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STATISTICS

Knowledge of Mathematics is absolutely essential for the statistician. Access to a computer is compulsory from the NQF Level: 6 onwards as CDs form part of the study material in certain modules. Credit for a BSc degree is granted for: (i) either STS111 and STS112 or STA121, 122, 123 and 124 or STA1501 and STA1502 (ii) either STS1113 or (STA121 and 122) or STA1501 and STA1502, (iii) either STS1124 or STA1501, (iv) either STA106 or STA124, (v) either STA1510 or STA1610, (vi) either STA1503 or STA2610, (vii) either STA121 and STA123 or STA1501, (viii) either STA121 and STA124 or STA1501 (ix). Credits for other previously passed Statistics courses is at the discretion of the Department.
NOTE: The modules STA1510 and STA1610 are both service modules and do not meet the requirements for admission to any second or third level modules. The same syllabus
is covered in both these service modules, but assessment at the two NQF levels differs. STA1510 and STA1610 may not both be included in one degree composition. The module
STA2610 is offered for BCom students only. STA1503 and STA2610 may not both be included in one degree.
Statistics for the generic Bachelor of Science degree
Major combinations:
NQF Level: 5: STA1501 STA1502 STA1503 plus MAT1512 MAT1503
NQF Level: 6: STA2601 STA2602 STA2603 and STA2604 plus MAT1613 DSC1630 MAT2615 MAT2611
NQF Level: 7: STA3701 STA3702 STA3703 STA3704 and STA3705 or STA3710
Statistics for the generic Bachelor of Commerce degree
Major combinations:
NQF Level: 5: STA1501, STA1502
NQF Level: 6: STA2601, STA2602, STA2603, STA2604, STA2610
NQF Level: 7: STA3701, STA3702, STA3703, STA3710, (STA3704 or STA3705)
General information: There is an increasing demand from employers that students in statistics be trained in the use of statistical software. First-year modules include computer printouts, but computer access is not essential.

Introduction to Statistics (Extended) - XTA1610
Under Graduate Degree Year module NQF level: 6 Credits: 12
Module presented in English
Purpose: To ensure that students are introduced to the most important basic statistical concepts. After completion students should have an informed understanding of different visual descriptions of data, including graphical and tabular techniques; measures of central location, dispersion and association. They should be able to use probability as a tool to create discrete and continuous probability distributions, used extensively in statistical inference; determine confidence intervals and perform hypothesis testing involving sample means and proportions; apply different forms of Chi-square testing; understand simple linear regression and correlation.
Probability and Stochastic Processes - STA4811
Honours Year module NQF level: 8 Credits: 12
Module presented in English Module presented online
Co-requisite: STA4801
Purpose: Abbreviated contents: Probability; Conditional probability and conditional expectation; Markov chains; Exponential distribution and the Poisson Process; Continuous time Markov chains.
Applied Statistics III - STA3701
Under Graduate Degree Semester module NQF level: 7 Credits: 12
Module presented in English
Pre-requisite: STA2601 Co-requisite: STA3703 & (MAT2611 or STA3710)
Purpose: To enable students to demonstrate an understanding of one- and two-way analysis of variance, fixed effects and mixed models, and simple and multiple linear regression. Access to computer is compulsory.
Inference - STA4812
Honours Year module NQF level: 8 Credits: 12
Module presented in English Module presented online
Co-requisite: STA4801
Purpose: About this module: There are three main subdivisions within statistics: efficient summarization, tabulation and graphical display of data; design of experiments; statistical inference. Data summarization was historically the first statistical activity. Experimental design is of crucial importance before data are collected. However, it is statistical inference which has seen most research and practical application in recent years, and it is the theory behind inference which forms the study material of this module. In statistical inference we use a sample of data to draw inferences about some aspect of the population (real or hypothetical) from which the data were taken. The most frequent approach to statistics is followed in this module. Abbreviated contents: Selected topics from statistical inference namely sufficiency, minimal sufficiency, Neyman-Pearson Lemma, Cramer-Rao inequality, uniformly most powerful tests, comparison of estimators, prior distributions, etc. are included in the study material.
Descriptive Statistics and Probability - STA1501
Under Graduate Degree Semester module NQF level: 5 Credits: 12
Module presented in English
Purpose: To have an informed understanding of exploratory data analysis as used in graphical and tabular techniques; measures of central location, variability and linear relationships; simple sampling procedures. Students should be able to use probability as a tool to create discrete and continuous probability distributions, used extensively in statistical inference. The contents of this module have important applications in finance and are useful in several management sciences.
