619-200 Applied Statistics

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Objectives:

Students completing this course should:

Comprehend:

• how statistical models are used to analyse data;

• the basic principles of experimental design.

Have developed the skills:

• to examine data to determine underlying structures;

• to formulate statistical models for a range of practical situations;

• to check the assumptions of the model in specific situations;

• to use the computer to carry out standard statistical analyses;

• to express the results of a statistical analysis in scientifically useful terms.

Appreciate:

• the importance of statistical methods for interpreting data;

• the role and interplay of exploratory and formal aspects of data analysis;

• the importance of experimental design;

• the application of statistical software.

Content:

Methods of statistical inference: estimation; confidence intervals; hypothesis testing including the power of tests. Determination of sample size using the width of confidence intervals and power.

Correlation and regression (linear and multiple): assumptions; method of least squares; interpretation; hypothesis testing; analysis of variance; confidence and prediction intervals; residuals; regression diagnostics; transformations; collinearity; methods of model selection; polynomial regression.

Analysis of Variance models (one-way and two-way with equal numbers of observations per cell): model; assumptions; estimation; hypothesis testing; planned and multiple comparisons; contrasts; interaction and its interpretation; transformations; residuals; diagnostics.

Factorial experiments: advantages over one factor at a time; analysis; interpretation.

Design of experiments: randomisation; replication; blocking. Standard designs including completely randomised, randomised block and Latin square designs. Introduction to confounding.

Analysis of Covariance: detailed treatment of the case with one factor and one covariate; extension to more complex situations including more than one factor, more than one covariate and blocking.

Contingency tables: tests for association; odds ratios, including confidence intervals; introduction to loglinear models.

Assessment: