## Stat2012 Assignment

## Table 1: Statistics

Unit of study | Credit points | A: Assumed knowledge P: Prerequisites C: Corequisites N: Prohibition | Session |
---|---|---|---|

## Statistics | |||

For a major in Statistics, the minimum requirement is 24 credit points from senior units of study listed below. | |||

## Junior units of study | |||

DATA1001Foundations of Data Science | 6 | N MATH1005 or MATH1905 or MATH1015 or MATH1115 or ENVX1001 or ENVX1002 or ECMT1010 or BUSS1020 or STAT1021 | Semester 1 Semester 2 |

## Intermediate units of study | |||

DATA2002Data Analytics: Learning from Data | 6 | A (Basic Linear Algebra and some coding) or QBUS1040 P [DATA1001 or ENVX1001 or ENVX1002] or [MATH10X5 and MATH1115] or [MATH10X5 and STAT2011] or [MATH1905 and MATH1XXX (except MATH1XX5)] or [BUSS1020 or ECMT1010 or STAT1021] N STAT2012 or STAT2912 | Semester 2 |

STAT2011Probability and Estimation Theory | 6 | P (MATH1X21 or MATH1931 or MATH1X01 or MATH1906 or MATH1011) and (MATH1XX5 or STAT1021 or ECMT1010 or BUSS1020) N STAT2901 or STAT2001 or STAT2911 | Semester 1 |

STAT2911Probability and Statistical Models (Adv) | 6 | P [MATH19X3 or MATH1907 or (a mark of 65 in MATH1023 or MATH1003)] and [MATH1905 or MATH1904 or (a mark of 65 in MATH1005 or ECMT1010 or BUSS1020)] N STAT2001 or STAT2901 or STAT2011 | Semester 1 |

STAT2912Statistical Tests (Advanced) | 6 | A STAT2911 P MATH1905 or Credit in MATH1005 or Credit in ECMT1010 or Credit in BUSS1020 N STAT2012 or STAT2004 or DATA2002 | Semester 2 |

## Senior units of study | |||

STAT3011Stochastic Processes and Time Series | 6 | P STAT2X11 and (MATH1X03 or MATH1907 or MATH1X23 or MATH1933). N STAT3911 or STAT3903 or STAT3003 or STAT3905 or STAT3005 | Semester 1 |

STAT3911Stochastic Processes and Time Series Adv | 6 | P (STAT2911 or a mark of 65 or above in STAT2011) and (MATH1X03 or MATH1907 or MATH1X23 or MATH1933) N STAT3011 or STAT3905 or STAT3005 or STAT3003 or STAT3903 | Semester 1 |

STAT3012Applied Linear Models | 6 | P (DATA2002 or STAT2X12) and (MATH1X02 or MATH1014) N STAT3002 or STAT3004 or STAT3902 or STAT3912 or STAT3904 | Semester 1 |

STAT3912Applied Linear Models (Advanced) | 6 | P [STAT2912 or (a mark of 65 or above in STAT2012 or DATA2002)] and (MATH2X61 or MATH1902 or MATH2X22) N STAT3012 or STAT3002 or STAT3902 or STAT3004 or STAT3904 | Semester 1 |

STAT3013Statistical Inference | 6 | P STAT2X11 and (DATA2002 or STAT2X12) N STAT3913 or STAT3001 or STAT3901 | Semester 2 |

STAT3913Statistical Inference Advanced | 6 | P STAT2911 and (DATA2002 or STAT2X12) N STAT3013 or STAT3901 or STAT3001 | Semester 2 |

STAT3014Applied Statistics | 6 | A STAT3012 or STAT3912 P DATA2002 or STAT2X12 N STAT3914 or STAT3002 or STAT3902 or STAT3006 | Semester 2 |

STAT3914Applied Statistics Advanced | 6 | A STAT3912 P STAT2912 or (a mark of 65 or above in STAT2012 or DATA2002) N STAT3014 or STAT3907 or STAT3902 or STAT3006 or STAT3002 | Semester 2 |

ENVX3002Statistics in the Natural Sciences | 6 | P ENVX2001 or BIOM2001 or STAT2X12 or BIOL2X22 or DATA2002 or QBIO2001 Interdisciplinary Unit | Semester 1 |

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### Statistics

For a major in Statistics, the minimum requirement is 24 credit points from senior units of study listed below.

