# Design of Experiments

**Institute/Department:**

Mathematical Statistics, Mathematics Centre

**Credits:**

7.5 credits (7.5 ECTS credits)

**Prerequisites:**

Basic course in mathematical statistics and experience of programming.

**Requirements for assessment:**

Written exam, written project report, and compulsory computer lab.

**Time and place:**

- The course will be given in English.
- Course start: Monday March 25, 8:15-10:00 in E:B.
- The schedule in TimeEdit for the course can be found here.

**Course Schedule:** (.pdf)

**Course literature:**

Main course litterature:

- "Statistics for Experimenters", by Box, Hunter and Hunter. Wiley, 2nd ed. (2005)
- Some reading guidelines:
- Chapter 1 (all)
- Chapter 2 (mostly repetition - 2.1-2.12 most important)
- Chapter 3 (3.1-3.5 most important)
- Chapter 4 (4.1-4.4 most important)
- Chapter 5 (5.1-5.10, 5.14 most important)
- Chapter 6 (6.1-6.6 most important)

**Computer labs:**

The computer labs are compulsory for the course. Labs will be done in the package R. You can download this for free and install on your computer. Can be found the R's project homepage.

**Project:**

A project with written project report shall be completed during the course. Preferably groupwise (2-3 students in each group).

**Examination:**

Written exam Monday June 3th, 8:00-13:00 in MA10.

Example exam: Exam 2016 and Formula sheet and statistical tables

Exam June 2019 (.pdf) Solutions (.pdf) (NEW! Exams will be displayed Tue June 18, 16.00-16.30)

## Lectures

There will be 7 lectures on this course. All chapter numberings refer to the course book by Box, Hunter and Hunter (2nd edition). Here is a preliminary outline:

- Introduction (.pdf) Ch. 1.
- Basics and Comparing Two Entities (.pdf , blackboard) Ch 2-3.
- Comparing a Number of Entities (.pdf) Ch 3-4.
- RCBD, Latin Square Design, Graeco-Latin Square Design (.pdf) Ch 4.
- Two Level Factorial Design (slides , blackboard , replicated design) Ch 5.
- Fractional Factorial Design (slides)
- Multivariate Regression (slides , blackboard) Ch 10.

## Exercises

There will be 6 exercise sessions in this course. See the course schedule for recommended weekly list of problems to solve.

**Exercises** (.pdf)

Answers - Exercises - Week 1 (.pdf)

Answers - Exercises - Week 2 (.pdf)

Answers - Exercises - Week 3 (.pdf)

Answers - Exercises - Week 5 (.pdf)

Answers - Exercises - Week 6 (.pdf)

Answers - Exercises - Week 7 (.pdf)

## Computer labs

There will be seven computer labs. Attendance and completion of all computer labs is compulsory for the course. Remember to sign up for each lab with Maria.

LAB 3. Datafiles to use: mollusc penicilin.

LAB 4. Datafile to use: BHHp8ch5.

LAB 5. Datafile to use: filelab5 write in R: data <- read.delim("filelab5.txt", header=TRUE)

*NEW!* For Lab 5 you can also do an additional analysis of the same problem by using the following script (highly recommended!): extendedLab5 Here you can calculate mean effects and graphically analyze significance of effects.

LAB 6. Datafiles to use: economic murder. Data from lab 4: lab4data

**Please sign up for the labs using this** link

## Project

**Two options:**

Option 1: Investigate and analyze a pre-defined experimental design problem (.pdf)

Option 2: Choose your own experiment by considering the following:

- Find a dataset within a topic that you are interested in or consider an experiment that would give you data about a phenomenon that you are interested in.
- Study as much as you can about the dataset or phenomenon: its origin, potential sources of systematic error, potential sources of noise.
- Formulate one or more hypothesis that can be investigated from the data.
- Structure an experimental design for your phenomenon and carry out the experiment, or if your starting point is an existing dataset: structure an "experimental design" around the data suitable for your hypothesis.
- Carry out relevant hypothesis testing.
- Validate and discuss your assumptions.
- Discuss your result.
- Write a short report on 1) through 7) and send it to me (fredriko@maths.lth.se)
- Do feel free to carry out the project either as individual or as a small group (2-3 students), subject to your own preference.

The final project report must be sent to the instructor (Fredrik Olsson) before May 31, 2019.

Example projects made by students: