Statistical Methods

Course Description

Statistical Estimation and the concept of Hypothesis Testing; Sampling Distribution of the Mean, Variance, Proportion, Difference between Means, Difference between Proportions and Ratio of Variances; Inference about the Mean, Variance and Proportion (Confidence Interval and Hypothesis Testing); Comparison of two Sample Means, Proportions and Ratio of Variances; Paired versus Independent Sample Comparisons; Sample Size in Comparative Studies; One-way ANOVA and Fisher’s Least Significant Difference; Chi-square Tests of Association; Non-parametric Methods.

Objectives

  • to introduce students to the Fundamental Statistical Methods for Data Analysis;
  • to introduce  students to an intermediate knowledge of statistical methods and a variety of applications of statistical inference in different situations including comparison of means, proportions, and standard deviations, non-parametric or distribution-free tests and introduction to analysis of variance;
  • to demonstrate the importance and usefulness of the above concepts in real applications;
  • to enable students to understand both the strengths and weaknesses of the hypothesis test approach to statistical analysis;
  • to introduce students to non-parametric tests purpose of statistical inference;
  • to equip students with applications of statistical ideas to solve problems from a wide range of disciplines;
  • to train students to communicate the results of their analyses in clear non-technical language;
  • to inculcate interest in Statistics and encourage students to study more advanced courses.

Learning Outcomes

At the end of the course students are expected to:

  • understand the difference between paired and independent data, and be able to recognize both in practice;
  • understand the framework of hypothesis testing for carrying out statistical inference and know what is meant by the null and alternative hypothesis, test statistic, rejection region, significance level, power of a test, p-value;
  • compare means and proportions of two independent or paired samples using interval estimation and/or hypothesis testing;
  • understand how to determine sample size in comparative experiments;
  • know inference concerning the variances of two normal populations;
  • compare means of more than two independent samples using analysis of variance;
  • carry out the sign test, the signed-ranks test and the Mann-Whitney U test, with due regard to the assumptions underlying these procedures;
  • interpret the results of statistical analyses correctly and in non-technical language.