BACHELOR OF SCIENCE HONOURS DEGREE IN APPLIED STATISTICS (HSTAT)
PROGRAMME OVERVIEW
Upon successful completion of the programme a graduate will be able to:
- Understand statistics and how its various disciplines are integrated.
- Work effectively in a broad range of scientific, government, financial, analytic,
health, technical and other related fields.
- Understand the relationship between theory and applications of statistics.
- Use statistical thinking, training, and approach to problem solving in a diverse
- variety of disciplines.
- Read and interpret statistical literature of various types, including online sources,
- survey articles and books.
- Modify and improve existing statistical models to solve real world problems.
- Use software and quantitative models to analyse statistical data.
- Communicate statistical information orally and in writing to a wide variety of audiences.
ENTRY REQUIREMENTS
For all entry pathways candidates must have at least five Ordinary Level subjects/ National
Foundation Certificates including English Language, Mathematics and a Science subject at grade C or better.
| Normal Entry: | At least two Advanced Level passes including Mathematics or its recognized equivalence (Mechanics, Statistics, Pure Mathematics) plus at least five Ordinary Level passes/ National Foundation Certificates including Mathematics and English Language OR National Certificate. |
| Special Entry: | National Diploma and Higher National Diploma. |
| Mature Entry: | At least 25 years plus relevant work experience. |
CAREER OPPORTUNITIES AND FURTHER EDUCATION
PROGRAMME STRUCTURE
| Module | Credits |
| Level I | |
| *HMAT131 Calculus 1 | 12 |
| *HMAT132 Linear Mathematics 1 | 12 |
| *HSTA132 Applied Statistics | 12 |
| *HSTA133 Probability Theory 1 | 12 |
| HCSCI132 Principles of Programming Languages | 12 |
| HSTA134 Statistical Computing 1 | 12 |
| HSTA105 Regression and ANOVA 1 | 12 |
| HMAT110 CALCULUS 2 | 12 |
| *HSTA107 Statistical Inference 1 | 12 |
| HSTA106 PROBABILITY THEORY 2 | 12 |
| HMAT109 Mathematical Discourse and Structures | 12 |
| Level II | |
| *HSTA231 Design and Design Issues 1 | 12 |
| *HSTA235 Hypothesis Testing Techniques | 12 |
| *HSTA239 Estimation Theory Techniques | 12 |
| *HSTA236 Survey Techniques | 12 |
| *TNCP201 Technopreneurship | 12 |
| *HSTA237 Time Series Analysis | 12 |
| *HSTA240 Operations Research 1 | 12 |
| HSTA231 Official, Social and Economic Statistics | 12 |
| HMAT231 ODEs | 12 |
| HSTA234 Statistical Computing 2 | 12 |
| *GS231 Gender Studies | 12 |
| HSTA238 Statistical Inference 2 | 12 |
| Level III | |
| Work-related Learning | 120 |
| Level IV | |
| *HSTA401 Linear Models | 12 |
| *HSTA402 Multivariate Analysis | 12 |
| *HSTA408 Econometrics | 12 |
| *HSTA409 Demography | 12 |
| *HSTA412 Survival Models | 12 |
| HSTA410 Stochastic Processes | 12 |
| HSTA405 Operations Research and Quality Control Techniques | 12 |
| HSTA406 Design and Design Issues 2 | 12 |
| HMAT436 Mathematical Programming | 12 |
| HSTA470 Research Project | 36 |
| Maximum MBKS Credits | 432 |
SYNOPSES
HMAT131 Calculus I
Number systems: The principle of mathematical induction. The real number system: Functions: Limits of functions. Continuity. Sequences: Differentiation: Derivatives of functions of a single variable. Integration: Method of substitution, integration by parts and reduction formulae, fundamental theorem of calculus.
HMAT132 Linear Mathematics I
Complex numbers: De Moivre’s theorem polynomials and roots of polynomial equations. Matrices and determinants: solutions of simultaneous linear equations, applications to geometry and vectors. Differential equations: separable, homogeneous, exact, integrating factors, linear equation with constant coefficients.
HSTA132 Introduction to Statistics
Measures of central tendency. Measures of variability. Empirical distributions. Moments. Skewness and Kurtosis. Indicators. Contingency Tables. Introduction to Time Series and Trends. Sampling. Introduction to estimation procedures: Judgemental method and Method of moments. Introduction to Hypothesis testing. Non-parametric statistics. Chi-square contingency methods, Goodness of fit tests, Q-Q plots, Z-test and t-test.
HSTA133 Probability Theory I
Axiomatic probability, sets and events, sample space, conditional probability, Independence, laws discrete and continuous random variables, probability density functions, mean, variance, expectation. Independence, Chebyshev’s inequality, moments and moment generating functions. Common Discrete and continuous Distributions. Joint Probability Distributions. Approximations, Law of large numbers, Central limit Theorem.
HSTA134 Statistical Computing 1
Introduction to use of statistical software. Training on database software including Microsoft Excel, Microsoft Access, SPSS, and STATA. Use of these softwares for data entry, data management and analysis. Interpretation of analysis results and statistical report writing.
