### About

At the end of this course, successful students will be able to

- Design and conduct an experiment that exhibits both a treatment design and randomization design that allow for the testing of differences between the levels of a single or multiple treatments of interest.
- Given a description of an experiment, correctly identify common design elements, including (a) Crossed factorial designs with interactions, (b) Nested factorial designs, (c) Blocking factors, (d) Nuisance variables, (e) Split-plot designs, (f) Repeated measures, and (g) Random effects.
- Specify an appropriate statistical model for observations resulting from a designed experiment exhibiting the elements in item 2.
- Identify estimable terms in a statistical model for an experiment, find the least squares estimator of estimable terms, and specify the statistical distribution of the estimator.
- Conduct and correctly interpret statistical hypothesis tests for the overall effect of a treatment and for the effects of contrasts.
- Correctly employ methods for multiple comparisons to control the experimentwise error rate when multiple hypothesis tests are conducted.
- Examine model assumptions using residual plots and a description of the experiment. Apply remedial measures such as transformations to the response when such transformations improve adherence to modeling assumptions.

### Course Topics

- Analysis of variance for single factor designs,
- Analysis of variance for multifactor designs,and
- Response surface methodology.

### Course Author(s)

Dr. Ephraim Hanks is the primary author of these course materials.

### Software

This course will use the statistical software program SAS. See the Statistical Software page for more information.

### Textbook

Dean, A., and Voss, D. (2017) *Design and Analysis of Experiments. *2nd Edition*. * Springer. ISBN-13: 978-3319522487

(available for free download from the PSU Library website)

Kutner, M., Nachtsheim, C., Neter, J., and Li, W. (2013) *Applied Linear Statistical Models*. 5th Edition. McGraw-Hill/Irwin. ISBN-13: 978-1259064746

(this text is recommended as a reference, but not required).

### Assessment Plan

*Homework:* The homework will consist of problems selected from the textbook or given within the notes and will be listed in the Homework folder.

*Participation: *The class will have discussion boards and you will be expected to follow the discussion boards and also participate in any discussions. You are also expected to keep up with all class communications and check Canvas on a regular basis.

*Mid-Terms:* The Midterms will be timed. They are to be submitted similarly to the Homework.

*Final Exam:* The final exam will be comprehensive and proctored (please see your course syllabus you receive upon enrollment for details).

*Project*: students will be required to design, carry out, and analyze an experiment. This project can be done in small groups, and you are encouraged to begin thinking now about an experiment that you could undertake during the semester. Additional details will be given after the first midterm.

### Prerequisites

- STAT 200, STAT 240, STAT 250, STAT 301 or STAT 401