## STATS 1005 - Statistical Analysis and Modelling I

### North Terrace Campus - Semester 2 - 2022

This is a first course in Statistics for mathematically inclined students. It will address the key principles underlying commonly used statistical methods such as confidence intervals, hypothesis tests, inference for means and proportions, and linear regression. It will develop a deeper mathematical understanding of these ideas, many of which will be familiar from studies in secondary school. The application of basic and more advanced statistical methods will be illustrated on a range of problems from areas such as medicine, science, technology, government, commerce and manufacturing. The use of the statistical package R will be developed through a sequence of computer practicals. Topics covered will include: basic probability and random variables, fundamental distributions, inference for means and proportions, comparison of independent and paired samples, simple linear regression, diagnostics and model checking, multiple linear regression, simple factorial models, models with factors and continuous predictors.

• General Course Information
##### Course Details
Course Code STATS 1005 Statistical Analysis and Modelling I School of Mathematical Sciences Semester 2 Undergraduate North Terrace Campus 3 Up to 5 hours per week Y At least a C- in both SACE Stage 2 Mathematical Methods and SACE Stage 2 Specialist Mathematics; or at least 3 in IB Mathematics: analysis and approaches HL; or MATHS 1013. MATHS 2107, STATS 1000, STATS 1004, STATS 1504, ECON 1008 This is a first course in Statistics for mathematically inclined students. It will address the key principles underlying commonly used statistical methods such as confidence intervals, hypothesis tests, inference for means and proportions, and linear regression. It will develop a deeper mathematical understanding of these ideas, many of which will be familiar from studies in secondary school. The application of basic and more advanced statistical methods will be illustrated on a range of problems from areas such as medicine, science, technology, government, commerce and manufacturing. The use of the statistical package R will be developed through a sequence of computer practicals. Topics covered will include: basic probability and random variables, fundamental distributions, inference for means and proportions, comparison of independent and paired samples, simple linear regression, diagnostics and model checking, multiple linear regression, simple factorial models, models with factors and continuous predictors.
##### Course Staff

No information currently available.

##### Course Timetable

The full timetable of all activities for this course can be accessed from Course Planner.

• Learning Outcomes
##### Course Learning Outcomes

1. Understand the foundations of basic probability, random variables, and expectation and variances of random variables and their linear combinations.
2. Understand hypothesis testing for one sample, two sample, and ANOVA. To be able to fit linear models to data and use these to predict future observation.
3. Be able to take data and describe it statistically and to use approriate graphics to visualise patterns in the data.
4. Be familiar with R and how to use it to perform a basic analysis of data.
5. Understand the importance of statistics in modern scientific research.
6. Appreciate the mathematical underpinnings of statistics.

This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

University Graduate Attribute Course Learning Outcome(s)

Attribute 1: Deep discipline knowledge and intellectual breadth

Graduates have comprehensive knowledge and understanding of their subject area, the ability to engage with different traditions of thought, and the ability to apply their knowledge in practice including in multi-disciplinary or multi-professional contexts.

1,2,3,4,5,6

Attribute 2: Creative and critical thinking, and problem solving

Graduates are effective problems-solvers, able to apply critical, creative and evidence-based thinking to conceive innovative responses to future challenges.

1,2,3,4,5,6
• Learning Resources
None
##### Recommended Resources
Moore, McCabe, and Craig: Introduction to the Practice of Statistics, 6th Edition
##### Online Learning
This course uses MyUni exclusively for providing electronic resources, such as lecture notes, assignment papers, sample solutions, discussion boards, etc. It is recommended that the students make appropriate use of these resources.

• Learning & Teaching Activities
##### Learning & Teaching Modes
This course introduces content in online topic videos. Workshops build on the online content by providing exercises and example problems to enhance the understanding obtained. These are further supported through practical sessions where computational literacy is developed. Three major weeks, staggered throughout semester, combine workshops and computer practicals to enable students to produce written assessment peices that form a major component of their assesment. This draws together all learned skills in a real-world simulation of application.