HSTA105 Regression and Analysis of Variance I
Method of least squares. General linear model assumptions. Checking validity of assumptions. Outliers. Pearson’s and Spearman’s correlation coefficients, predictions. Regression in terms of sums of squares and sums of products. Estimation of parameters. Multiple linear regression. Testing and inference in multiple linear regression using matrices. Partial correlation. Analysis of variance (ANOVA). Assumptions underlying ANOVA. One-way, balanced design ANOVA
HSTA107 Statistical Inference 1
Deductive inference, population and sample concepts as the basis of statistical inference, parameters and statistics, review of probability theory. Central Limit Theorem, Chi-square, student-t and F distributions, distribution of min and max. Estimation: methods of estimation, properties of estimators and their sampling distributions. Interval estimation. and Hypothesis testing.
HMAT231 Ordinary Differential Equations
Modelling with first order ODEs in population dynamics, and second order ODEs (mass-spring systems, RLC circuits). Methods of undetermined coefficients, reduction of order and method of variation of parameters. Existence and uniqueness of solutions, revision of continuous functions and Lipschitz conditions. Series solutions of ODEs, solutions near ordinary and singular points. Systems of linear first order ODEs, solution and stability. Differential equations of special functions. Laplace transforms and inverse Laplace transforms, applications to solving IVPs, Heaviside and Dirac functions.
HSTA231 Design and design issues 1
Principles of experimentation. Completely randomized designs, randomized block designs, Latin square design. Ecological Studies, Cross Sectional Studies, Correlational studies, Case control studies, Cohort and randomized control trials. Epidemiology Methods, Framingham Heart Study, Measurement in Epidemiology, Binary Outcomes, Definition of Prevalence, Determinants of Prevalence, Incidence, Measures of Association, Odds Ratio, Attributable Proportions.
HSTA236 Survey techniques
Uses, scope and advantage of sample surveys. Types of surveys. The phases of a survey. Survey organisation. Questionnaire design, dummy tables, pre-tests, training of field workers. Report writing. Errors in surveys, monitoring reviews, quality control. Sampling techniques, sample design. Further sampling theory. Estimation of means, totals, proportions. Ratio estimation. Variance calculations. Practical work.
HSTA237 Time series analysis
Time series models. Box-Jenkins model building technique, white noise, and random walk. Autocovarince functions. Autocorrelation functions, Yule-Walker equations. General linear process. Autocovariance generating function. Stationarity and Inevitability. Autoregressive processes and Moving average process. Yule-Walker equation. ARIMA models for non-stationary processes. Parameter estimation. Goodness of fit tests. Forecasting. Application to SARIMA processes. Time series in frequency domain.
HSTA239 Estimation techniques
General Minimum Variance Unbiased Estimation, Cramer-Rao Lower Bound, Linear Models & Unbiased Estimators, Maximum Likelihood Estimation, Least squares estimation, Bayesian Estimation, Statistical Detection Theory, Deterministic Signals, Random Signals, Non-parametric and robust detection. Case studies and mini project.
HSTA240 Operations Research I
M-technique, Dual linear programming methods. Dynamic programming. Project scheduling: network construction, PERT-CPM methods, project control. Queuing theory: single and multi-queuing models, finite queue variation and P. K. formula. Inventory Control Models. Probability models. Decision Analysis: Bayesian methods, mini-max, maxi-maxi criteria, maximum likelihood, maximal opportunity criteria, introduction to Utility Theory.
HSTA238 Statistical inference II
Types of statistical data. Order statistics. Exact and asymptotic distribution of order statistics. Wilcoxon one-sample and two sample tests. Tests of location a tests of variability. Non-parametric tests. Test for extreme reactions. Hollander. Tests for dichotomised or cardinal data. Kendal’s measures. Fisher’s exact test. Chi-square based tests. Kolmogorov’-Smirnov, generation of random numbers. Bootstrap and Jackknife estimation. Resampling. M-, L- and R-estimator.
TCNP201 Technopreneurship
Introduction: nature and importance of technopreneurship, Differences between
technopreneurship and entrepreneurship; Relationship between technopreneurship and the national economy; Innovation and creativity, Qualities of an entrepreneur. Small business model and financial issues: developing a business model, basics of small business management, risks and stages of funding, sources of funding, financial funding for growth, product valuation, how to form and register a small business in Zimbabwe. New Product Development (NDP): Opportunity recognition and creation, Sources of opportunity, Screening technology opportunities, Designing your product/service: design thinking; process thinking, strategic thinking; the NPD process: idea generation, idea screening, concept testing, market strategy development, business financial analysis, prototyping, test marketing, commercialization. Developing and Protecting Intellectual Property: Concept of intellectual property, theory behind IP protection, Intellectual Property (IP)-driven vs non-IP driven technopreneurship Trade secrets, Copyrights, Trademarks, Patent and Trademark protection and its significance, Basics of patenting, legislation governing IP in Zimbabwe. Case studies of successful technopreneurs. Project.
