Statistics
ST311: Applied Statistics I (5 ECTS)
An introduction to methods and applications in applied statistical inference. This module is offered as an optional module, building on the statistical inferential methods demonstrated in pre-requisite module MA238/ST238 or MA228 or similar modules.
Various non-parametric hypothesis tests are demonstrated and a comparison of suitability of applying non-parametric and parametric methods is discussed. The module also builds on regression modelling, where topics covered include model estimation, model checking and inference for simple linear regression and multiple linear regression models, and procedures in variable selection. Models discussed are applicable for a single quantitative response with quantitative and/or qualitative predictors.
Taught in Semester(s) I. Examined in Semester(s) I.
Workload: 36 hours (24 Lecture hours, 12 Tutorial hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- demonstrate various non-parametric testing procedures, identify suitability of parametric methods and the their non-parametric alternative test method, discuss the advantages and disadvantages of parametric and non-parametric testing, define the the power of a test and intrepret its meaning in applications, formulate the power function and sketch power curves;
- carry out parametric and non-parametric testing procedures with the use of software, Minitab;
- calculate and interpret correlations between variables and make inferences about relationships;
- formulate a linear regression model, calculate and interpret estimated coefficients and make statistical inferences on the fitted model by carrying out statistical tests using parameter estimates and using the ANOVA table. Regression models discussed include a single quantitative response explained by a single explanatory variable or mutliple explanatory variables which include quantitative and/or categorical explanatory variables and interactions between variables;
- obtain fitted values and predictions at new data points, together with associated prediction and confidence intervals;
- by calculating regression diagnostics and producing relevant plots check the adequacy of the model specification for the data presented and to check model assumptions, including linearity, normality, constant variance, independence and the presence of outliers and influential points;explore the need for transformations of response and explanatory variables;
- interpret and use output from variable selection procedures to choose adequate models, including the best subsets procedure and step-wise;
- carry out the regression analysis with the use of software, Minitab;
- compile a statistical report, i.e. prepare a typed document which introduces the statistical research question being explored, describes the data collection method applicable to the research, describes relevant features of the sample data obtained, and outlines conclusions from inferential statistical analysis carried out using the sample data, incorporating output and plots from statistical software.
Indicative Content
This module gives a basic introduction to applied statistics with applications in regression modelling and non-parametric testing.
The analysis is demonstrated with the use of statistical software, MINITAB. Various non-parametric hypothesis tests are demonstrated and a comparison of suitability of applying non-parametric and parametric methods is discussed. Regression models discussed include a single quantitative response explained by a single explanatory variable or mutliple explanatory variables which include quantitative and/or categorical explanatory variables and interactions between variables.
In particular the module explains the calculations behind the fitting procedure of these models, and the calculations for the statistical hypothesis tests that lead the researcher to infer aspects about the relationships between the variables under study.
The module presents how the estimated relationships obtained as a result of fitting these models can be assessed for suitability to the application and for compliance with model assumptions, i.e. model diagnostics, and presents how the most approporiate fitted model can be determined when multiple candidate explanatory variables are to be considered. The module then presents how the estimated relationship can be used for prediction.
Module Resources
Applied Linear Regression Models by Kutner, Nachtsheim & Neter; McGraw Hill
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