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
• Quadratic discrimination
• 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

Your final mark F in the paper will be calculated according to this formula:

F = max(E, (2E + A)/3)

where:

• E is the Exam mark
• A is the Assignments mark

and all quantities are expressed as percentages.

### Students must abide by the University’s Academic Integrity Policy

Academic integrity means being honest in your studying and assessments. It is the basis for ethical decision-making and behaviour in an academic context. Academic integrity is informed by the values of honesty, trust, responsibility, fairness, respect and courage.

Academic misconduct is seeking to gain for yourself, or assisting another person to gain, an academic advantage by deception or other unfair means. The most common form of academic misconduct is plagiarism.

Academic misconduct in relation to work submitted for assessment (including all course work, tests and examinations) is taken very seriously at the University of Otago.

All students have a responsibility to understand the requirements that apply to particular assessments and also to be aware of acceptable academic practice regarding the use of material prepared by others. Therefore it is important to be familiar with the rules surrounding academic misconduct at the University of Otago; they may be different from the rules in your previous place of study.

Any student involved in academic misconduct, whether intentional or arising through failure to take reasonable care, will be subject to the University’s Student Academic Misconduct Procedures which contain a range of penalties.

If you are ever in doubt concerning what may be acceptable academic practice in relation to assessment, you should clarify the situation with your lecturer before submitting the work or taking the test or examination involved.

Types of academic misconduct are as follows:

#### Plagiarism

The University makes a distinction between unintentional plagiarism (Level One) and intentional plagiarism (Level Two).

• Although not intended, unintentional plagiarism is covered by the Student Academic Misconduct Procedures. It is usually due to lack of care, naivety, and/or to a lack to understanding of acceptable academic behaviour. This kind of plagiarism can be easily avoided.
• Intentional plagiarism is gaining academic advantage by copying or paraphrasing someone elses work and presenting it as your own, or helping someone else copy your work and present it as their own. It also includes self-plagiarism which is when you use your own work in a different paper or programme without indicating the source. Intentional plagiarism is treated very seriously by the University.

#### Unauthorised Collaboration

Unauthorised Collaboration occurs when you work with, or share work with, others on an assessment which is designed as a task for individuals and in which individual answers are required. This form does not include assessment tasks where students are required or permitted to present their results as collaborative work. Nor does it preclude collaborative effort in research or study for assignments, tests or examinations; but unless it is explicitly stated otherwise, each students answers should be in their own words. If you are not sure if collaboration is allowed, check with your lecturer..

#### Impersonation

Impersonation is getting someone else to participate in any assessment on your behalf, including having someone else sit any test or examination on your behalf.

#### Falsiﬁcation

Falsiﬁcation is to falsify the results of your research; presenting as true or accurate material that you know to be false or inaccurate.

#### Use of Unauthorised Materials

Unless expressly permitted, notes, books, calculators, computers or any other material and equipment are not permitted into a test or examination. Make sure you read the examination rules carefully. If you are still not sure what you are allowed to take in, check with your lecturer.

#### Assisting Others to Commit Academic Misconduct

This includes impersonating another student in a test or examination; writing an assignment for another student; giving answers to another student in a test or examination by any direct or indirect means; and allowing another student to copy answers in a test, examination or any other assessment.

Further information

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.