Breadcrumb
Statistics 1 (MATH 11400)
Contents of this document:
- Administrative information
- Unit aims, General Description, and Relation to Other Units
- Teaching methods and Learning objectives
- Assessment methods and Award of credit points
- Transferable skills
- Texts and Syllabus
Administrative Information
- Unit number and title: MATH 11400 Statistics 1
- Level: C/4 (Honours)
- Credit point value: 10 credit points
- Year: 08/09
- First Given in this form: 2001/2 (Previously given as part of a 20cp unit)
- Unit Organiser: Sean Collins
- Lecturer: Dr. E. J. Collins
- Teaching block: 2
- Prerequisites: Probability 1 (MATH 11300). Corequisites: Analysis 1 (MATH11006) and Calculus 1 (MATH11007), or equivalent, are normally required but may be taken concurrently.
Unit aims
To introduce the role of statistics in contemporary applications and to develop an elementary understanding of, and fluency in, the statistical paradigm of data collection, exploration, modelling and inference.
General Description of the Unit
Computer technology has revolutionised both the scope and method of statistics, and this unit aims to give a basic grounding in statistical methodology that reflects this contemporary view. The role of statistics in the modern world is becoming ever-wider and applications can be found in almost all fields of human endeavour - in science, medicine, industry, social science, commerce and government. Taking real-life examples as motivation, this unit aims to develop an understanding of the basic principles of statistics, combining exploratory techniques and the machinery of probability theory to build a toolkit that can be used to uncover and identify relationships in the presence of random variation.
Relation to Other Units
This unit is part of the foundation for all statistics units in later years.
Teaching Methods
Lectures supplemented by weekly small group tutorials for first year students. Weekly problem sheets, with outline solutions available a fortnight later.
Learning Objectives
- Students should be able to:
- Use exploratory techniques to identify simple relationships in data;
- Formulate simple statistical models as appropriate to particular applications;
- Understand the principles of parametric modelling, and be able to derive parameter estimates for simple models using method-of-moments and maximum likelihood;
- Derive the simple linear regression model and implement it in appropriate situations;
- Simulate samples from specified distributions and understand why simulation techniques are a useful statistical tool;
- Use simulation techniques to explore sample variation;
- Calculate and understand confidence intervals for simple models by both exact and simulation methods;
- Formulate and carry out hypothesis tests by exact and simulation methods;
- Use the statistical software system R to support each of the above tasks.
Assessment Methods
The final mark for Statistics 1 is calculated from one 1½ -hour written examination in May/June. This examination paper is in two sections.
- Section A contains 5 short questions, ALL of which should be attempted. Section A contributes 40% of the mark for this paper.
- Section B has 3 longer questions; you should attempt TWO. If you attempt more than two, your best two answers in Section B will be used for assessment. Section B contributes 60% to the mark for this paper.
Calculators of the approved type (non-programmable, no text facility) are required for the examination. Statistical tables will be provided for the examination (see under Texts below).
Award of Credit Points
You gain the credit points for the unit either if
- EITHER your final assessment mark is at least 40 on the standard Science Faculty scale,
- OR your mark lies in the interval [30, 39] and
- first-year students must satisfy the conditions on handing-in of homework and attendance at tutorials described in the First Year Handbook.
- students in their second, third or fourth years must have handed in attempts to 75% of the homework.
Transferable Skills
Use of statistical software for elementary statistical analysis on the computer.
Texts
- The recommended text is:
- J. A. Rice, Mathematical statistics and data analysis, Wadsworth and Brooks Cole.
There are many other elementary texts on Probability and/or Statistics that you may find useful. However, the book by Rice may be recommended for the Statistics 2 course as well.
As part of the Statistics syllabus, students are required to develop familiarity with the statistical software package R. The use of R is continued in Statistics units in years 2, 3 and 4. The recommended text for R is:
P. Dalgaard, Introductory Statistics with R, Springer
- You are advised to buy a copy of the following tables, because they are identical to those used in the examinations, and you will need to be familiar with them.
- D. V. Lindley and W. F. Scott, New Cambridge Statistical Tables, (2nd Ed.) CUP.
Syllabus
Teaching block 2 (weeks 13 - 24), Dr. E. J. Collins
- Modern applications of statistics; Data exploration; Use of R. [2].
- Model formulation; Parametric models; Parameter estimation; Method of moments and maximum likelihood; Assessment of fit. [4]
- The simple linear regression model; Motivation by example and simulation; Least squares estimation; Model assessment (through residuals) and interpretation. [2].
- Sampling variation; Assessment by simulation; Sample mean and variance etc.[2]
- Central limit theorem - mathematical proof and interpretation by simulation; implications for large sample inference; approximation to Binomial.[2].
- Exact Normal theory: the t and chi-squared distributions.[2]
- Confidence intervals; Interpretation via simulation; Exact results for Normal population mean; Effect of sample size and choice of confidence level. [2].
- Hypothesis testing; Interpretation via simulation; Exact theory for Normal population mean; Error types and size of test. [2].
- Theory and examples for paired sample inferences and two-sample inferences. [2].
- Simple linear regression; confidence intervals and hypothesis tests. [2].