Statistical Inference III - STA3702
Under Graduate Degree Semester module NQF level: 7 Credits: 12
Module presented in English
Pre-requisite: STA2603 or (STA2602 & STA2610)
Purpose: To gain theoretical insight into likelihood, data reduction, point estimation and interval estimation.
Environmental Engineering - EEN101M
Baccalareus Technologiae Degree Year module NQF level: 5 Credits: 24
Module presented in English
Purpose: The qualifying students will be able to apply the principles underlying the application of pollution management strategies. This module also enable students to develop skills in environmental engineering that can be applied in businesses, commerce, government, communities and ther areas of life.
Statistical Inference I - STA1502
Under Graduate Degree Semester module NQF level: 5 Credits: 12
Module presented in English
Co-requisite: STA1501
Purpose: To have a basic perspective of the role of the sampling distribution of the mean, a proportion and the difference between two means in statistical inference, interval estimation and hypothesis testing. Students will be able To estimate single and combinations of population parameters; understand one-way analysis of variance; apply parametric and nonparametric tests such as two Chi-squared tests and the Wilcoxon signed rank sum test. They will also be familiar with simple linear regression and correlation, as well as with the basics of time series analysis and forecasting. The contents of this module are relevant in a wide variety of applications in business and economics and represent a significant contribution to the development of the student as a statistics practitioner.
Distribution Theory III - STA3703
Semester module NQF level: 7 Credits: 12
Module presented in English
Pre-requisite: (STA2603 & MAT2615) or (STA2603 & STA2610) Co-requisite: STA3710 ( only for BCom students)
Purpose: To gain insight into distributions and their relationships. After completion students should comprehend non-centrality; understand compounding and generalization as methods for finding parameter-rich distributions; use bivariate and multivariate distributions to describe normal and non-normal variables.
Chemical Engineering Fundamentals II - CHF2601
Year module NQF level: 6 Credits: 12
Module presented in
Purpose: The purpose of this module is to introduce students to equations of state, such as the ideal gas law and thermodynamic laws, in particular, the principle of conservation of energy. Students completing this module will acquire the skills required in application of these concepts and laws to formulating and solving energy balance problems and combined material and energy balances in chemical engineering situations.
Distribution Theory I - STA1503
Under Graduate Degree Semester module NQF level: 5 Credits: 12
Module presented in English
Pre-requisite: STA1501 Co-requisite: STA1502 & (MAT1512 or DSC1620)
Purpose: Qualifying Students will have a solid fundamental introductory knowledge of and skills in statistical theory and have a clear understanding of the nature of mathematical statistics in terms of its objective, namely statistical inference. These competencies include knowledge of different theoretical distributions for populations, using probability theory, to progress to statistical inference in an accurate mathematical manner. In this process, distribution theory models will be applied in specific discrete and continuous random variables. This module will support further studies and applications in the sector of statistical theory in the field Statistics, as part of the Bachelor of Science and Bachelor of Commerce qualifications. This module will be an illustration of Mathematical Statistics as a theory of information to contribute to the development of communities and of research in Southern Africa, Africa or globally, utilizing mathematics extensively, but only as a tool.
Time Series III - STA3704
Under Graduate Degree Semester module NQF level: 7 Credits: 12
Module presented in English
Pre-requisite: STA2604
Purpose: To gain insight into Box-Jenkins methodology, AR, MA and ARIMA models; also to use statistical software for practical modelling of time series.
Information Administration III (Theory) - IAD3701
Diploma Semester module NQF level: 7 Credits: 12
Module presented in English Module presented online
Pre-requisite: IAD2601 or IAD2M1X
Purpose: Students who successfully complete this module will be able to explain how Information Technology (IT) fits into business strategies and organizational activities as a point of strength in any organization. Students gain an understanding of Information Technology's (IT) role in daily business activities and global business technology to provide a competitive edge. This module will provide students with knowledge, competencies and skills to enable them to maximize their business acumen, whether they major in operations management, manufacturing, sales or marketing. Students who understand business along with the power associated with the Information Age will create their own opportunities and perhaps even new industries.
Basic Statistics - STA1510
Under Graduate Degree,Diploma Semester module NQF level: 5 Credits: 12
Module presented in English
Purpose: To ensure that students are introduced to the most important basic statistical concepts. After completion students should have an informed understanding of different visual descriptions of data, including graphical and tabular techniques; measures of central location, dispersion and association. They should be able to use probability as a tool to create discrete and continuous probability distribution, used extensively in statistical inference; determine confidence intervals and perform hypothesis testing involving a sample mean and proportion; apply different forms of Chi-square testing; understand simple linear regression and correlation.
