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Unformatted text preview: Lecture 6 Lamb and C. McLaren A Spreadsheet Demonstrating the Interaction of the Magnitude of the Error Term and the Treatment Effect in an One-Way ANOVA Using Simulated Data Steven W. Lamb, Indiana State University Constance H. McLaren, Indiana State University The purpose of the Excel spreadsheet is to allow the student to quickly grasp the impact that various magnitudes of treatment effects and various magnitude of the standard deviation of the error term will have in determining significance in a One-way ANOVA. The students will gain insight in the nature and attributes of the theoretical model. The spreadsheet developed by the authors allows the students to input three values into the theoretical model = + Xij µ βj + eij (where eij are N(0, σ ℯ ) Those input values are the value of the Grand Mean, µ; the treatment effects βj ’s, (where β1 equals -k, β2 equals 0, and β3 equals +k); there are three treatments, and finally the population value of the standard deviation of the error term σe . Students will also easily be able to determine the impact of error terms which do not sum to zero (where the statistics associated with the error terms differ significantly from their parameters) upon the estimates of the Treatment Effects, as well as upon the estimate of other parameters. The spreadsheet is set up so that three sets of 30 normal error terms are sampled from a Normal Distribution with mean zero, and standard deviation equal to one. Of course, these sampled error terms most likely will not have a sample mean equal to one, and the sample standard deviation will certainly deviate from the designated parameter as well. The student will be able to easily grasp the impact of this deviation upon the estimate of the parameters as well as upon the outcome associated with the one-way ANOVA. Learning Points Immediately Apparent as Well as Discussion Points • Other things being equal, as the error term increases, as within treatment variance increases, the F value decreases, the p value increases; significance becomes less probable. a. The students will quickly discern that large internal variance may remove the ability to detect treatment effects. The smaller the treatment effects, the more quickly an increase in internal variance will mask the treatment effects....
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This note was uploaded on 08/24/2010 for the course MATH 267 taught by Professor Chandrasekhar during the Summer '10 term at Anna University Chennai - Regional Office, Coimbatore.
- Summer '10