Group A (Marks: 20)
(Related Course - STAT-403: Multivariate Analysis)
This course focuses on implementing practical multivariate analysis-related problems using the statistical software R.
Course Objectives:
The objectives of this course are to:
- Understand the main features of multivariate data;
- Apply factor analysis and cluster analysis to solve social problems;
- Estimate canonical correlation to represent the relationship of multiple causes and effects of real phenomena;
- Carry out multivariate statistical techniques and methods efficiently and effectively. Implement all of the above using standard statistical packages (e.g., R);
- Reproduce the results obtained in statistical packages (e.g., R) using spreadsheets (e.g., Excel).
Learning Outcomes:
At the end of the course, students will be able to:
- Calculate Euclidean and statistical distances;
- Construct contours and assess multivariate normality;
- Analyze multivariate data and the dependence structure of variates to extract useful information from a massive dataset;
- Apply suitable tools for exploratory data analysis, dimension reduction, and classification to formulate and solve real-life problems;
- Calculate factors from large data sets and interpret factor rotation and factor scores;
- Solve discrimination and classification problems;
- Apply cluster analysis;
- Implement multivariate analysis techniques with statistical software such as R in a manner that the methodology adopted is motivated by appropriate statistical theory.
Contents:
- Determining Euclidean and statistical distances, constructing contours, assessing multivariate normality, and Box-Cox transformation of multivariate data.
- Construction of confidence regions for different testing problems, Hotelling's T2, principal components, factor analysis, canonical analysis, classification, and grouping techniques of data by discrimination and classification.
- Cluster analysis of categorical data by different measures.
Rationale:
Group B (Marks: 15)
(Related Course - STAT-402: Non-Parametric Methods)
This course is designed to provide a strong conceptual foundation in the methods of nonparametric tests, with an emphasis on practical aspects of the interpretation and communication of statistically-based conclusions in statistical research.
Course Objectives:
The objectives of the course are to:
- Make the students understand how to apply different nonparametric tests;
- Acquaint/Equip students with a statistical toolkit which will enable them to apply their knowledge and skills to real-world tasks.
Learning Outcomes:
Upon successful completion of this course, students will acquire knowledge and skills to:
- Articulate practical ideas of non-parametric methods, their properties, problems, and examples;
- Understand different methods of non-parametric tests and concepts related to the test of hypothesis;
- Obtain practical knowledge on the analysis of nonparametric data.
Contents:
- Test of randomness (one-sample, two-sample);
- Wilcoxon Signed-Rank test, Mann-Whitney U-test, Median tests (two or more samples), Kolmogorov-Smirnov tests, different location and scale problem tests, Kruskal-Wallis test, different tests of measures of association.
Rationale:
Group C (Marks: 15)
(Related Course - STAT-406: Survival Analysis)
This course is designed to provide students with practical knowledge related to survival analysis.
Course Objectives:
The objectives of this course are to:
- Get a clear idea about survival data and related lifetime distribution;
- Learn to get information from incomplete data or censoring mechanisms;
- Compare the efficiency of different survival curves;
- Develop statistical models, specified for health-related data;
- Cover the appropriate application, calculation, and interpretation of statistical tests for incomplete data;
- Learn to analyze and interpret real-life survival data using statistical software.
Learning Outcomes:
After completing this course, students will be able to:
- Apply descriptive techniques commonly used to summarize public health data;
- Obtain the Kaplan-Meier estimate of survival function with confidence intervals;
- Construct likelihood functions for censored data and calculate necessary statistics;
- Fit Cox proportional hazard models and measure the impact of factors on this function;
- Apply basic statistical concepts commonly used in Health and Medical Sciences;
- Interpret results of statistical analyses found in public health studies;
- Build statistical models over real health data;
- Estimate and compare the efficiency of models.
Contents:
- Survival Analysis: Fitting of survival distributions, non-parametric estimation of survival and hazard functions, standard errors, and confidence intervals.
- Comparison of two survival curves, Cox PH, and fitting Cox PH models.