Sampling Techniques - STA3705
Under Graduate Degree Semester module NQF level: 7 Credits: 12
Module presented in English
Pre-requisite: STA2601
Purpose: To gain more advanced insight into stratified random sampling; systematic and cluster sampling; estimation of the sample size; ratio and regression estimation; sampling with unequal probabilities; complex surveys; non-response.
Research Project in Statistics - HRSTA82
Honours Year module NQF level: 8 Credits: 36
Module presented in English Module presented online
Co-requisite: STA4801
Purpose: The purpose of this module is to prepare the student for research-based postgraduate study. Students completing this module successfully will be able to plan and conduct statistical research under supervision, and can present the findings of the research in an appropriately structured written research report. They will be able to adopt a critical and ethical approach to conducting statistical analysis and research as well as reporting on it, both in their own work and in that of others.
Descriptive Statistics and Probability (Extended) - XTA1501
Under Graduate Degree Year module NQF level: 5 Credits: 12
Module presented in English
Purpose: To have an informed understanding of exploratory data analysis as used in graphical and tabular techniques; measures of central location, variability and linear relationships; simple sampling procedures. Students should be able to use probability as a tool to create discrete and continuous probability distributions, used extensively in statistical inference. The contents of this module have important applications in finance and are useful in several management sciences.
Mathematical Techniques in Statistics - STA3710
Under Graduate Degree Semester module NQF level: 7 Credits: 12
Module presented in English
Pre-requisite: STA2603 or STA2610
Purpose: To gain a basic understanding of matrix presentations and be able to apply calculus in statistical calculations. After completion of this module students should have mastered the basics of matrix calculations; know about linear dependence and independence; determine the three matrix reductions; invert a matrix; find eigen values; apply all these techniques in statistics. Students should be able to solve problems where differentiation and integration techniques have to be applied. Other topics include generalized inverses, Kronecker products and matrix differentiation.
Statistical Inference I (Extended) - XTA1502
Under Graduate Degree Year module NQF level: 5 Credits: 12
Module presented in English
Co-requisite: XTA1501 (or STA1501)
Purpose: To have a basic perspective of the role of the sampling distribution of the mean, a proportion and the difference between two means in statistical inference, interval estimation and hypothesis testing. Students will be able To estimate single and combinations of population parameters; understand one-way analysis of variance; apply parametric and nonparametric tests such as two Chi-squared tests and the Wilcoxon signed rank sum test. They will also be familiar with simple linear regression and correlation, as well as with the basics of time series analysis and forecasting. The contents of this module are relevant in a wide variety of applications in business and economics and represent a significant contribution to the development of the student as a statistics practitioner.
Matrix Methods in Statistics - STA4801
Honours Year module NQF level: 8 Credits: 12
Module presented in English Module presented online
Purpose: About this module: Matrices play an important role in the design of experiments, statistical estimation, statistical inference, probability theory and stochastic processes. This module concentrates on matrix topics that are particularly relevant to statistics. A study guide is included in the study material. Abbreviated contents: includes topics such as orthogonal matrices, idempotent matrices, partitioned matrices, generalised inverses, systems of linear equations, characteristic roots and vectors, the singular value decomposition.
Distribution Theory I (Extended) - XTA1503
Under Graduate Degree Year module NQF level: 5 Credits: 12
Module presented in English
Pre-requisite: XTA1501 (or STA1501) Co-requisite: XTA1502 (or STA1502) & (MAT1512(or XAT1512) or DSC1620)
Purpose: Qualifying Students will have a solid fundamental introductory knowledge of and skills in statistical theory and have a clear understanding of the nature of mathematical statistics in terms of its objective, namely statistical inference. These competencies include knowledge of different theoretical distributions for populations, using probability theory, to progress to statistical inference in an accurate mathematical manner. In this process, distribution theory models will be applied in specific discrete and continuous random variables. This module will support further studies and applications in the sector of statistical theory in the field Statistics, as part of the Bachelor of Science and Bachelor of Commerce qualifications. This module will be an illustration of Mathematical Statistics as a theory of information to contribute to the development of communities and of research in Southern Africa, Africa or globally, utilizing mathematics extensively, but only as a tool.
