Unit of study_

# BSTA5002: Principles of Statistical Inference (PSI)

## Overview

The aim of this unit is to develop a strong mathematical and conceptual foundation in the methods of statistical inference, which underlie many of the methods utilised in subsequent units of study, and in biostatistical practice. The unit provides an overview of the concepts and properties of estimators of statistical model parameters, then proceeds to a general study of the likelihood function from first principles. This will serve as the basis for likelihood-based methodology, including maximum likelihood estimation, and the likelihood ratio, Wald, and score tests. Core statistical inference concepts including estimators and their ideal properties, hypothesis testing, p-values, confidence intervals, and power under a frequentist framework will be examined with an emphasis on both their mathematical derivation, and their interpretation and communication in a health and medical research setting. Other methods for estimation and hypothesis testing, including a brief introduction to the Bayesian approach to inference, exact and non-parametric methods, and simulation-based approaches will also be explored.

### Unit details and rules

Unit code BSTA5002 Public Health 6 None BSTA5100 or (BSTA5001 and BSTA5023) None None No

### Teaching staff

Coordinator Liz Barnes, liz.barnes@sydney.edu.au

## Assessment

Type Description Weight Due Length
Assignment Assignment 2
Multiple questions covering material from all modules (Modules 1-6)
40% Formal exam period
Due date: 11 Jun 2023 at 23:59
8-10 pages
Outcomes assessed:
Small continuous assessment Module exercises
One exercise for submission per Module (best 5 to count 4% each)
20% Multiple weeks 2-3 pages per Module
Outcomes assessed:
Assignment Assignment 1
Multiple questions covering material in Modules 1-3
40% Week 08
Due date: 23 Apr 2023 at 23:59
8-10 pages
Outcomes assessed:

### Assessment summary

• 6 submissible module exercises, of which the best 5 module marks will each contribute towards the total mark.
• 1 major written assignment covering Modules 1 to 3
• 1 major written assignment covering Modules 1 to 6 (with a focus on Modules 4 to 6)

Detailed information for each assessment can be found on Canvas

### Assessment criteria

 Grade Mark Range Description AF Absent fail Range from 0 to 49 To be awarded to students who fail to demonstrate the learning outcomes for the unit at an acceptable standard through failure to submit or attend compulsory assessment tasks or to attend classes to the required level. FA Fail Range from 0 to less than 50 To be awarded to students who, in their performance in assessment tasks, fail to demonstrate the learning outcomes for the unit at an acceptable standard established by the faculty. PS Pass Range from 50 to less than 65 To be awarded to students who, in their performance in assessment tasks, demonstrate the learning outcomes for the unit at an acceptable standard. CR Credit Range from 65 to less than 75 To be awarded to students who, in their performance in assessment tasks, demonstrate the learning outcomes for the unit at a good standard. D Distinction Range from 75 to less than 85 To be awarded to students who, in their performance in assessment tasks, demonstrate the learning outcomes for the unit at a very high standard. HD High distinction Range from 85 to 100 inclusive To be awarded to students who, in their performance in assessment tasks, demonstrate the learning outcomes for the unit at an exceptional standard.

* Your best five module marks will each contribute 4% towards the total of 20% for the module exercises

### Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

• Deduction of 5% of the maximum mark for each calendar day after the due date.
• After ten calendar days late, a mark of zero will be awarded.

This unit has an exception to the standard University policy or supplementary information has been provided by the unit coordinator. This information is displayed below:

Standard BCA policy for late penalties for submitted work is a 5% deduction from the earned mark for each day the assessment is late, up to a maximum of 50%.

The Current Student website  provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

## Learning support

### Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

### Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

### Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

## Weekly schedule

WK Topic Learning activity Learning outcomes
Multiple weeks Module 1 - Estimation concepts Independent study (20 hr)
Module 2 - Hypothesis testing concepts Independent study (20 hr)
Module 3 - Likelihood and estimation methods Independent study (20 hr)
Module 4 - Hypothesis testing methods Independent study (20 hr)
Module 5 - Bayesian inference Independent study (20 hr)
Module 6 - Further inference topics Independent study (20 hr)

### Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

TEXTBOOK:

Marschner, I.C.(2014). Inference Principles for Biostatisticians. Chapman and Hall / CRC. ISBN: 9781482222234.  http://www.crcpress.com/product/isbn/9781482222234

Note, a digital copy of this text may be available through the university library if you do not wish to purchase a copy.

Sterne, J.A., Smith, G.D. (2001). Shifting the evidence-what's wrong with significance tests? BMJ, 322: 226-231.  http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1119478/

Reese, R.A. (2004). Does significance matter? Significance, 1: 39-40. http://onlinelibrary.wiley.com/doi/10.1111/j.1740-9713.2004.00009.x/pdf

## Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

At the completion of this unit, you should be able to:

• LO1. Calculate and interpret important properties of point and interval estimators
• LO2. Calculate and interpret p-values, power and confidence intervals correctly.
• LO3. Write a likelihood function.
• LO4. Derive and calculate the maximum likelihood estimate.
• LO5. Derive and calculate the expected information.
• LO6. Derive a Wald test, Score test and likelihood ratio test.
• LO7. Use a Bayesian approach to derive a posterior distribution.
• LO8. Calculate and interpret posterior probabilities and credible intervals.
• LO9. Apply and explain an exact method, non-parametric and sampling-based method.

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

 GQ1 Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline. GQ2 Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem. GQ3 Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context. GQ4 Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies. GQ5 Inventiveness Generating novel ideas and solutions. GQ6 Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues. GQ7 Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries. GQ8 Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context. GQ9 Influence Engaging others in a process, idea or vision.

### Outcome map

GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

## Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

PSI is delivered in both Semester 1 and Semester 2 each year. From Semester 1 2022, there were major changes to some of the core units in the BCA program. PSI has added additional material in Module 1 – this material was previously covered in PDT and therefore may be revision for some students. Other PSI modules have also been rearranged. Based on feedback from previous deliveries, we have introduced recorded video lectures to complement the textbook readings, recorded worked video solutions to the non-assessed module exercises to further reinforce concepts, and provide the opportunity for live consultation (either in the form of tutorial or Q&A sessions, depending on module content) via videoconferencing to increase engagement and interactivity with the teaching team.