The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

 Activity Quantity Workload hours Content Videos 3-5 weekly 36 Workshops 9 27 Computer Labs 6 24 Assignments 3 48 TOTALS 135
##### Learning Activities Summary
Topic Outline

1. Set theoretic probability. Important definitions.
2. Conditional probability, independent events, Bayes’ theorem.
3. Random variables, probability mass function, probability density, cumulative distribution function.
4. Means and variances.
5. Independent random variables.
6. Covariance and correlation.
7. Linear combinations of independent random variables.
8. Binomial distribution.
9. Normal distribution.
10. Quantile plots.
11. Inference for a single normal mean; review of z.
12. Review of significance and confidence.
13. Introduction of t.
14. Mean and variance of sample mean from the linear combinations formula.
15. Mean and variance of sample mean from a simple random sample in a finite population.
16. Two independent samples.
17. Two independent samples vs paired data.
18. Non-parametric methods for means and proportions.
19. The simple linear regression model.
20. Derivation of least squares estimates.
21. Least squares estimates as linear combinations of the data.
22. Residuals and model checking for simple linear regression.
23. Transformations and simple linear regression.
24. Prediction for simple linear regression with and without transformation.
25. Multiple linear regression, principle of least squares.
26. Interpretation of coefficients.
27. Prediction for multiple linear regression. Diagnostics for multiple linear regression. Collinearity. Multiple vs simple regression.
28. The one-way layout and ANOVA.
29. Analysis for the one-way layout via multiple regression with indicator variables. The no-interaction model for two factors.
30. Factorial experiments vs block designs.
31. Parallel and non-parallel regression models.
32. Categorical data, basic tests for proportions.
33. Independence for the r × s contingency table.
34. General goodness of fit tests.
35. Review lecture.
36. Review lecture

Workshop Topics

1. Probability, random variables.
2. Means, variance, covariance, correlation.
3. Linear combinations, binomial, normal.
4. Inference for single normal mean, significance, confidence.
5. T-test, sample mean.
6. Two sample testing.
7. Linear regression.
8. Linear regression II.
9. Multiple linear regression, ANOVA.
10. Multiple linear regression II.
11. One-way ANOVA.
12. Factorial design.

Computer practical topics - Using R

1. Introduction, data input, basic descriptive statistics and graphics.
2. Customised graphics.
3. Probability calculation.
4. Quantile plots and one-sample t-procedures
5. Illustration of sampling properties via simulation.
6. Two sample t procedures.
7. Simple linear regression.
8. Diagnostics from linear regression
9. Multiple regression.
10. Diagnostics for multiple regression.
11. Simple factorial models.
12. Parallel and non-parallel regression models.
• Assessment

The University's policy on Assessment for Coursework Programs is based on the following four principles:

1. Assessment must encourage and reinforce learning.
2. Assessment must enable robust and fair judgements about student performance.
3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
4. Assessment must maintain academic standards.

##### Assessment Summary
 Component Weighting Outcomes Assessed Assignments x3 60% All Weekly quizzes x10 20% All Mid-Semester Quiz 10% All End of Semester Quiz 10% All
##### Assessment Related Requirements
Aggregate score of at least 50%
##### Assessment Detail
 Assessment Item Distributed Due Date Weighting Assignment 1 Week 4 Week 4 15% Mid-semester Quiz Week 6 Week 6 10% Assignment 2 Week 8 Week 8 15% Assignment 3 Week 12 Week 12 30% Final Quiz Week 13 Week 13 10%
##### Submission

All written assignments are to be submitted to the designated hand in boxes within the School of Mathematical Sciences with a signed cover sheet attached.

Late assignments will not be accepted.

Assignments will have a two week turn-around time for feedback to students.

Grades for your performance in this course will be awarded in accordance with the following scheme:

M10 (Coursework Mark Scheme)
FNS   Fail No Submission
F 1-49 Fail
P 50-64 Pass
C 65-74 Credit
D 75-84 Distinction
HD 85-100 High Distinction
CN   Continuing
NFE   No Formal Examination
RP   Result Pending

Further details of the grades/results can be obtained from Examinations.

Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

Final results for this course will be made available through Access Adelaide.

• Student Feedback

The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

• Student Support
• Policies & Guidelines
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