##### Junior units of study

**DATA1001 Foundations of Data Science **

Credit points: 6 Teacher/Coordinator: Dr Di Warren Session: Semester 1,Semester 2 Classes: lecture 3 hrs/week; computer tutorial 2 hr/week Prohibitions: MATH1005 or MATH1905 or MATH1015 or MATH1115 or ENVX1001 or ENVX1002 or ECMT1010 or BUSS1020 or STAT1021 Assessment: assignments, quizzes, presentation, exam Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

DATA1001 is a foundational unit in the Data Science major. The unit focuses on developing critical and statistical thinking skills for all students. Does mobile phone usage increase the incidence of brain tumours? What is the public's attitude to shark baiting following a fatal attack? Statistics is the science of decision making, essential in every industry and undergirds all research which relies on data. Students will use problems and data from the physical, health, life and social sciences to develop adaptive problem solving skills in a team setting. Taught interactively with embedded technology, DATA1001 develops critical thinking and skills to problem-solve with data. It is the prerequisite for DATA2002.

Textbooks

Statistics, Fourth Edition, Freedman Pisani Purves

##### Intermediate units of study

**DATA2002 Data Analytics: Learning from Data **

Credit points: 6 Teacher/Coordinator: Jean Yang Session: Semester 2 Classes: lecture 3 hrs/week; computer tutorial 2 hr/week Prerequisites: [DATA1001 or ENVX1001 or ENVX1002] or [MATH10X5 and MATH1115] or [MATH10X5 and STAT2011] or [MATH1905 and MATH1XXX (except MATH1XX5)] or [BUSS1020 or ECMT1010 or STAT1021] Prohibitions: STAT2012 or STAT2912 Assumed knowledge: (Basic Linear Algebra and some coding) or QBUS1040 Assessment: written assignment, presentation, exams Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Technological advances in science, business, engineering has given rise to a proliferation of data from all aspects of our life. Understanding the information presented in these data is critical as it enables informed decision making into many areas including market intelligence and science. DATA2002 is an intermediate course in statistics and data sciences, focusing on learning data analytic skills for a wide range of problems and data. How should the Australian government measure and report employment and unemployment? Can we tell the difference between decaffeinated and regular coffee ? In this course, you will learn how to ingest, combine and summarise data from a variety of data models which are typically encountered in data science projects as well as reinforcing their programming skills through experience with statistical programming language. You will also be exposed to the concept of statistical machine learning and develop the skill to analyze various types of data in order to answer a scientific question. From this unit, you will develop knowledge and skills that will enable you to embrace data analytic challenges stemming from everyday problems.

**STAT2011 Probability and Estimation Theory **

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory week. Prerequisites: (MATH1X21 or MATH1931 or MATH1X01 or MATH1906 or MATH1011) and (MATH1XX5 or STAT1021 or ECMT1010 or BUSS1020) Prohibitions: STAT2901 or STAT2001 or STAT2911 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit provides an introduction to univariate techniques in data analysis and the most common statistical distributions that are used to model patterns of variability. Common discrete random models like the binomial, Poisson and geometric, continuous models including the normal and exponential will be studied along with elementary regression models. The method of moments and maximum likelihood techniques for fitting statistical distributions to data will be explored. The unit will have weekly computer classes where candidates will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method.

**STAT2911 Probability and Statistical Models (Adv) **

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: [MATH19X3 or MATH1907 or (a mark of 65 in MATH1023 or MATH1003)] and [MATH1905 or MATH1904 or (a mark of 65 in MATH1005 or ECMT1010 or BUSS1020)] Prohibitions: STAT2001 or STAT2901 or STAT2011 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is essentially an advanced version of STAT2011, with an emphasis on the mathematical techniques used to manipulate random variables and probability models. Common distributions including the Poisson, normal, beta and gamma families as well as the bivariate normal are introduced. Moment generating functions and convolution methods are used to understand the behaviour of sums of random variables. The method of moments and maximum likelihood techniques for fitting statistical distributions to data will be explored. The notions of conditional expectation and prediction will be covered as will be distributions related to the normal: chi^2, t and F. The unit will have weekly computer classes where candidates will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method.

