Module Catalogues, Xi'an Jiaotong-Liverpool University

Module Code: MTH205
Module Title: Introduction to Statistical Methods
Module Level: Level 2
Module Credits: 5.00
Semester: SEM1
Originating Department: Mathematical Sciences
Pre-requisites: MTH104 MTH113

 Aims To introduce statistical methods with a strong emphasis on applying standard statistical techniques appropriately and with clear interpretation. Interspersed with graphical and robust techniques. The emphasis is on applications.
 Learning outcomes A Calculate summary statistics, fitted values and residuals, Construct and interpret ANOVA tables B Demonstrate understanding of the concepts of: a random variable, a distribution, a statistical model, a parameter, a fitted value and a residual C Demonstrate understanding of the sum of squares as a tool for assessing the adequacy of a model D Demonstrate understanding of the principles of hypothesis testing and confidence intervals E Demonstrate understanding of the significance of regression models and ANOVA tables F Interpret the output from standard computer packages to draw statistical conclusions G Be aware of the significance of statistical variability in relation to the interpretation of data and the confidence with which conclusions can be reached H Be aware that the validity of statistical conclusions depends in the appropriateness of the techniques used, and the skill and independent judgment with which techniques are selected and used and conclusions drawn
 Method of teaching and learning This module will be delivered by a combination of formal lectures and tutorials.
 Syllabus Estimation Point and interval estimation. Unbiased estimators. Confidence intervals for means, proportions, and their differences. Required sample size for given margin of error. Hypothesis Testing: One Sample Introduction to hypothesis testing. Acceptance and rejection regions. Type I and Type II errors and their probabilities. Hypotheses about means, proportions and matched pairs, Student t-distribution. Power function of a test involving the mean and proportion. Hypothesis testing and confidence interval for the variance, Chi-squared distribution.Hypothesis Testing: Two Samples Distribution of the difference of two sample means and proportions. Comparisons of two means and two proportions, including paired Student t-test. Comparison of two variances, F-distribution. Chi-square testsGoodness of fit tests for uniform, binomial, Poisson and Normal distributions. Tests of homogeneity and independence of contingency tables.Analysis of VarianceOne way analysis of variance. Two way analysis of variance.Linear RegressionLinear regression model, least squares method. Estimation of the intercept and slope, confidence intervals and tests. Predictions and their confidence or prediction intervals. Multiple regression, regression ANOVA and the F-test. Coefficients of correlation and determination. Polynomial regression. Outline of model selection and residual analysis.Non-parametric Tests/Resampling MethodsSelection of non-parametric tests from the following list: Sign test, Mann-Whitney test, Wilcoxon signed-ranks test, Kruskal-Wallis test, Kolmogorov-Smirnov test, or resampling methods for estimation and test.
Delivery Hours
 Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total Hours/Semester 39 13 98 150

## Assessment

 Sequence Method % of Final Mark 1 Formal Examination 70.00 2 Coursework 1 15.00 3 Coursework 2 15.00
 Module Catalogue generated from SITS CUT-OFF: 12/9/2019 11:38:18 PM