STA320 Final Exam Team 2

1 Research Question & Response Variable

What is your research question and your response variable? Give a detailed answer.

2 Factors, Levels, and Design Choice

List your factors and their levels. What is your design choice? Discuss any constraints or restrictions on randomization. Report your design table which includes run randomization. Discuss how you should employ randomization and blocking in this experiment.

3 Analysis Results

Write a comprehensive paragraph on the results of your statistical analysis. Use APA style. Refer to the interaction plots if necessary.

Response : response
                                 Df Sum Sq Mean Sq F value    Pr(>F)    
MODEL                            15 36.027  2.4018  8.0018 4.860e-07 ***
 FactorA                          1 12.727 12.7273 42.4018 2.489e-07 ***
 FactorB                          1  3.592  3.5923 11.9680 0.0015537 ** 
 FactorA:FactorB                  1 12.286 12.2862 40.9322 3.448e-07 ***
 FactorC                          1  0.167  0.1671  0.5568 0.4610065    
 FactorA:FactorC                  1  0.033  0.0329  0.1097 0.7426348    
 FactorB:FactorC                  1  0.073  0.0730  0.2432 0.6252730    
 FactorA:FactorB:FactorC          1  0.189  0.1890  0.6298 0.4332827    
 FactorD                          1  1.056  1.0562  3.5187 0.0698296 .  
 FactorA:FactorD                  1  0.503  0.5027  1.6748 0.2048826    
 FactorB:FactorD                  1  0.004  0.0042  0.0140 0.9066870    
 FactorA:FactorB:FactorD          1  0.224  0.2236  0.7451 0.3944625    
 FactorC:FactorD                  1  0.007  0.0073  0.0243 0.8770860    
 FactorA:FactorC:FactorD          1  4.837  4.8370 16.1148 0.0003364 ***
 FactorB:FactorC:FactorD          1  0.214  0.2141  0.7133 0.4046114    
 FactorA:FactorB:FactorC:FactorD  1  0.114  0.1141  0.3802 0.5418589    
RESIDUALS                        32  9.605  0.3002                      
CORRECTED TOTAL                  47 45.632                              
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Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

4 Power

Calculate the post-hoc power for this design. Use the effect size from your output.

The four-way interaction effect size is eta²=0.109001. Degrees of freedom for the power calculation is df=1.

5 Residual Analysis

Are your assumptions met? Use the plots to support your argument.

6 Factorial Regularities

Do the results of your factorial experiment display sparsity, heredity, and hierarchy? Support your answer with your results.

7 Limitations & What You’d Do Next

Discuss issues you see with this design. Do you have issues with Confounding effects? Are there design weaknesses? Give follow up experiment ideas.