**STAT2912 Statistical Tests (Advanced) **

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: MATH1905 or Credit in MATH1005 or Credit in ECMT1010 or Credit in BUSS1020 Prohibitions: STAT2012 or STAT2004 or DATA2002 Assumed knowledge: STAT2911 Assessment: One 2-hour exam, assignments and/or quizzes, computer practical reports and one computer practical exam (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is essentially an advanced version of STAT2012 with an emphasis on both methods and the mathematical derivation of these methods: Tests of hypotheses and confidence intervals, including t-tests, analysis of variance, regression - least squares and robust methods, power of tests, non-parametric methods, non-parametric smoothing, tests for count data, goodness of fit, contingency tables. Graphical methods and diagnostic methods are used throughout with all analyses discussed in the context of computation with real data using an interactive statistical package.

##### Senior units of study

**STAT3011 Stochastic Processes and Time Series **

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures and one 1 hour tutorial per week; ten 1 hour computer laboratories per semester. Prerequisites: STAT2X11 and (MATH1X03 or MATH1907 or MATH1X23 or MATH1933). Prohibitions: STAT3911 or STAT3903 or STAT3003 or STAT3905 or STAT3005 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Section I of this course will introduce the fundamental concepts of applied stochastic processes and Markov chains used in financial mathematics, mathematical statistics, applied mathematics and physics. Section II of the course establishes some methods of modeling and analysing situations which depend on time. Fitting ARMA models for certain time series are considered from both theoretical and practical points of view. Throughout the course we will use the S-PLUS (or R) statistical packages to give analyses and graphical displays.

**STAT3911 Stochastic Processes and Time Series Adv **

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lecture, one 1 hour tutorial per week, plus an extra 1 hour lecture per week on advanced material in the first half of the semester. Seven 1 hour computer laboratories (on time series) in the second half of the semester (one 1 hour class per week). Prerequisites: (STAT2911 or a mark of 65 or above in STAT2011) and (MATH1X03 or MATH1907 or MATH1X23 or MATH1933) Prohibitions: STAT3011 or STAT3905 or STAT3005 or STAT3003 or STAT3903 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This is an Advanced version of STAT3011. There will be 3 lectures in common with STAT3011. In addition to STAT3011 material, theory on branching processes and Brownian bridges will be covered.

**STAT3012 Applied Linear Models **

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratories per week. Prerequisites: (DATA2002 or STAT2X12) and (MATH1X02 or MATH1014) Prohibitions: STAT3002 or STAT3004 or STAT3902 or STAT3912 or STAT3904 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This course will introduce the fundamental concepts of analysis of data from both observational studies and experimental designs using classical linear methods, together with concepts of collection of data and design of experiments. First we will consider linear models and regression methods with diagnostics for checking appropriateness of models. We will look briefly at robust regression methods here. Then we will consider the design and analysis of experiments considering notions of replication, randomization and ideas of factorial designs. Throughout the course we will use the R statistical package to give analyses and graphical displays.

**STAT3912 Applied Linear Models (Advanced) **

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: [STAT2912 or (a mark of 65 or above in STAT2012 or DATA2002)] and (MATH2X61 or MATH1902 or MATH2X22) Prohibitions: STAT3012 or STAT3002 or STAT3902 or STAT3004 or STAT3904 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is essentially an Advanced version of STAT3012, with emphasis on the mathematical techniques underlying applied linear models together with proofs of distribution theory based on vector space methods. There will be 3 lectures per week in common with STAT3012 and some advanced material given in a separate advanced tutorial together with more advanced assessment work.

**STAT3013 Statistical Inference **

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: STAT2X11 and (DATA2002 or STAT2X12) Prohibitions: STAT3913 or STAT3001 or STAT3901 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

In this course we will study basic topics in modern statistical inference. This will include traditional concepts of mathematical statistics: likelihood estimation, method of moments, properties of estimators, exponential families, decision-theory approach to hypothesis testing, likelihood ratio test as well as more recent approaches such as Bayes estimation, Empirical Bayes and nonparametric estimation. During the computer classes (using R software package) we will illustrate the various estimation techniques and give an introduction to computationally intensive methods like Monte Carlo, Gibbs sampling and EM-algorithm.

