**Module aims**

To provide the learner with the statistical concepts and tools necessary for any engineering or science graduate. To do this, the learner will cover the fundamental ideas of probability and descriptive statistics, moving on to Hypothesis testing and the design of experiments.

**Learning outcomes**

- Summarize large sets of data, including grouped data, using the standard measures of central tendency and dispersionand their definitions and properties, and represent it graphically, by following an agreed set of conventions.
- Apply the laws of probability to questions involving random variables and events, and move on to the concept of a randomvariable and its distribution, the meaning of expected values, and the properties of common distributions such as thenormal, binomial, Poisson and exponential distributions.
- Interpret the concept of a statistic as a random variable arising from sample data, with the central limit theoremdetermining the behaviour of such statistics and thereby underpinning many statistical tests.
- Frame and use an appropriate test for a statistical problem, based on their knowledge of hypothesis testing, the centrallimit theorem and those distributions used in a range of common statistical tests. This will include multivariate analyses –Manova, Mancova.
- Design or explain the chosen structure of an experiment and the meaning of any data analysis produced for thatexperiment, based on the students understanding of the properties of Analysis of Variance and Analysis of Covarianceand other statistical tests.
- Apply their knowledge of techniques derived from linear algebra to the matrix formulation of the general linear model,including eigenvector decompositions of the covariance matrix and their application to Principal Component Analysis.

**Indicative module assessment**

- Hypothesis testing I: The student will be given an assignment on Hypothesis testing, implementing a range of the statistical tests covered in the module, including tests on means and variances, tests on group means, correlation and regression, and tests for goodness-of-fit and independence. The student will be assessed on their ability to establish the conceptual framework of any test, the Null and alternative Hypothesis, identify the parameters of a given test and draw the correct conclusions and the meaning of type I and II errors. (20%)
- Hypothesis testing II: The student will be given an assignment on Analysis of Variance, where they will identify a range of experimental designs testing scientific Hypotheses, the corresponding test and the required partitions of sums of squares for the analysis of variance layout. The student will be assessed on their ability to establish the conceptual framework of the tests and drawing the correct conclusions. (25%)
- Probability: The student will be set a number of questions on the theoretical, probability element of the module, including its application to problems such as reliability and quality control, the fundamental definitions of probability, the Central limit theorem and its implications, the properties and definitions of common distributions and the theory of the general linear model. (30%)
- Case study: Interpreting the results of an analysis of an existing or historical data set, writing up a report at an appropriate academic standard on these results, and interpreting them for peers and non-technical colleagues. (25%)