University of Technology Sydney

35513 Statistical Methods

Warning: The information on this page is indicative. The subject outline for a particular session, location and mode of offering is the authoritative source of all information about the subject for that offering. Required texts, recommended texts and references in particular are likely to change. Students will be provided with a subject outline once they enrol in the subject.

Subject handbook information prior to 2020 is available in the Archives.

UTS: Science: Mathematical and Physical Sciences
Credit points: 6 cp
Result type: Grade and marks

There are course requisites for this subject. See access conditions.

Description

This subject gives an introduction to probability theory and statistics. Students learn how to describe random phenomena using the language of probability, and how this is applied in a statistical framework to solve real world problems. The first half of the subject introduces the students to important concepts in probability, such as random variables and their probability distributions. Fundamental properties such as expectations, independence and the Central Limit Theorem are discussed. The second half of the course introduces classical statistical inference and its connection to probability theory. Sampling distributions and their use in constructing confidence intervals and hypothesis testing are discussed. The course ends by introducing simple linear regression and analysis of variance techniques.

Subject learning objectives (SLOs)

Upon successful completion of this subject students should be able to:

1. understand how to use descriptive statistics to properly summarize a dataset;
2. understand basic properties of random variables and their probability distributions;
3. determine an appropriate statistical model for a given dataset and conduct sensible statistical inference;
4. formulate a linear regression model and carry out appropriate statistical inference. Understand the limitations of the linear regression model and the implications of model misspecification;
5. analyse real-world datasets using modern statistical software. Apply theoretical knowledge from the lectures and tutorials to solve real-world problems;

Contribution to the development of graduate attributes

This subject teaches students basic concepts in probability theory and their application in statistical modelling and inference. Students learn how to formulate an appropriate statistical model for a given dataset and how to carry out sensible statistical inference. The subject also trains the students in using modern statistical software to solve real-world problems and how to effectively communicate these solutions. Thus this subject is contributing to the following graduate attributes:

Graduate Attribute 1 - Disciplinary knowledge.

The lectures develop the theoretical understanding of the material. The tutorials allow the students to apply the theory to solve exercises and deepen their understanding of the material.

Graduate Attribute 2 - Research, inquiry and critical thinking.

The lectures present approaches to formulate statistical models of various types of data. The students will develop skills in determining the correct approach themselves in the tutorial classes.

Graduate Attribute 3 - Professional, ethical and social responsibility.

The tutorial classes encourage the students to work in groups under the supervision of a tutor. The computer lab is done in small groups and trains the students' ability to work effectively and responsibly.

Graduate Attribute 4 - Reflection, innovation, creativity.

The lectures teach the students to develop a creative mindset to solve a statistical problem. The tutorials give the students the opportunity to train their ability to design creative solutions to statistical problems. The computer labs train the students ability to critically evaluate statistical procedures and interpretation of results.

Graduate Attribute 5 - Communication.

Presentation of solutions to problems using appropriate professional language is emphasised in the computer labs.

Teaching and learning strategies

The subject consist of a combination of complementary in-class and self-study activities. Before class meetings, students are expected to engage with background material that will introduce the fundamental concepts covered in the subject. The face-to-face classes (one 90 minutes + one 60 minutes of weekly lectures, one 120 minutes weekly tutorial, and two 180 minutes computer labs) will incorporate a range of teaching and learning strategies, including individual and collaborative group work, presentation of worked examples and applying modern statistical software to analyse real-world datasets. Students are to review the relevant material made available on UTSOnline prior to classes.

Content (topics)

The major topics covered in this subject are:

  • Basic concepts in probability theory
  • Statistical inference and its connection to probability theory
  • Critical thinking about data-based claims

Assessment

Assessment task 1: Online Exercises

Intent:

This assessment task contributes to the development of the following graduate attributes:

1. disciplinary knowledge

2. research, inquiry and critical thinking

4. reflection, innovation and creativity

Objective(s):

This assessment task addresses subject learning objective(s):

1, 2 and 3

Type: Exercises
Groupwork: Individual
Weight: 30%
Criteria:

Students will be assessed on:

  • the accuracy of their analysis.

Assessment task 2: Computer lab exercises

Intent:

This assessment task contributes to the development of the following graduate attributes:

1. disciplinary knowledge

2. research, inquiry and critical thinking

3. professional, ethical and social responsibility

4. reflection, innovation and creativity

5. communication

Objective(s):

This assessment task addresses subject learning objective(s):

1, 3, 4 and 5

Type: Exercises
Groupwork: Group, group assessed
Weight: 20%
Criteria:

Students will be assessed on:

  • clarity of communication
  • appropriateness of the analysis
  • appropriateness of their implementation
  • evidence of appropriate behaviour in the group

Assessment task 3: Examination

Intent:

This assessment task contributes to the development of the following graduate attributes:

1. disciplinary knowledge

2. research, inquiry and critical thinking

4. reflection, innovation, creativity

Objective(s):

This assessment task addresses subject learning objective(s):

1, 2, 3 and 4

Type: Examination
Groupwork: Individual
Weight: 50%
Criteria:

Students will be assessed on:

  • accuracy of analysis
  • clarity of communication

Minimum requirements

Student must obtain at least 40% of the marks available for the final examination in order to pass this subject. If 40% is not reached, an X grade fail may be awarded for the subject, irrespective of an overall mark greater than 50.

Students should demonstrate competence in all aspects of the assessment in order to pass the subject. To pass the subject, a student must achieve a final result of 50% or more. The final result is simply the sum of all the marks gained in each piece of assessment.

Recommended texts

Probability & Statistics for Engineers & Scientists - 9th Edition by Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying Ye. Pearson 2016

This textbook can be purchased as an eBook direct from Pearson for $AUD 60.00. See links in UTSOnline under Subject Orientation. Alternative suppliers will also this text.

NOTE: The tutorials rely on having access to the textbook above, as the exercises to be solved are taken from the textbook. Students are strongly recommended to have a copy, either hard or electronic, with them to each tutorial session.