Statistics
ST238: Introduction to Statistical Inference (5 ECTS)
This module is an introduction to the ideas and commoly used techniques in analysing data from experiments and observational studies. Participants learn the role of probability in statistical inference, review the ideas in sampling distributions, learn concepts of interval estimation and hypothesis tests, learn standard one and two-sample procedures for quantitative data, learn basic enumerative data analysis, and simple correlation and linear regression
Taught in Semester(s) II. Examined in Semester(s) II.
Workload: 34 hours (24 Lecture hours, 10 Tutorial hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Understand the difference between Probability and Statistics and the role of 2. Probability in solving statistical inference problems.
- Perform probability calculations about the sample mean and use them to make inferential statements.
- Understand some basic ideas about interval estimation; be familiar with Type I and Type II errors in hypothesis tests and be able to calculate the p-value and power of various statistical tests.
- Find confidence intervals and perform hypothesis tests about a single population mean, a single population proportion, the difference between two population means, and a single population variance.
- 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, and make statistical inferences about the slope of the underlying population equation, and perform basis prediction.
- Understand the basics of some survey designs.
- Understand when and in what ways a randomised block experimental design is often superior to the completely randomised design.
Indicative Content
This module provides a basic introduction to statistical inference, capitalising on students' prior knowledge of descriptive statistics and basic probability. Topics covered are:
1. Difference between Probability and Statistics and the role of Probability in solving statistical inference problems.
2. Explanation of statistics through practical examples of its applications.
3. Review of normal distributions and the sampling distribution of the mean.
4. Concepts of point and interval estimation; concepts in hypothesis testing including Type I and Type II errors, p-value and power.
5. Confidence intervals and hypothesis tests about a single population mean, a single population proportion, the difference between two population means and a single population variance.
6. The analysis of enumerative data, including chi-squared goodness-of-fit and contingency table tests.
7. Correlation and linear regression analysis, including least squares estimation of the parameters of the simple linear regression model, inferences about these parameters, and prediction.
8. Some survey and experimental designs.
Module Resources
- Freund, John E., Modern elementary statistics. Prentice Hall, 1997.
- Bluman, A. 2003, Elementary Statistics – a step by step approach. McGraw Hill.
- Hinde, J, & Newell, J. (compilers) 2004, Introduction to Probability and Statistics by DeVeaux & Velleman, Pearson Custom Publishing
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