STATS 1005 - Statistical Analysis & Modelling 1
North Terrace Campus - Semester 2 - 2015
General Course Information
Course Code STATS 1005 Course Statistical Analysis & Modelling 1 Coordinating Unit Statistics Term Semester 2 Level Undergraduate Location/s North Terrace Campus Units 3 Contact Up to 5 hours per week Available for Study Abroad and Exchange Y Prerequisites MATHS 1011 or MATHS 1013 Incompatible STATS 1000, STATS 1004, STATS 1504, ECON 1008 Course Description 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 Coordinator: Associate Professor Gary GlonekDr Jono Tuke
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning Outcomes
- Understand the foundations of basic probability, random variables, and expectation and variances of random variables and their linear combinations.
- 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.
- Be able to take data and describe it statistically and to use approriate graphics to visualise patterns in the data.
- Be familiar with R and how to use it to perform a basic analysis of data.
- Understand the importance of statistics in modern scientific research.
- Appreciate the mathematical underpinnings of statistics.
University Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University Graduate Attribute Course Learning Outcome(s) Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. all The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner. 6 An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. all A proficiency in the appropriate use of contemporary technologies. 5 A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. 6 An awareness of ethical, social and cultural issues within a global context and their importance in the exercise of professional skills and responsibilities. 6
Recommended ResourcesMoore, McCabe, and Craig: Introduction to the Practice of Statistics, 6th Edition
Online LearningThis 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.
Link to MyUni login page:
Learning & Teaching Activities
Learning & Teaching ModesThis 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 SummaryLecture 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
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.
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.
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- Assessment must encourage and reinforce learning.
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Component Weighting Outcomes Assessed Assignments 30% All Exam 70% All
Assessment Related RequirementsAggregate score of at least 50%
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%
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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) Grade Mark Description 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
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