**STAT3913 Statistical Inference Advanced **

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: STAT2911 and (DATA2002 or STAT2X12) Prohibitions: STAT3013 or STAT3901 or STAT3001 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is an Advanced version of STAT3013, with emphasis on the mathematical techniques underlying statistical inference together with proofs based on distribution theory. There will be 3 lectures per week in common with some material required only in this advanced course and some advanced material given in a separate advanced tutorial together with more advanced assessment work.

**STAT3014 Applied Statistics **

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: DATA2002 or STAT2X12 Prohibitions: STAT3914 or STAT3002 or STAT3902 or STAT3006 Assumed knowledge: STAT3012 or STAT3912 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit has three distinct but related components: Multivariate analysis; sampling and surveys; and generalised linear models. The first component deals with multivariate data covering simple data reduction techniques like principal components analysis and core multivariate tests including Hotelling's T^2, Mahalanobis' distance and Multivariate Analysis of Variance (MANOVA). The sampling section includes sampling without replacement, stratified sampling, ratio estimation, and cluster sampling. The final section looks at the analysis of categorical data via generalized linear models. Logistic regression and log-linear models will be looked at in some detail along with special techniques for analyzing discrete data with special structure.

**STAT3914 Applied Statistics Advanced **

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures and one 1 hour computer laboratory per week plus an extra hour each week which will alternate between lectures and tutorials. Prerequisites: STAT2912 or (a mark of 65 or above in STAT2012 or DATA2002) Prohibitions: STAT3014 or STAT3907 or STAT3902 or STAT3006 or STAT3002 Assumed knowledge: STAT3912 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is an Advanced version of STAT3014. There will be 3 lectures per week in common with STAT3014. The unit will have extra lectures focusing on multivariate distribution theory developing results for the multivariate normal, partial correlation, the Wishart distribution and Hotelling's T^2. There will also be more advanced tutorial and assessment work associated with this unit.

**ENVX3002 Statistics in the Natural Sciences **

Credit points: 6 Teacher/Coordinator: Dr Floris Van Ogtrop Session: Semester 1 Classes: one 2-hour workshop per week, one 3-hour computer practical per week Prerequisites: ENVX2001 or BIOM2001 or STAT2X12 or BIOL2X22 or DATA2002 or QBIO2001 Assessment: One exam during the exam period (50%), five assessment tasks (50%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Interdisciplinary Unit

This unit of study is designed to introduce students to the analysis of data they may face in their future careers, in particular data that are not well behaved. The data may be non-normal, there may be missing observations, they may be correlated in space and time or too numerous to analyse with standard models. The unit is presented in an applied context with an emphasis on correctly analysing authentic datasets, and interpreting the ouput. It begins with the analysis and design experiments based on the general linear model. In the second part, students will learn about the generalisation of the general linear model to accommodate non-normal data with a particular emphasis on the binomial and poisson distributions. In the third part linear mixed models will be introduced which provide the means to analyse datasets that do not meet the assumptions of independent and equal errors, for example data that is correlated in space and time. The units ends with an introduction to machine learning and predictive modelling. A key feature of the unit is using R to develop coding skills that are become essential in science for processing and analysing datasets of ever increasing size.

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## STAT2012 Statistical Tests

## General Information

This page contains information on the Intermediate Unit of Study STAT2012 Statistical Tests.

This unit is offered in Semester 2.

Lecturer(s): Ellis Patrick and Michael Stewart

For further information on Intermediate Mathematics and Statistics, refer to the Intermediate Handbook. In particular, see the STAT2012 handbook entry for further information relating to STAT2012.

You may also view the description of STAT2012 in the central units of study database.

- Credit point value: 6CP.
- Classes per week: Three lectures, one tutorial and one computer laboratory session.

Email enquiries about STAT2012 may be sent to STAT2012@sydney.edu.au.

Students: Please give your name and SID when emailing us. Anonymous emails will not be replied to.

Students have the right to appeal any academic decision made by the School or Faculty. For further information, see the Science Faculty web site.

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