IE533: Industrial Applications of Statistics

Homework #3

Due: 3:00 PM 18 February 2020 via Gradescope

Purpose: Practice using software to perform Kruskal-Wallis test, Random Effects ANOVA, and Randomized Complete Block Design analysis.

Output: Please address the following items in a report (word doc or PDF) no longer than 4 pages. Succinctness and orderly formatting are prized and rewarded (0.5 Points).

1. (1.25 Points) Use the data set provided on Blackboard (HW 3 Problem 1) to perform an

ANOVA, check the assumptions and indicate if there is any reason to do a nonparametric test (include plot supporting your decision). Regardless of your decision, fit a Kruskal-Wallis test to the data. Include the ANOVA table and the Kruskal-Wallis output. What do you conclude about the impact of storage medium on tastiness with respect to the output and assumption checks?

2. (1.25 Point) Generate a data set to mimic the location tag experiment from lecture. Use the following generating distributions to draw 20 observations for each of three locations: Location1 ~ ( = 3.2) Location2 ~ ( = 5.2) Location3 ~ ( = 11.5) Perform a Mixed Effects Model with a single random effect (location) for the number of items of your brand purchased. Include the ANOVA table, what is your conclusion about the impact of location on the number of buys? What is the value of the Intra-Class Correlation coefficient from your model? What is the variance estimate for location effect? Why is the Standard Error of the location variance so large?

3. (0.5 Point) Use the data set provided on Blackboard (HW 3 Data Problem 3) to analyze the Randomized Complete Block design as in lecture. Include the ANOVA table, what do you conclude about the impact of tire tread on noise level?

4. (0.5 Point) Using the data from problem 3, check your assumption about no interaction. Include the interaction plot and comment on if the assumption appears to hold.

5. (0.5 Point) Refit your model form #3 without trailer batch (ignore the blocking variable). Include your ANOVA table, what has changed in your ANOVA table due to failure to account for the blocking variable?

6. (0.5 Point) Delete observations 17-20 so that an entire trailer batch is lost. Fit a general linear model to the data. Include your ANOVA table, what has changed in your ANOVA table due to the missing value?

7. (0.25 Points – Optional) Identify a published experiment (journal article, white paper, blog, etc.) that uses a randomized complete block design to generate their data. Include a citation/link/DOI to the study and name the blocking variable that was used.