## MAS370 Sampling Theory and Design of Experiments

 Semester 2, 2021/22 10 Credits Lecturer: Dr Kevin Walters Timetable Reading List Aims Outcomes Teaching Methods Assessment Full Syllabus

The results of sample surveys through opinion polls are commonplace in newspapers and on television. The objective of the Sampling Theory section of the module is to introduce several different methods for obtaining samples from finite populations. Experiments which aim to discover improved conditions are commonplace in industry, agriculture, etc. The purpose of experimental design is to maximise the information on what is of interest with the minimum use of resources. The aim of the Design section is to introduce some of the more important design concepts.

Prerequisites: MAS223 (Statistical Inference and Modelling)
No other modules have this module as a prerequisite.

## Outline syllabus

• This course deals with two different areas where the important features are the planning before the data are collected, and the methods for maximising the information which will be obtained. The results of sample surveys through opinion polls, etc., are commonplace in newspapers and on television. The Sampling Theory component of the course introduces several different methods for obtaining samples from finite populations and considers which method is most appropriate for a given sampling problem. Experiments which aim to discover improved conditions are commonplace in industry, agriculture, etc. The purpose of experimental design is to maximise the information on what is of interest with the minimum use of resources. The Experimental Design component of the course introduces some of the more important design concepts.

## Aims

• To consolidate some previous mathematical and statistical knowledge.
• To introduce statistical ideas used in sample surveys and the design of experiments.

## Learning outcomes

• recognise the possible pitfalls in published survey data; and understand the need for randomness and the desirability of stratification in sampling;
• understand the main stages in experimental research and know the desirable properties and the criteria of optimality of experimental designs;
• understand the main features of block designs, factorial and fractional factorial designs and know simple methods for their construction;
• understand the result of the General Equivalence Theorem and apply it to obtain optimal experimental designs;

## Teaching methods

Lectures, problem solving

20 lectures, no tutorials

## Assessment

One formal 2 hour written examination contributing 100% to the module mark. Exam format: all questions compulsory

## Full syllabus

1. Experimental Design

• A review of linear models: matrix notation; least squares estimation; orthogonality; prediction; confidence regions.
• Optimality criteria: D-optimal, G-optimal, V-optimal and A-optimal designs.
• Completely randomised designs and randomised block designs.
• Latin squares and balanced incomplete block designs.
• Factorial designs: complete factorial designs; fractional factorial designs; screening experiments.
• Designs for mixture experiments.
• Continuous and exact designs, and the Generalised Equivalence Theorem.
2. Sampling Theory
• Simple random sampling.
• Stratified sampling.
• Cluster sampling.
• Ratio and regression estimators.
• Capture-recapture sampling
• Questionnaire design.

Type Author(s) Title Library Blackwells Amazon
B Barnett Sample Survey; Principles and Methods 519.6 (B) Blackwells Amazon
B Box, Hunter and Hunter Statistics for experimenters: design, innovation, and discovery 519.5(B) Blackwells Amazon
B Morris Design of experiments: an introduction based on linear models 001.434 (M) Blackwells Amazon
C Atkinson and Donev Optimum Experimental Designs 519.52 (A) Blackwells Amazon
C Box and Draper Empirical model building and response surfaces 519.52 (B) Blackwells Amazon
C Cornell Experiments with mixtures 519.52 (C) Blackwells Amazon
C Cox and Reid The theory of the design of experiments 519.52 (C) Blackwells Amazon
C Goos and Jones Optimal design of experiments : a case study approach 670.285 (G) Blackwells Amazon

(A = essential, B = recommended, C = background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.