Te Tari Pāngarau me te Tatauranga
Department of Mathematics & Statistics

STAT251 Design of Research Studies

First Semester
18 points
Not available after 2018

What proportion of New Zealanders favour legalisation of cannabis? How many manatees inhabit the waters of Florida? Is aspirin a useful way of reducing the risk of a heart attack? These questions are typical of those posed by scientists working in the natural and life sciences. In this course, we focus on how research can best be carried out in order to help answer such questions. We consider some straightforward concepts as well as formulae that can help us decide how large our research study needs to be.

PLEASE NOTE: The contents of this page are meant only as a guideline of what to expect during the paper. The lecturers reserve the right to adjust some details of the paper during the year, as is deemed appropriate.

Paper details

In this course we aim to give students an understanding of the ideas and methods that are useful in designing a research study in the natural, life and social sciences. This is achieved by relating the appropriate methods of analysis to real-life research situations, and by considering some of the most common mistakes that occur when designing a research study. The emphasis is on understanding the motivation, principles and methods rather than the mathematics underlying them. The course is designed for both general science students and those wanting to specialize in statistics.

Some of the topics covered include random and systematic sampling, cluster sampling, stratified sampling, basic experimental designs, replication, power analysis, experimental units, blocking, factorial designs, nested designs and repeated measurement designs.

Potential students

Any student who has taken either of the 100-level statistics papers can take this paper. It is suitable for any student majoring in sciences as a key to carrying out a scientific research project. This paper will help students to understand the basic principles of sampling, as well as the design of experiments and surveys.


STAT110 or STAT115 or BSNS102 or BSNS112

Main topics

The course is divided into four sections of material. These sections may include the following topics:

Study Design Theory

  • types of studies: observational, quasi-experimental, experimental
  • hypotheses and theories
  • relationship between objectives and design
  • correlation and causation
  • constraints on study design
  • bias and variance
  • uncertainty
  • experimental units
  • replication
  • pseudoreplication
  • sample size
  • error rates
  • data types: continuous, discrete, binomial, categorical
  • effect size estimation

Sampling Design

  • sources of heterogeneity and variance
  • sampling frame and population of inference
  • simple random sampling
  • stratified random sampling
  • systematic sampling
  • cluster sampling
  • model building
  • pre-experimental data simulation and analysis
  • covariates and confounding variables

Experimental Design

  • controlled experiments
  • treatments
  • classical designs

Required text


Reference (copies on hold in Science Library)

The design and analysis of research studies, Bryan Manly (Q180.55 S7 M858)

Introductory Statistics with R, Peter Dalgaard (QA276.4.D3584)


Austina S S Clark, room 117


5 lectures per fortnight; Monday, Wednesday and alternate Friday at 11am in room 241.


1 hour per week, either Friday at 12pm or Tuesday at 3pm in lab B21.

Expected Workload

12 hours per week

Internal Assessment

The internal assessment is made up of 6 bi-weekly assignments worth 15% of the final mark, which will consist of questions related to lecture and lab material, and a 1-hour mid-semester test worth 25% of the final mark.

Late assignments are subject to a 10% penalty per day, unless prior permission has been received by the lecturer.

Final Exam format

3 hours long, with 6 questions of equal value, all of which are to be answered.

Final mark

While we strive to keep details as accurate and up-to-date as possible, information given here should be regarded as provisional. Individual lecturers will confirm teaching and assessment methods.
Suppose a dermatologist wants to study the effectiveness of two different preparations of a skin lotion using two different forms of application, such as one versus two applications per day. She has 12 patients with a certain skin disease and can apply one form of medication to each arm of each patient. Even though the patients have the same disease, there exists considerable variation among them. The two arms of a patient are expected to respond similarly.
An ecological experiment at the University of Minnesota, designed to explore the way plant communities will respond to environmental changes which are believed to be occurring on a global scale. The square plots are the experimental units.