Multivariate Distribution Theory - STA4802
Honours Year module NQF level: 8 Credits: 12
Module presented in English Module presented online
Co-requisite: STA4801
Purpose: About this module: Matrix notation and theory are used extensively; therefore STA4801 is one of the prerequisite modules. It is expected that the student is familiar with basic distributions such as the normal, gamma, beta, t, and F and with concepts of jointly distributed random variables, marginal distributions, moments, conditional distributions, and independence as well as characteristic functions.Abbreviated contents The basic central distribution and building block in classical multivariate analysis is the multivariate normal distribution. The student will be introduced to the multivariate normal distribution and its properties, as well as spherical and elliptical distributions. The Jacobean of transformations are also included. The Wishart and multivariate beta distributions are covered in the study material.
Basic Statistics (Extended) - XTA1510
Diploma,Under Graduate Degree Year module NQF level: 5 Credits: 12
Module presented in English
Purpose: To ensure that students are introduced to the most important basic statistical concepts. After completion students should have an informed understanding of different visual descriptions of data, including graphical and tabular techniques; measures of central location, dispersion and association. They should be able to use probability as a tool to create discrete and continuous probability distribution, used extensively in statistical inference; determine confidence intervals and perform hypothesis testing involving a sample mean and proportion; apply different forms of Chi-square testing; understand simple linear regression and correlation.
Linear Models - STA4803
Honours Year module NQF level: 8 Credits: 12
Module presented in English Module presented online
Co-requisite: STA4801
Purpose: About this module: This module teaches both the underlying theories of linear models and their practical applications in business administration, economics, engineering, and the social, health, and biological sciences. Analysis of real-life data is used to help the students understand the theories and applications of linear modelling. Abbreviated contents: Generalised inverses of matrices; Distributions and quadratic forms; Regression and/or full-rank models; Anova and Ancova models; Mixed effects models.
Introduction to Statistics - STA1610
Under Graduate Degree Semester module NQF level: 6 Credits: 12
Module presented in English
Purpose: To ensure that students are introduced to the most important basic statistical concepts. After completion students should have an informed understanding of different visual descriptions of data, including graphical and tabular techniques; measures of central location, dispersion and association. They should be able to use probability as a tool to create discrete and continuous probability distributions, used extensively in statistical inference; determine confidence intervals and perform hypothesis testing involving sample means and proportions; apply different forms of Chi-square testing; understand simple linear regression and correlation.
Regression - STA4804
Honours Year module NQF level: 8 Credits: 12
Module presented in English Module presented online
Co-requisite: STA4801 & STA4803
Purpose: About the module: This module teaches both the underlying theory of regression analysis/models and its/their practical applications in business administration, economics, engineering, and the social, health, and biological sciences. Analysis of real-life data is used to help the students understand the theories and applications of regression modeling and of making valid inferences from regression analysis. Abbreviated contents: Simple and Multiple linear regression models; Model diagnostics; General linear F-test; Model building; Anova and Ancova models.
Applied Statistics II - STA2601
Under Graduate Degree Semester module NQF level: 6 Credits: 12
Module presented in English
Pre-requisite: STA1501 (or XTA1501) & STA1502 (or XTA1502)
Purpose: To enable students to identify the correct technique, manage the statistical software JMP to do the computations and interpret the results for decisions regarding tests for normality, independence and hypotheses concerning means, variances and regression. Access to a computer is compulsory.
Research Project in Statistics - STA4805
Honours Year module NQF level: 8 Credits: 12
Module presented in English Module presented online
Co-requisite: STA4806
Purpose: About this module: The purpose of this module is to provide students with practical experience of conducting statistical research and of writing scientific reports on their findings. These reports will be submitted by the students for evaluation. Abbreviated contents: Introduction; Literature view; Theory and Methods; Results and Discussion; Conclusion.
Statistical Inference II - STA2602
Under Graduate Degree Semester module NQF level: 6 Credits: 12
Module presented in English
Pre-requisite: STA1501 (or XTA1501) & STA1502 (or XTA1502) Co-requisite: STA1503 (or XTA1503) or STA2610
Purpose: To enable students to gain insight in statistical inference using different properties of estimation and methods of estimation. Included are linear models and estimation by least squares as well as designing experiments and analysis of variance procedures.
Time Series - STA4807
Honours Year module NQF level: 8 Credits: 12
Module presented in English Module presented online
Co-requisite: STA4801
Purpose: Abbreviated contents: The approach in this module is both theoretical and practical. Contents include model identification, state space models, the Kalman filter, power spectrum and the transfer function. Discussions on process identification, non-stationary processes and seasonal processes and spectral estimation techniques are also covered.