HSTA401 Linear Models
Regression: Linear regression model, point and interval estimation of parameters. Pure error and lack of fit. Residual analysis. Multiple regression: estimation and confidence intervals. General linear hypothesis. Stepwise methods. Experimental design models: one factor models. Fixed and random effects. Two factor models, with and without interaction. Qualitative and quantitative contrasts.
HSTA402Multivariate Analysis
Multivariate data, descriptive statistics, graphical techniques. Random vectors and matrices. Multivariate normal distribution. Wishart distribution. Transformation to near normality. Inferences about mean vector. Comparison of several multivariate means: one-way MANOVA. Simultaneous confidence intervals for treatment effects, profile analysis, ideas of two-way MANOVA. Principal component analysis. Factor analysis, Canonical correlation and Discriminant analyses
HSTA470 Research project
The research project involves an experimental or observational investigation of a fundamental or practical problem in Applied Statistics, or product development. With guidance from an academic supervisor, each student should choose and propose his/her own project theme. Each student is required to submit a proposal, carry out an independent research project or develop a product; submit a final written report, and to deliver an oral presentation.
HSTA408 Econometrics
Role of Econometrics in Zimbabwe. Review of general linear model. Linear restrictions, Generalised least squares, GLS estimator, heteroscedasticity, pure and mixed estimation, group observations and grouping of equations. Autocorrelation. Heteroscedasticity. Multicollinearity. Stochastic regressors. Simultaneous equations systems. Restrictions on structural parameters. Two stage and three stage least squares.
HSTA409 Demography
Basic techniques of demographic analysis. Sources of data available for demographic research. Population composition and change measures will be presented. Measures of mortality, fertility, marriage and migration levels and patterns will be defined. Life table, standardization and population projection techniques. Case studies.
HSTA410 Stochastic processes
Integer-valued variables: probability generating functions, convolutions. Markov chains: transition probabilities, classifications of states, stationary distributions, transient states. Gambler ruin, random walk. Markov processes: Chapman-Kolmogorov equations, transition rate matrix, forward and backward systems. Poisson process, normal equations, machine operation machinery breakdown, queuing model.
HSTA412 Survival models
Survival time, survival function, hazard function, types of censoring and truncation. Methods (including life table, Kaplan Meier and Nelson Aalen) for estimating survival function, hazard function. Semi parametric (e.g., Cox-Proportional hazards model) survival models and parametric survival models. Evaluation of the proportional hazards assumption. Practical work on fitting semi parametric and parametric survival models in Stata or R software.
HSTA401: Linear models
Regression: Linear regression model, point and interval estimation of parameters. Pure error and lack of fit. Residual analysis. Multiple regression: estimation and confidence intervals. General linear hypothesis. Stepwise methods. Experimental design models: one factor models. Fixed and random effects. Two factor models, with and without interaction. Qualitative and quantitative contrasts.
HSTA402: Multivariate analysis
Multivariate data, descriptive statistics, graphical techniques. Random vectors and matrices. Multivariate normal distribution. Wishart distribution. Transformation to near normality. Inferences about mean vector. Comparison of several multivariate means: one-way MANOVA. Simultaneous confidence intervals for treatment effects, profile analysis, ideas of two-way MANOVA. Principal component analysis. Factor analysis, Canonical correlation and Discriminant analyses.
HST405: Operations Research and Quality Control Techniques
OR techniques with a strong orientation towards computer based solution techniques and case studies. LP problem formulation as an illustration of alternatives and objectives. Transportation problems and algorithms, Assignment problems, Hungarian method with emphasis on formulation, structure and computer solution. Multi-objective programming making emphasis on goal programming and integer linear programming. Dynamic programming, Napsack problem, Advanced linear programming, non-linear programming algorithms, classical optimization theory, unconstrained and constrained problems with practical problems. Control charts, 𝑋̅ charts, R charts, S charts, P chart. Average run length capability analysis or indices. Reliability of system, structures of the system, parallel and series system, system life as a function, expected system life and failure rate
HSTA406: Design and design issues 2
Issues in the design of Balanced incomplete designs, crossover designs, nested designs, split plot designs, repeated measures, factorial designs, fractional factorial designs. Open and Closed Cohort, Prospective and Retrospective Cohort Studies. Threats to validity of results; Bias, Confounding. Controlling for confounding at both design and analysis stage. Missing observations. Prospective Cohort Studies. Retrospective Cohort Studies.
HSTA407 Statistical Ecology
The course covers aspects on setting up an ecological study, spatial pattern analysis, species abundance relations, community classification and community ordination. Estimation of population parameters (population size, survival, detectability). Mark recapture and related methods. Population modelling, matrix models, integral population modelling, stochastic matrix model. Combining models and data, Bayesian hierarchical modelling, models with density dependence. Behavioural statistics especially analysis of event sequences.
HMAT436 Mathematical Programming
Introduction to mathematical programming problems: Linear programming problem formulation; simplex method; Chmens and two phase techniques; sensitivity analysis; duality in LP; Dual simplex method; transportation and assignment methods; integer programming; dynamic programming; quadratics and separable programming; K T conditions for optimality.