used to test for differences among three or more groups, with the two-group case relegated to the t-test (Gossett, 1908, as cited in http://en.wikipedia.org/wiki/Analysis_of_variance)), which is a special case of the ANOVA. The relation between ANOVA and t is given as F = t2.

(2) One-way ANOVA for repeated measures is used when the subjects are subjected to repeated measures; this means that the same subjects are used for each treatment. Note that this method can be subject to carryover effects.

(3) Factorial ANOVA is used when the experimenter wants to study the effects of two or more treatment variables. The most commonly used type of factorial ANOVA is the 2×2 (read: two by two) design, where there are two independent variables and each variable has two levels or distinct values. Factorial ANOVA can also be multi-level such as 3×3, etc. or higher order such as 2×2×2, etc. but analyses with higher numbers of factors are rarely done because the calculations are lengthy and the results are hard to interpret.

(4) When one wishes to test two or more independent groups subjecting the subjects to repeated measures, one may perform a factorial mixed-design ANOVA, in which one factor is independent and the other is repeated measures. This is a type of mixed effect model.

(5) Multivariate analysis of variance (MANOVA) is used when there is more than one dependent variable. (see http://www.southampton.ac.uk/~cpd/anovas/datasets/index.htm, as cited in http://en.wikipedia.org/wiki/Analysis_of_variance).

Certain assumptions must be met in order for the ANOVA to be robust (be sensitive to differences): (1) Independence of cases - this is a requirement of the design, (2) Normality - the distributions in each of the groups are normal (use the Kolmogorov-Smirnov and Shapiro-Wilk normality tests to ...