MATH219 - Statistics and Probability

Year

Credit points

Campus offering

Prerequisites

MATH107 Introduction to Logic and Algebra

Incompatible

STAT201 Statistics and Probability, STAT206 Introductory Statistics for Science

Teaching organisation

Unit rationale, description and aim

Statistics informs many aspects of contemporary society through applications in business, education, science and the household and at all levels; globally, locally, socially and economically. As a result, some level of statistical literacy is essential in science and social science disciplines.

This unit provides an introduction to descriptive statistics, simple combinatorics and probability and their use in inferential statistics. Discrete and continuous distributions will be considered with a focus on the normal distribution. The unit will also consider sampling distributions and the examination of estimation and hypothesis testing including analysis of variance and some non-parametric tests. Bivariate data analysis on quantitative data using regression and correlation and on qualitative data using cross-tabulations will also be introduced. Appropriate technology for statistical analysis will be used including computer packages such as Microsoft Excel and, most particularly R. The importance of correct and ethical use of statistics will be discussed including references to real cases including examples from the first peoples’ perspective.

The aim of this unit is to provide students with a reasonably sophisticated understanding of statistics, the ability to understand statistical statements and to judge the appropriateness of any chosen statistical test.

Learning outcomes

To successfully complete this unit you will be able to demonstrate you have achieved the learning outcomes (LO) detailed in the below table.

Each outcome is informed by a number of graduate capabilities (GC) to ensure your work in this, and every unit, is part of a larger goal of graduating from ACU with the attributes of insight, empathy, imagination and impact.

Explore the graduate capabilities.

On successful completion of this unit, students should be able to:

LO1 - Select appropriate statistical procedures to analyse a variety of types of data sets. (GA4, GA5) 

LO2 - Use technology to efficiently to solve problems by analysing and critically evaluating data. (GA4, GA5, GA6, GA7, GA8, GA10)

LO3 - Use basic concepts in probability and distributions to calculate and interpret probabilities in chance situations. (GA4, GA5, GA8, GA10) 

LO4 - Determine correct inferences from a variety of data sets using Hypothesis testing or otherwise. (GA3, GA4, GA5, GA8, GA9, GA10) 

LO5 - Communicate a variety of statistical knowledge to others. (GA3, GA5, GA9, GA10) 

LO6 - Determine the role of ethical and valid uses of statistics. (GA2, GA3, GA4, GA5, GA6) 

Graduate attributes

GA2 - recognise their responsibility to the common good, the environment and society 

GA3 - apply ethical perspectives in informed decision making

GA4 - think critically and reflectively 

GA5 - demonstrate values, knowledge, skills and attitudes appropriate to the discipline and/or profession 

GA6 - solve problems in a variety of settings taking local and international perspectives into account

GA7 - work both autonomously and collaboratively 

GA8 - locate, organise, analyse, synthesise and evaluate information 

GA9 - demonstrate effective communication in oral and written English language and visual media 

GA10 - utilise information and communication and other relevant technologies effectively.

Content

Topics will include: 

1. Introduction to Statistics and statistical programs
2. Introduction to Data analysis
3. Introduction to probability, combinatorics and set counting techniques
4. Discrete probability distributions including binomial, Poisson and discrete uniform cases
5. Continuous distributions including uniform, exponential and normal distributions
6. Hypothesis testing and confidence intervals
7. Chi-squared distribution and the Student t-distribution
8. Snedecor’s F-distribution and ANOVA (Analysis of Variance)
9. Analysis of Variance and Fisher’s F test
10. Correlation and regression and analysis of qualitative bivariate data 

Learning and teaching strategy and rationale

 As is common in Mathematics a variety of Active Learning approaches promote the best acquisition of skills and understanding. Lectures will typically be structured to provide explanations of the material to be covered, along with examples of the applications of that material, as well as formal and informal tasks for students that will reinforce that learning. Splitting the taught content of the lectures into short topics will ensure increased student engagement with the material, as well as providing opportunities for students to consolidate their learning before new material is covered. This allows students to learn the skills and then build understanding, competence and confidence via (ideally, face-to-face) tutorials involving cooperative groups, peer review and other relevant strategies. In all cases this should be supported using available online technology.

 This unit will normally include the equivalent of 24 hours of lectures (typically 2 hours per week for 12 weeks) together with 24 hours attendance mode tutorials. Lectures will also be recorded and, where possible or required, students may have access to an online tutorial.

 150 hours in total with a normal expectation of 48 hours of directed study and the total contact hours should not exceed 48 hours. The balance of the hours becoming private study.

Assessment strategy and rationale

To successfully complete an undergraduate Mathematics sequence, students need an understanding of a variety of basic Mathematical topics and an ability to apply that understanding to a variety of problems. To succeed at problem solving in Mathematics, students must have these skills at their fingertips and be able to recall them and choose an appropriate approach under some pressure. The assessment strategy chosen, while traditional, tests and supports student learning by providing opportunities to develop and test their problem-solving skills through the unit.

The continuous assessment component allows for the early detection of problems a student might be having and so ensures that appropriate guidance can be given early enough to support later learning in the unit. Students will be required to submit responses to questions dealing with simple statistical problems. As specified times, through the semester, students will submit responses to some of the questions to allow for the provision of feedback and learning support to students.

The examination components ensure that students have fully integrated the learning and can bring a variety of strategies to bear under pressure.

Typing of Mathematical notation either requires a significant investment of time, or knowledge of advanced Mathematical typesetting software. Neither of those skills are suitable for an undergraduate course in Mathematics. Consequently, assignments, tests and examinations are typically handwritten and either submitted as hardcopy or scanned and submitted to a dropbox, rather than through Turnitin. Students may choose to type their responses and submit them electronically, but this is not a requirement of the unit.

The continuous assessment task will include specific examples that demonstrate how statistical hypothesis testing may be used to detect differences in a variety of situations. These should include, for example, differences in educational, life expectancy, health, incarceration rates, employment outcomes, and so on, between indigenous groups and the remainder of the population or between other commonly considered sections of a relevant population. This aspect will also provide students with the opportunity to collect data, as well as simply using provided data, to support their conclusions.

Overview of assessments

Representative texts and references

Bluman, A. (2017) Elementary Statistics- A step by step approach, 10th Edition. New York: McGraw-Hill

De Veaux, R., Velleman, P. & Bock, D. (2015) Stats: Data and Models, New York: Addison Wesley

Freedman, D., Pisani, R. & Purves, R. (2011) Statistics, 4th Edition. Viva Books

Huff, D. (1991) How to Lie with Statistics, London: Penguin

Pearl, J. (2009) Causality: Models, Reasoning and Inference, Cambridge: Cambridge University Press

Salkind, N. (2019) Statistics for People Who (Think They) Hate Statistics, 7th Edition, Sage Publications

Weinberg, S.L., Harel, D. & Knapp, S. (2020) Statistics Using R : An Integrative Approach. Cambridge: Cambridge University Press