MASTER OF SCIENCE (STATISTICS)

Study Duration
Minimum 2 semesters (1 year)
Maximum 4 semesters (2 years)

Intake
Intake – 2 times a year (March & October)
*subjected to UKM academic calendar

STPD6024 Research Methodology
This course provides guidance in planning, implementing and succeed in a scientific research. Students are introduced to the science philosophy and ethics necessary to be adopted by researchers. Students are given exposure to determine and manage risks in scientific research. Apart from that, issues and rules related to research such as intellectual property, copyright, plagiarism etc. will be discussed.  Subsequently, students are guided to plan their research and prepare a research proposal. For this, students are trained with techniques in information search both manually and on-line, identifying issues and research objectives, planning research and experimental design within their period of study. Students are required to prepare their research proposal according to the format and making sure that it is free from plagiarism by introduction of plagiarism checker system. Students are given the opportunity to present their proposal in a seminar and defend them. Students will be evaluated based on written and oral presentation of the research proposal, and final examination

STQS6004 Calculus and Matrix Algebra for Statistics
The aim of this course is to introduce students to the use of calculus and matrix algebra in the field of statistics. The concept of limit is given intuitively. The concept of differentiation, rate of change and problem of extremum are discussed. Integration as anti derivative and several integration techniques are discussed. Various basic concepts about matrices are given: inverse, transpose, determinant, trace, quadratic form and orthogonal. Various basic concepts about vectors are discussed: vector, linearly dependent and not linearly dependent, eigen values and eigen vectors. Introduction is given on generalized inverse and partitioning of matrix. Several examples for linear model are given.

STQS6014 Mathematical Statistics
The aim of this course is to introduce students to the concept of statistical thinking and tools. The concept of random variables and several distribution functions. Distributions function of random variables and the techniques to identify the particular distribution: distribution function technique, transformation technique and moment generating function technique. Bivariate and multivariate distribution are discussed in the aspects of joint densities, joint distribution function, marginal distribution, conditional distribution, independence between random variables, conditional expectation and correlation coefficient. Chebyshev theorem and bivariate normal. Order statistics and sampling distribution. Several distributions related to normal distribution such as t distribution, Chi-square and F. Law of large numbers and central limit theorem. Methods of point estimation, maximum likelihood technique and method of moment. Point estimation and interval estimation involves estimation of one population parameter and one population parameters. Hypothesis testing covers one and one populations.

STQS6024 Modeling and Data Analysis
The aim of this course is to introduce students to the practical use of statistical software in doing statistical tests. The topics covered are test of hypothesis, error measurement, power of the test, test to compare means such as t test, analysis of variance (ANOVA), analysis of covariance (ANCOVA); goodness of fit test for distributions; test for linear relationship which covers correlation, simple regression and multiple regression as well as introduction to the analysis of residuals. Several related topics on nonparametric statistics will also be discussed.

STQS6034 Statistical Inference
The aim of this course is to enhance understanding of students in the theory of statistics, point estimations and the properties of the estimators. The properties discussed include efficiency, unbiasedness, minimum variance unbiased estimator, sufficiency and completeness. Rao-Cramer Inequality and Rao-Blackwell Theorem are discussed. The estimation methods studied include maximum likelihood, method of moment and least square. Asymptotic evaluations of the estimators are also covered. Various topics under hypothesis testing such as best critical region and likelihood ratio are also discussed.

STQS6064 Medical Statistics
Several important statistical concepts in medicine are discussed in detail. Basic analysis methods will be examined including the evaluation of the diagnostic tests. Topics that will be discussed are risk, relative risk, odds and odds ratio, prevalence and incidence, attributal risk, confounding and interaction, detection of and adjustment for confounding effects. Observational studies such as cohort studies, control-case will be covered; intervention methods; sample size determination. Other topics discussed are modelling in medicine, classical linear model, logistic model and survival model.

STQS6094 Sampling Techniques
This course introduces sampling designs and the related theories. The discussion will begin with various important statistics obtained from surveys and the necessary measures for initiating a survey. Simple random sampling will be discussed in detail, the theory, practical aspects, and mathematical derivations. Estimators and the properties will be studied mathematically and supported using computing techniques. Stratified sampling will be explored in details – include mathematical derivation, computing and the practical aspects. Simulation methods will be utilized for data generation and for investigating the properties of the estimators. Single and one stages cluster sampling will also be studied. Similar approaches as used for stratified sampling will be implemented in investigating the properties of estimators produced by cluster sampling. This course covers sampling design for wildlife population and spatial sampling.

STQS6234 Bayesian Inference
This course introduces to the students on Bayesian’s theories. Bayesian inference for normal distributions is also discussed. Other than that, Bayesian inference for distributions other than normal, for example Binomial and Poisson is also explained. Other topics include hierarchical Bayesian model, empirical Bayesian, hypothesis testing, correlation, regression and analysis of variance.

