## STATS 1005 - Statistical Analysis & Modelling 1

### North Terrace Campus - Semester 2 - 2016

The course information on this page is being finalised for 2016. Please check again before classes commence.

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 & Modelling 1 School of Mathematical Sciences Semester 2 Undergraduate North Terrace Campus 3 Up to 5 hours per week Y MATHS 1011 or MATHS 1013 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

Course Coordinator: Dr Tyman Stanford

Dr Jono Tuke
##### 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.

No information currently available.

• 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 relies on lectures as the primary delivery mechanism for the material. Tutorials supplement the lectures by providing exercises and example problems to enhance the understanding obtained through lectures. A sequence of written assignments provides the assessment opportunities for students to gauge their progress and understanding.

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

 Activity Quantity Workload hours Lectures 36 72 Tutorials 12 18 Assignments 5 48 Practicals 12 18 TOTALS 156
##### Learning Activities Summary
Lecture 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

Tutorial Outline

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.

Practical Outline

1. Introduction, data input, basic descriptive statistics and graphics.
2. Customised graphics. SPSS menu commands and code.
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 30% All Exam 70% All
##### Assessment Related Requirements
Aggregate score of at least 50%
##### Assessment Detail
 Assessment Item Distributed Due Date Weighting Assignment 1 Week 1 Week 3 6% Assignment 2 Week 3 Week 5 6% Assignment 3 Week 5 Week 7 6% Assignment 4 Week 7 Week 9 6% Assignment 5 Week 9 Week 11 6%
##### 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

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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.

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• Policies & Guidelines
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