Statistics
Te Tari Pāngarau me te Tatauranga
Department of Mathematics & Statistics

## STAT242 Multivariate Methods

 Second Semester
18 points
Not available after 2018

Multivariate analysis is a 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 patterns in the data. Several of the techniques are data exploratory rather than hypothesis testing.

What are the attitudes of young teenagers to smoking? Factor analysis identifies the predominant attitudes from a survey of 13 year old children in New Zealand and suggests anti-smoking policies to be developed.

How do you identify the origin of oysters which have caused food poisoning in a restaurant? Are they from Foveaux Strait or another part of New Zealand or even from another country? Trace element readings answer this questions using discriminant function analysis and principal components. Similar analyses apply to the country of origin of manuka honey, a valuable export for New Zealand, and the country location of processed fish foods from New Zealand. These techniques are widely used in forensic science and two court cases will be described where statistical evidence is crucial in successful prosecution.

What are the attitudes of visitors to New Zealand from Germany, Japan and Australia; in particular why do these tourists come to New Zealand and how do they rate the accommodation and attractions both before and after a visit? How should New Zealand be promoted in these countries.

How do student attitudes to sustainability change as a result of their time at university. Confirmatory factor analysis identifies four attitudes to monitor while students are at university.

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

What is the relationship between genetic variables and environmental variables for a particular population. Canonical correlation analysis provides 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. Also areas of application include ecology, environmental science, the biological sciences in general, forensics, food science and geography. Rather than concentrating on the mathematical aspects of the methods covered, the paper emphasizes applications and data analysis through the use of the statistics packages SPSS24, AMOS24 and R.

### Potential students

Undergraduate students in any of the subjects listed above will find this paper surprisingly relevant. The goal is that students will be able to go away and carry out these techniques for themselves in their own time on their own data.It is also a paper for anyone majoring in statistics and it presents methods which are not developed in other statistics courses.

But, in addition, the paper could be a very 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 STAT342 with the only difference being that STAT342 has an additional project worth 25% of the assessment with the final exam counting 75%.

### Main topics

• Multivariate analysis of variance
• Principal component analysis
• Fisher discriminant function analysis
• Logistic and multinomial regression for discrimination with categorical variables
• Cluster Analysis
• Exploratory factor analysis
• Confirmatory factor analysis using AMOS
• Canonical correlation analysis
• Measures of distance
• Scaling and ordination including multidimensional scaling
• Correspondence analysis

### Prerequisites

STAT 110 or STAT 115 or BSNS102 or BSNS112

### Recommended text

Multivariate Statistical Methods, a Primer, B.F.J. Manly

(This book is on close reserve in the Science Library.)

A course reader is available at the start of Semester 2 free of charge online (through the course resource page) and purchase of a hardcopy through Uniprint is therefore optional. Students are encouraged to bring the course reader to lectures.

### Lecturer

Associate Professor John Harraway, room 238 Science III

### Lectures

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

Tuesday ( ), Thursday( ) and Friday( ) all at 1.00pm with rooms still to be announced. No lectures will be held in the first week of the second semester in 2018 as Associate Professor Harraway will be at a conference in Japan.

### Tutorials

One hour per week on Monday, Wednesday and Thursday at 2pm (MAB21). Students ca attend more than one tutorial.

Support class Tuesday 12 midday (MAB21) if needed. Tutorials will start in the third week of lectures or possibly at the end of the second week.

### Internal Assessment

Eight or nine exercises contributing varying marks each as advised when each exercise is released. Marks will be noted for each exercise. The assignment total is converted in proportion to a mark out of 100.

### Exam format

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

### 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.

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:
We use canonical correlation analysis to answer these questions.

How do you identify oysters being illegally sold as Bluff oysters? Trace element readings answer these questions using discriminant function analysis.

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 342. The study is making a valuable contribution to determining the levels of sustainable tourism in this country.