STQS6244 Stochastic Process
The aim of this course is to introduce the students to the theory of stochastic process. Among the topics to be discussed include discrete and continous time Markov chain. This include subtopics regarding the Chapman-Kolmogorov equation, Birth and Death process, limiting probabilities and some important properties of Markov process. Other topics to be discussed include the Poisson process and the Renewal process which include the subtopics of Homogeneous and Nonhomogeneous Poisson process, compound Poisson Process, decomposition of Poisson Process, Renewal equation, mean-value function, limit theorem and etc. The students will also be expose with the topics of Reliability theory, Brownian motion and the aplication of Markov Chain Monte Carlo method.

STQS6254 Design and Analysis of Experiments
The aim of this course is to explain the role of statistics in the scientific method which is a prerequisite to design an efficient experiment. This course will cover the basic principles of experimentation; randomization, and replication. RRL & one-way ANOVA; linear contrasts; underlying assumptions in ANOVA; analysis of residuals; additivity and interaction; transformation of data to satisfy ANOVA assumptions; block design; incomplete block design; properties of orthogonality and balance; rule of assignment of treatments in blocks; 2n factorial designs; blocking and confounding in factorial experiments; fractional factorial designs; confounding systems and aliases; design resolutions. Other topics covered will be fractional factorial designs; response surface methodology; and covariance analysis.

STQS6274 Statistical Computing
Students will be equipped with sufficient computing knowledge that useful for data analysis and statistical inferences. For these objectives they are given programming skills using R. Utilizing the skills the students will be trained to write function for obtaining various statistical summaries, empirical distribution, nonparametric measures using quantiles and the quantile based distribution summaries. In addition the students will also be exposed to various methods for simulating random data. R computing for classical and Bayesian statistical inference will be discussed. All the discussions are data and practical problems based. Re-sampling techniques for statistical inference – bootstrap and jackknife, order statistics will be explored together with testing hypothesis using permutation and Monte Carlo methods.

STQS6284 Multivariate Analysis
This course introduces the nature of multivariate as compare to univariate data. The practices of univariate data analysis are extended to multivariate data. Estimation theories and statistical inferences for multivariate distributions will be covered. Multivariate methods such as multivariate analysis of variance, principle component analysis, factor analysis, canonical correlation analysis, discriminants analysis and cluster analysis are explained. The mathematics, computing and data analysis will be integrated in the course.

STQS6424 Nonparametric Methods
This course begins with introducing students to the basic assumptions behind non-parametric methods. Topics discussed include the rules for one sample, one dependent samples and one independent samples; normal approximation to such tests; tests for three or more samples; tests for flow and correlation; trimmed data analysis; Kaplan-Meier test and Mann-Whitney test itlak Gehan; and non-parametric butstrap methods. Other topics include some methods of smoothing and model matching.

STQS6444 Time Series Modeling and Forecasting
The objectives of this course are estimating simple regression models, explaining the techniques for modeling trend and volatility in time series data, explaining the cointegrating relation between one or more time series, and at the same time highlighting several major issues in time series analysis that are related to stationarity, trend, volatility, and cointegration. In particular, for modeling trend and volatility, the focus will be on the ARCH-GARCH models. As for cointegration, the error-correction mechanism and the Johansen approach will be discussed. At the end of the semester, the students will be required to write one short report on the application of statistical testing methods and model analyses that are covered during the semester.

STQS6584 Statistical Modeling
This course begins by introducing the concept of modeling through simple linear regression, multiple linear regression and nonlinear regression where error terms is assumed to be normally distributed. Diagnostic checking on fitted model and model assumptions will be further discussed. The course continue to model where the normality assumption is not met. Students will be exposed to the concepts of generalized linear model such as logistic models, Poisson and log-linear models. The concepts of maximum likehood estimation, likehood ratio test and the concept of deviance will be introduced.

STQS6988 Research Project
Research project is a compulsory course work involving case study/literature survey/research. The student is required to conduct the research study under supervision of a supervisor. The student is also required to select a pertinent topic as agreed to by the supervisor. The students are required to write up a comprehensive and scientific report on the study that he/she has conducted.

• Bachelor’s Degree in relevant field with minimum CGPA 2.50 or equivalent, from any institutions of higher learning  recognized by the UKM Senate; or
• Bachelor’s Degree in relevant field with minimum CGPA 2.00 – 2.49 or equivalent, with minimum of 5 years working experience or research project in relevant field. Proof of the working experience of a foreign candidate should be acknowledge by the embassy of the respective country; or
• Fulfill Accreditation of Prior Experiential Learning (APEL A) for local candidates only:
  • should be more than 30 years of age in the year of application; and
  • possess at least STPM or diploma in relevant field or other equivalent qualification recognized by the Government of Malaysia and approved by the UKM Senate; and
  • possess a certificate of MQA APEL with MQF Level 7
• An international student shall obtain minimum results of TOEFL iBT score 46 / IELTS band 5.5 / CEFR band B2 / MUET band 3 (An international student who comes from a country where English is the official language, or who has obtained academic qualifications from any institution of higher learning that uses English as the medium of instruction may be exempted from the requirement for TOEFL / IELTS / MUET); and
• Fulfill other requirements prescribed by the UKM Senate from time to time.