Distribution Theory II - STA2603
Under Graduate Degree Semester module NQF level: 6 Credits: 12
Module presented in English
Pre-requisite: (STA1502 (or XTA1502) & DSC1620) or (STA1503 (or XTA1503) & MAT1512 (or XAT1512) Co-requisite: STA2610 (only for BCom students)
Purpose: To gain insight into the role that formal theory plays in data analytic methods, discussing a wide variety of discrete and continuous distributions simultaneously. After completion students should understand the joint probability structure of two random variables (discrete and continuous case); be able to calculate expectation, variance, covariance, conditional expectation and moment-generating functions; have insight into distributions of functions of independent random variables; prove the law of large numbers and the central limit theorem under fairly strong assumptions; comprehend how the Chi-square, t, and F distributions are derived from the normal distribution.
Survival Analysis - STA4808
Honours Year module NQF level: 8 Credits: 12
Module presented in English Module presented online
Purpose: About this module: This module explores different aspects of survival analysis as data analysis methodology. The presentation is practical and accessible with statistical software enabling the learner to explore and analyze a wide spectrum of problems on time to event data. Students are prepared for the workplace as Survival Analysis has a multitude of applications in the fields of health, engineering, economics, biology and the physical sciences.Abbreviated contents: Students learn to describe the distribution of failure times (time to event), analysis times and Hazard models (Parametric and Semi-parametric), Censoring, truncation and the recording of survival data. Nonparametric analysis of survival data, the Cox proportional hazards model, building a Cox proportional hazards model, diagnostics to check model for misspecification, outliers, influential points and most importantly, the proportional hazards assumption fall within the scope of this module contents. This module makes extensive use of computer statistical software and hence a student must have access to a computer.
Forecasting II - STA2604
Under Graduate Degree Semester module NQF level: 6 Credits: 12
Module presented in English
Pre-requisite: STA1501 (or XTA1501) & STA1502 (or XTA1502)
Purpose: To see forecasting as a structured process of classified techniques. After completion students can explore time series data, looking at seasonality, stationarity and trend; classify techniques for forecasting and asses accuracy of forecasts; deal with different characteristics of time series, such as smoothing methods and seasonal models; establish credibility in forecasting and implement the forecasting process.
Nonparametric Regression - STA4809
Honours Year module NQF level: 8 Credits: 12
Module presented in English Module presented online
Co-requisite: STA4801
Purpose: About this module: Special attention is given to different aspects of nonparametric regression as an explorative tool and non-linear relationships in a wide variety of applications. The presentation is practical and accessible with statistical software enabling the learner to explore and analyze a wide spectrum of data. The incentive behind the development of this module was the Honours degree in Data mining, but at the same time it prepares the student for the workplace as Nonparametric regression has applications in the fields of economy, biology and the physical sciences. Abbreviated contents: Students will learn to understand the differences between parametric and nonparametric regression and the difference between model driven and data driven approaches. Attention is given to nonparametric density estimation in practice and theory for univariate and multivariate analyses as well as models for nonparametric regression and the smoothing parameters. Advanced tools such as semi-parametric regression, additive models and in particular generalised additive models are also included. This module makes extensive use of computer statistical software and hence a student must have access to a computer.
Statistical Distributions - STA2610
Under Graduate Degree Semester module NQF level: 6 Credits: 12
Module presented in English
Pre-requisite: STA1501 Co-requisite: STA1502 & DSC1620
Purpose: To have a solid fundamental introductory knowledge of and skills in statistical theory and have a clear understanding of the nature of mathematical statistics in terms of its objective, namely statistical inference. These competencies include knowledge of different theoretical distributions for populations, using probability theory, to progress to statistical inference in an accurate mathematical manner. In this process, distribution theory models will be applied in specific discrete and continuous random variables. This module will support further studies and applications in the sector of statistical theory in the field Statistics, as part of the Bachelor of Science and Bachelor of Commerce qualifications. This module will be an illustration of Mathematical Statistics as a theory of information to contribute to the development of communities and of research in Southern Africa, Africa or globally, utilizing mathematics extensively, but only as a tool.
Methods of Multivariate Analysis - STA4810
Honours Year module NQF level: 8 Credits: 12
Module presented in English Module presented online
Co-requisite: STA4801, STA4802 & (HRSTA82 applicable to 98922)
Purpose: About the module: This module is about tests of hypotheses on means, multivariate analysis of variance, inference from covariance matrices, as well as principle components and factor structure of multivariate data. Abbreviated contents: The topics covered in this module include Hotelling's T², multi-variate analysis of variance, analysis of repeated measurements, canonical correlation, interpretation of principle components, biplots, the evaluation of factors, the properties of factor model estimation, etc.