CLG Topic 12

# CLG Topic 12 - Topic 12 Handout CARS example Learning...

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Topic 12 Handout: CARS example Learning Goals : (1) Explore the difference between balanced and unbalanced ANOVA designs; (2) Further understanding of interactions; (3) Learn about confounding of effects in ANOVA. The questions are based on the following scenario. 36 people were sent to 36 used car dealers and an offer was obtained by each for a 1995 Chevy Lumina in reasonably good condition. The design chart is shown at the bottom of the page. 12.1 What can be said about the balance of the design with respect to: a. Each effect individually b. Age*Gender Interaction c. Age*Time Interaction d. Gender*Time Interaction e. Age*Gender*Time Interaction 12.2. For the moment, ignore gender and focus only on Age and Time. Plots for the interaction and main effects, along with ANOVA output, are shown on pages 1-3 of the output. Draw whatever conclusions are appropriate based on the output. 12.3. Now ignore time and focus on Age and Gender. Plots and ANOVA are shown on pages 4-6 of the output. Draw whatever conclusions are appropriate. 12.4. Lastly, consider the analysis of Gender and Time – the additional output is shown on page 7. Draw whatever conclusions are appropriate. 12.5. Now consider the three-way ANOVA (using all of the variables). a. Based on the full model ANOVA output on the top of page 8, which interactions do you believe can be removed from the model? Which type of SS should you use in determining this? What procedures should you follow? Why is this important? b. Now remove the 3-way interaction. Consider the questions in part (a) again. Continue this path to develop your “final” model. Do you buy the final model developed by this approach? 12.6. Is gender important? (Be very careful in your response). Is there anything else you would do (or do differently) in order to analyze this question? Design Chart

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Output Page # 2 Age Young Middle Elderly Young Middle Elderly Weekday xxxx xxx xxxxx xx xxx x Weekend xx xxx x xxxx xxx xxxxx Gender Male Female Time
Output Page # 3 Age/Time Analysis (ignoring gender) *Create Main Effects Plots; data a1; set means; if _TYPE_= 1 ; data a2; set means; if _Type_= 2 ; symbol1 font = v =dot i =join h = 2 c =black; axis1 label =( angle = 90 'Mean Offer' ) order = 21 to 28 by 1 ; axis2 offset =( 3 , 3 ); proc gplot data =a1; plot mean_offer*age / vaxis =axis1 haxis =axis2; proc gplot data =a2; plot mean_offer*time / vaxis =axis1 haxis =axis2; run ; *Interaction Plot; symbol1 font =ORFONT v =F i =join h = 3 c =magenta; symbol2 font =ORFONT v =K i =join h = 3 c =blue; data a3; set means; if _Type_= 3 ; axis1 label =( angle = 90 'Mean Offer' ); proc gplot data =a3; plot mean_offer*age=time / vaxis =axis1; run ; Interaction Plot Main Effects Plots

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Output Page # 4 proc glm data =cash; class age time; model offer=age|time; lsmeans age*time / slice =time adjust =tukey tdiff ; lsmeans age*time / slice =age; run ; Analysis of Variance Sum of Source DF Squares Mean Square F Value Pr > F
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## This note was uploaded on 02/20/2012 for the course STAT 502 taught by Professor Staff during the Fall '08 term at Purdue.

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CLG Topic 12 - Topic 12 Handout CARS example Learning...

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