STATS 1005 - Statistical Analysis and Modelling I
North Terrace Campus - Semester 2 - 2021
General Course Information
Course Code STATS 1005 Course Statistical Analysis and Modelling I Coordinating Unit School of Mathematical Sciences 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 At least a C- in both SACE Stage 2 Mathematical Methods (formerly Mathematical Studies) and SACE Stage 2 Specialist Mathematics; or a 3 in International Baccalaureate Mathematics HL; or MATHS 1013. Incompatible MATHS 2107, 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: Dr Melissa Humphries
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) Deep discipline knowledge
- informed and infused by cutting edge research, scaffolded throughout their program of studies
- acquired from personal interaction with research active educators, from year 1
- accredited or validated against national or international standards (for relevant programs)
1,2,3,4,5,6 Critical thinking and problem solving
- steeped in research methods and rigor
- based on empirical evidence and the scientific approach to knowledge development
- demonstrated through appropriate and relevant assessment
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 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 SummaryTopic 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.
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.
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
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 RequirementsAggregate score of at least 50%
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%
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) 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
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.
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