Miami University Exploratory Data Analysis & Underlying Assumptions Project

Use the provided file homework3.Rmdto complete this homework. When saved into the same folder as the datafiles below, the knitted Markdown document will provide the diagnosticplots for problem 1 and some data handling for problems 2 and 3. Makesure to update the document with your name.

In problem 1 you are simply analyzing the provided diagnostic plots.For Problem 2 and Problem 3 perform a complete analysis of the describedproblem, this includes:

• Exploratory data analysis
• Checking the underlying assumptions
• Proper statistical inference
• Any follow-up procedures
• Conclusions in the context of the problem (You need to report the F statistics along with the degrees of freedom and the p-value)

Problem 1 (10pts) – Model Diagnostics

In this problem, an ANOVA model is fit three data sets and thediagnostic figures are provided. Please provide comments on thesefigures and discuss whether the underlying assumptions of ANOVA aresatisfied or not. Make sure to specific which, if any, assumptions areviolated.

Data 1 – Seaweed grazers

Description: To study the influence of ocean grazerson the regeneration of seaweed in the Intertidal zone, a researcherscraped rock plots free of seaweed and observed the degree ofregeneration when certain types of seaweed-grazing animals were deniedaccess. The grazers were limpets (L), small fishes (f) and large fishes(F). A plot was taken to be a square rock surface, 100 cm on each side.Each plot received one of six treatments, named here by which grazerswere allowed access: LfF, fF, Lf, F, L and Control. Because theintertidal zone is a highly variable environment, the researcher appliedthe treatment in eight blocks of 12 plots each. With each block, sherandomly assigned treatments to plots so that each treatment was appliedto two plots. The data set is in file seaweed.csv

Data Source: Ramsey, F.L. and Schafer, D.W. (2013),”The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed)”,Cengage Learning.

Data 2 – Soybeans

Description: In a completely randomized design with a2x3x5 factorial treatment structure, researchers randomly assigned oneof 30 treatment combinations to open-topped growing chambers, in whichtwo soybean cultivars were planted. The responses for each chamber werethe yields of the two types of soybean. The diagnostic figure providedis for a model with only one factor. The data set is in file soybean1.csv

Data Source: Ramsey, F.L. and Schafer, D.W. (2013),”The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed)”,Cengage Learning.

Data 3 – Mice lifetimes

Description: Female mice were randomly assigned tosix treatment groups to investigate whether restricting dietary intakeincreases life expectancy. There are six diet treatments. The data setis in file lifetime.csv

Data Source: Ramsey, F.L. and Schafer, D.W. (2013),”The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed)”,Cengage Learning.

Problem 2 (15pts)

Description: A completely randomized factoriallaboratory experimental design was used to study the effects of washingcycles and pre-washed methods on the abrasion of denim jeans.Pre-washed, stone-washed, and cellulase enzyme washed jeans were thegarment washed denim treatments. The laundering cycles were zero(control group), five, and 25; Edge abrasion is the measure response. Atotal of 90 samples were utilized; 30 of each of the three garmentwashed denim treatments (pre-washed, stone-washed, and cellulase enzymewashed). From each group of 30 samples, ten samples were randomlyassigned to each of the three laundering cycles (0/5/25). Samples wereindependently rated for edge abrasion after a fixed laundering interval.The data set is in file denim_abrasion.csv

Below is the information for each column of the data set:

Laundry Cycles (1= Control (0), 2=5 Launderings, 3=25)
Denim Treatment (1=Pre-washed, 2=Stone-Washed, 3=Enzyme Washed)
Edge abrasion Score

Data Source : A. Card, M.A. Moore, M. Ankeny (2006).”Garment Washed Jeans: Impact of Launderings on Physical Properties,”International Journal of Clothing Science and Technology, Vol. 18, 1/2,pp. 43-52.

Problem 3 (15pts)

Description: The effect of germination time (48, 96,and 144h) on malt quality of four sorghum varieties was investigated todetermine the potential of grain sorghum cultivars in the local breweryindustry. The four evaluated sorghum varieties were Gambella 1107,Macia, Meko, and Red-Swazi. It is known that germination time will beinfluenced by other environmental effects (temperature, humidity,etc…). Due to limitations in the availability of equipment to performthe experiment, 12 samples were randomly assigned to each treatment andthe experiment was repeated at three distinct time points (differentdays) resulting in 36 total observations. The data set is in file mat_var_germ1.csv

Below is the information for each column of the data set:

Variety (1-4 for 4 varieties)
Germination (1-48h, 2-96h, 3-144h)
Malting weight loss (MWL)
Time (1-3, three time points)

Data source:A. Bekele, G. Bultosa, and K. Belete (2012). “The Effect of GerminationTime on Malt Quality of Six Sorghum (Sorghum Bicolor) Varieties Grownat Melkassa, Ethiopia,” Journal of Brewing, Vol. 118, Issue 1, pp.76-81.

Notes:

• Use headers to separate each question part, and label them meaningfully (e.g. “Problem 3, Part 2”). See in-class Markdown examples of this and use them in your assignment.
• All questions must include written answers in full problem context. Submitting only a Markdown with compiled R code but no supporting answers will only receive limited credit.
• You will upload your final knitted HTML to Canvas for grade. Make sure you place your name and homework number in the Markdown header, e.g.
  • title: “Homework #3”
  • author: “Your Name Here”
  • date: “September .., 2020”
  • output: html_document

Reminder: Assignments in STA 363 aredesigned in such a way that we will be able to detect academicdishonesty. If you turn in another student’s generated Markdowndocument, we will know and proceed with an academic dishonesty claim.