Schools
 
Undergraduate
Stats
Papers
STAT242
 
Department

Search Maths/Stats: 
 
Advanced Search



A recent study of colonies of butterfly involved measuring various environmental and biological variables. The environmental variables were altitude, rainfall, and minimum and maximum temperatures, while the biological variables were gene frequencies. Two questions that can be answered by analysing these data are:
  • Are the gene frequencies similar for colonies that are close in space?
  • What is the extent to which the gene frequencies relate to the environmental variables?
We use canonical correlation analysis to answer these questions.







A study was carried out to try to differentiate between Crohn’s disease and other forms of inflammatory bowel disease using rectal biopsy measurements.

Eighty biopsies were studied, comprising 20 patients with normal biopsies, 20 with Crohn’s disease, and 20 with each of two other types of bowel disease. There were 12 variables measured from each biopsy. A stepwise discriminant function analysis developed two functions, involving five of the variables, that maximised the differences between the four groups, and assisted in more accurate diagnosis of the diseases.






The natural areas of New Zealand are coming under increasing pressure from recreation and tourism interests, and this is affecting both resource conservation and visitor satisfaction.

A survey of 2000 overseas tourists was conducted at Christchurch and Auckland airports to establish the visitors’ perceptions of the walking tracks and tourist destinations in New Zealand. Factor analysis and multidimensional scaling can be used to identify the attitudes of tourists, and to identify perceptions held by tourists from different countries.

The data, along with responses from domestic tourists, are analysed in Stat 242. The study is making a valuable contribution to determining the levels of sustainable tourism in this country.

STAT242 Multivariate Methods

Second Semester, 18 points
Multivariate analysis is an important branch of statistics dealing with procedures for summarising, representing and analysing multiple quantitative measurements obtained on a number of individuals or objects. The procedures identify clearly patterns in the data if these patterns exist. Several of the techniques are hypothesis generating rather than hypothesis testing.

What are the attitudes of young teenagers to smoking? Factor analysis identifies these from a survey of 13 year old children and allows anti-smoking policies to be developed.

How do you identify oysters being illegally sold as Bluff oysters. How do you identify the origin of oysters which have caused food poisoning in a restaurant. Trace element readings answer this question using discriminant function analysis. It is like a story out of CSI. Similar analysis applies to the origin of honey and other food products such as fish illegally caught.

What are the attitudes of visitors to New Zealand from Germany, Japan and Australia; in particular why these tourists come to New Zealand and how do they rate the accommodation and attractions?

How do students attitudes to sustainability change as a result of their experience at university. Confirmatory factor analysis identifies four attitudes which are being monitored over a three to four year period.

How do you identify the growth of farmed mussels and wild mussels in the Marlborough Sounds. Principal components answer this question.

What is the relationaship between genetic variables and environmental variables for a particular population. Canonical correlations provide the answer.

Paper details

This is a paper in advanced statistical methods. Applications are widespread in the analysis of psychological, sociological and other types of behavioural data including market research. Other areas of application include medicine, ecology, environmental science, geography and the biological sciences in general. Rather than concentrating on the mathematical aspects of the methods covered, the paper emphasizes applications and data analysis through the use of the statistics package, IBM SPSS 19 and the AMOS package.

Potential students

Undergraduate students in any of the subjects listed above will find this paper surprisingly relevant. It is also a paper for anyone majoring in statistics as it presents methods which are not developed in other statistics courses.

But, in addition, the paper could be the most useful quantitative paper for graduate and research students in all areas. These students, who enrol in the paper as part of their research programme, will find they are already meeting the techniques in their own reading and data analysis. These students can instead be registered for the equivalent paper STAT 342 with the only difference being that STAT342 has an additional project worth 25% of the assessment.

Main topics

  • Multivariate analysis of variance
  • Discriminant function analysis
  • Logistic and multinomial regression for discrimination
  • Clustering
  • Principal component analysis
  • Exploratory factor analysis
  • Confirmatory factor analysis using AMOS
  • Canonical correlation analysis
  • Measures of distance
  • Methods of scaling and ordination
  • Principal coordinates
  • Correspondence analysis
  • Repeated measures

Prerequisites

STAT 110 or STAT 115

Recommended text

Multivariate Statistical Methods, a Primer, B.F.J. Manly
(This book is on close reserve in the Science Library.)
A book of course notes will be available from the University Print Shop at the start of Semester 2

Lecturer

John Harraway, room 238 Science III

Lectures

Five lectures per fortnight on average during the semester giving 32 lectures in total.

Tutorials

One hour per week at times to be arranged

Internal Assessment

Ten exercises contributing varying marks each, but giving a total internal assessment (A) out of 100 marks.

Exam format

A three-hour written examination, also worth 100 marks.

Final mark

The final mark F is calculated from:
F = max { E, (2E + A)/3 }
where E (exam mark) is out of 100, A (internal assessment) is out of 100.

The “max” corresponds to plussage: if your internal assessment mark is greater than your exam mark then it is combined in the proportion shown. If it is less then it is ignored and the exam mark itself is used.


Plagiarism

Students should make sure that all submitted work is their own. “Plagiarism is a form of dishonest practice. Plagiarism is defined as copying or paraphrasing another’s work and presenting it as one’s own” (University of Otago Calendar). In practice this means that plagiarism includes any attempt in any piece of submitted work (e.g. an assignment or test) to present as one’s own work the work of another (whether of another student or a published authority). Any student found to be responsible for plagiarism in any piece of work submitted for assessment shall be subject to the University’s dishonest practice regulations which may result in various penalties, including forfeiture of marks for the piece of work submitted, a zero grade for the paper, or in extreme cases exclusion from the University. The University of Otago reserves the right to use plagiarism detection tools.

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.