(1) State the Assumptions of ANOVA.
(2) Describe the Rationale of ANOVA stating the ANOVA table.
(3) Solve the following problem using One-Way ANOVA
Four types of advertising displays were set up in 12 retail outlets, with three outlets randomly assigned to each of the displays, for the purpose of studying the point-of-sale impact of the displays. The relevant information is given in the following table.
Type of Display Sales
A1 40 44 43
A2 53 54 59
A3 48 38 46
A4 48 61 47
(i) State the Null Hypothesis and Alternative Hypothesis.
Give Step by Step solution using all the required formulas. Give the
ANOVA table and comment on the conclusion.
(ii) Use excel to solve the above problem using the data given in the above table and
comment on the conclusion.
For full description of the question, please see the attached question file.
Assumptions: (1)Several sample means were obtained from ..................
(2)The procedure has been found to be relatively .................
The basic rationale underlying the analysis of variance is as follows:
(1) compute the mean for each sample group.....................................
(2) Now, given the formula .................
(3) Compute the variance separately for each .....................
(4) If the Null Hypothesis that ...
In this solution, the assumptions of ANOVA are stated, the Rationale involved in ANOVA problems is described point to point. All the formulas used for the solution of the ANOVA problem are briefly described and used to solve the following problem.
Four types of advertising displays were set up in 12 retail outlets, with three outlets randomly assigned to each of the displays, for the purpose of studying the point-of-sale impact of the displays. ( information of the table given in attached solution file).
Carry out the Analysis of Variance to test the differences among the mean sales values for the four types of displays, using the 5 percent level of significance using step by step method all formulas and working. Also use excel to solve the problem using excel functions, and interprete the results.
In this solution, the problem is solved using two methods, one by hand calculations involving all the formulas and working, second by using excel. The screen shots of each step of excel screen is given in graphics in the document and the steps of each action is explained clearly, so that the student would be able to work out other problems of ANOVA using excel just by referring this method explained.
Please download the attached solution file to see the excellent presentation which enables even a lay man to understand and follow easily.