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Factorial Analysis of Variance

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** Please see the attached files for the complete problem description **

Please see attached problem with formulas. An experiment was designed to test the relative effectiveness of a computer-taught method of instruction compared with a conventional lecture method. Two samples of three subjects each were selected from among students of good aptitude and assigned to the two methods of instruction, as shown below
(please see the attached file)

Two samples of the same size were selected from among students of ordinary ability and assigned to the same methods of instruction. In the test trial, the 12 students earned the scores shown in the table above.
(a) Find df_total, df_R, df_C, df_WC, and df_RXC

(b) Find SS_total, SS_R, SS_C, SS_WC, and SS_RXC

(c) Calculate the several variance estimates appropriate to a two-way ANOVA, and present the results thus far developed in an analysis of variance table

(d) Calculate the Fs required to test the main effects and the interaction effect. Draw the statistical conclusions appropriate when α = .05 and α = .01
(e) Calculate the effect size, ω

(f) Construct a graph of the cell means - the possible outcomes of a hypothetical 2x2 design (6 graphs) and a hypothetical 2x3 design (2 graphs).

(g) In light of the statistical outcome (d) and the graph (e), what appears to be the essential outcome of the study?

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Solution Summary

This solution provides a complete tutorial displaying how to solve the given factorial analysis of variance problems.

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A manufacturing company designed a factorial experiment

A manufacturing company designed a factorial experiment to determine whether the number of defective parts produced by two machines differed and if the number of defective parts produced also depended on whether the raw material needed by each machine was loaded manually or by an automatic feed system. The following data give the numbers of defective parts produced.

Use ? = .05 to test for any significant effect due to machine, load system, and interaction.

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