Mathematics
MA419: Statistics (5 ECTS)
This module is an introductory statistics course for students in areas such as Environmental Science, Microbiology, Analytical Biochemistry and Chemistry. Emphasis is on basic probability and a battery of applied statistical techniques for analysing qualitative and quantitative data from experiments and observational studies.
Taught in Semester(s) I+II. Examined in Semester(s) Spring.
Workload: 34 hours (24 Lecture hours, 10 Tutorial hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Describe data sets graphically and numerically
- Understand and apply some basic probability rules for calculating the probability of compound events
- Perform probability calculations relating to hypergeometric and binomial distributions to model count variables that arise in the applied sciences.
- Understand some basic ideas about confidence intervals and hypothesis tests.
- Find confidence intervals and perform hypothesis tests about a single population mean, a single population proportion, and the difference between two population means when the data points are from a completely randomised experimental design (i.e. independent random samples) and when they arise from a randomised block design (i.e. paired random samples).
- Analyse enumerative data through chi-squared goodness-of-fit and contingency table tests.
- Calculate and interpret the linear correlation coefficient for relating two variables; fit the least squares line to data pairs; interpret inferences about the slope of the underlying population equation, and perform basis prediction.
- Use a statistical software package to analyse data sets.
Indicative Content
This module provides a basic introduction to statistics inference, with emphasis on applications in biostatistics. Topics covered are:
- Explanation of statistics through practical examples of its applications in the applied sciences
- Descriptive statistics.
- Basic probability rules and some important discrete distributions and their means and variances
- Normal distributions and the sampling distribution of the mean.
- Concepts of point and interval estimation and concepts in hypothesis testing including Type I and Type II errors and p-value of tests.
- Confidence intervals and hypothesis tests about a single population mean, a single population proportion, and the difference between two population means.
- The analysis of enumerative data, including chi-squared goodness-of-fit and a tst of independence of two categorical variables.
- Correlation and simple linear regression analysis, including fitting a straight line to data, intepretation of inferences about the slope parameter and basic prediction.
- Basic principles of experimental design.
- Implementation of descriptive and inferential statistics using a statistical package.
Module Resources
- Weiss, Neil A., Introductory Statistics. Pearson Higher Ed. 2010.
- Rosner, Bernard, Fundamentals of Biostatistics. Thomson-Brooks/Cole 2006
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