STA320 Final Exam Team 3

0.0.1 don’t touch above 117 - all appearance

1 Research Question & Response Variable -Arin

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

We are working with a service organization to identify factors and interactions affecting process optimization, specifically processing time per client in minutes.

2 Factors, Levels, and Design Choice -Arin

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.

We are investigating four factors each with two levels (low and high): A = training level (Training), B = software interface (Interface), C = shift scheduling (Shift), and D = task batching (Batch). Design is limited by high day-to-day variability and only one replicate per treatment is possible. This is an unreplicated 2^4 factorial design.

3 Analysis Results -Arin

Write a comprehensive paragraph on the results of your analysis. Include an explanation of how you reached your conclusions, which tables and graphs you used, etc.

Because our full model lacks replication, we cannot state factor significance based on F- and p-values, so we are limited to interpretation factors’ sum of squares. Our greatest sums of squares belong to Training (985.2), Interface (769.9), Batch (362.2), Shift (318.6), Interface:Batch (318.3), and Training:Shift:Batch (152.8).

After reducing the model as described in Q4, we can draw conclusions from p-values. At an alpha level of 0.05, Training (p = .00113), Interface (p = .00258), Shift (p = .0282), Batch (p = .0211), and Interface:Batch (p = .0283) all significantly affect processing time per client.

4 Model Reduction -Sebastian

Is it possible for you to reduce the model? Explain why or should not, or if you should and how you would do it.

We are able to reduce our model with the four-way interaction being as insignificant as it is. We reduce our model to analyze effects of Training, Interface, Shift, Batch, and Interface:Batch. All of these effects are significant with the greatest p-value being p = .0283. We justify this cut-off by looking at the Pareto plot, there is a significant drop in absolute effect size beyond “BD” representing the interaction between Interface and Batch.

Experimental Design Run Order

Training	Interface	Shift	Batch	RunOrder
Low	Low	Low	High	1
High	Low	Low	High	2
Low	Low	High	High	3
Low	Low	High	Low	4
High	Low	Low	Low	5
Low	Low	Low	Low	6
Low	High	High	Low	7
Low	High	High	High	8
High	High	High	High	9
Low	High	Low	High	10
High	Low	High	High	11
High	High	High	Low	12
High	High	Low	High	13
High	High	Low	Low	14
High	Low	High	Low	15
Low	High	Low	Low	16

Response : response
                                Df Sum Sq Mean Sq F value Pr(>F)
MODEL                           15 3239.3  215.95               
 Training                        1  985.2  985.17               
 Interface                       1  769.9  769.95               
 Training:Interface              1   47.3   47.28               
 Shift                           1  318.6  318.56               
 Training:Shift                  1   38.4   38.39               
 Interface:Shift                 1   22.3   22.26               
 Training:Interface:Shift        1   81.5   81.47               
 Batch                           1  362.2  362.21               
 Training:Batch                  1   21.9   21.88               
 Interface:Batch                 1  318.3  318.27               
 Training:Interface:Batch        1   43.5   43.55               
 Shift:Batch                     1   61.4   61.38               
 Training:Shift:Batch            1  152.8  152.80               
 Interface:Shift:Batch           1   16.0   15.95               
 Training:Interface:Shift:Batch  1    0.1    0.14               
RESIDUALS                        0    0.0                       
CORRECTED TOTAL                 15 3239.3                       

Response : response
                 Df Sum Sq Mean Sq F value    Pr(>F)    
MODEL             5 2754.2  550.83 11.3549 0.0007236 ***
 Training         1  985.2  985.17 20.3085 0.0011317 ** 
 Interface        1  769.9  769.95 15.8717 0.0025845 ** 
 Shift            1  318.6  318.56  6.5668 0.0282481 *  
 Batch            1  362.2  362.21  7.4666 0.0211021 *  
 Interface:Batch  1  318.3  318.27  6.5610 0.0283034 *  
RESIDUALS        10  485.1   48.51                      
CORRECTED TOTAL  15 3239.3                              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

5 Power -Benjamin

Explain why calculating power in this design is meaningless.

Calculating power is difficult due to a lack of degrees of freedom, to estimate error variance. Lack of replication risks including unusual responses such as outliers which would distort the results.

6 Factorial Regularities -Sebastian

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

All factorial regularities hold in this instance. Only five of the 13 possible effects are active (38.5%); active interaction effects tend to have active parent effects with higher absolute effect size than those of non-active interactions; single-factor effects are greater than two-factor interactions, and two-factor interactions are greater than three-way interactions.

7 Limitations & What You’d Do Next -Sebastian, Benjamin, Arin

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

This design is limited by its high variability day-to-day and lack of treatment replication. It is very difficult to detect confounding effects with a single replicate per treatment. One confounding variable is the task the client needs assistance with and how long that task may take. A task that has a greater base processing time may be more affected by staff training level, as the client is spending more time interacting with the staff. The full factorial design is weak because of the lack of degrees of freedom, preventing us from interpreting results with p- and F-values, and from estimating error. We strengthened the design in part by reducing the model to focus solely on significant factors, allowing us to work with residuals where we had none before.