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Statistics Undergraduate Calendar Entries

*Please note: P1 stands for Pietermaritzburg Campus, First Semester. W1 stands for Westville Campus, First Semester. P2 stands for Pietermaritzburg Campus, Second Semester. W2 stands for Westville Campus, Second Semester. PB stands for Pietermaritzburg Campus both semesters and WB stands for Westville Campus both semesters.

**Introduction to Statistics**

STAT130 PB WB (39L-36T-0P-0S-65H-13R-0F-0G-7A-13W-16C)

**Prerequisite Requirement:** Higher Grade D or Standard Grade A for Matric Mathematics or NSC Level 5 Maths.

**Aim:** To introduce a wide range of statistical techniques required for the analysis of quantitative data.

**Content:** Descriptive statistical methods. Measures of central tendency and dispersion. Permutations and

Combinations. Basic probability concepts. Discrete random variables and their properties: Bernoulli, Binomial,

Poisson, Hypergeometric. Normal distributions. Point and interval estimation. Correlation and simple linear regression.

Hypothesis tests for proportions, means and variances. Reporting on the output of appropriate statistical computing

packages.

**Assessment:** Two tests (30%); 3 h exam (70%).

**DP Requirement:** 30% Class mark, 80% attendance at tutorials.

**Credit may not be obtained for both STAT130 and STAT370.**

**Statistical Methods**

STAT140 P2 W2 (39L-36T-0P-0S-65H-13R-0F-0G-7A-13W-16C)

**Prerequisite Requirement:** 40% in MATH130.

**Prerequisite Modules:** STAT130.

**Corequisite:** MATH140.

**Aim:** To introduce the student to basic probability concepts and theory as well as nonparametric techniques.

**Content:** The axioms of probability. Conditional probability and Bayesâ€™ Theorem. Random variables, probability

density functions and distribution functions. Expectation and variance of discrete and continuous random variables.

Linear functions of a random variable. Discrete bivariate distributions. Tests of independence and homogeneity.

Nonparametric methods: sign test, Wilcoxon signed rank test, Mann-Whitney test, Kruskal Wallis test, Friedman test.

**Assessment:** Two tests (30%); 3 h exam (70%).

**DP Requirement:** 30% Class mark, 80% attendance at tutorials.

**Sampling and Nonparametric Methods**

STAT221 P1 W1 (39L-18T-18P-0S-63H-13R-0F-0G-9A-13W-16C)

**Prerequisite Requirement:** 40% in one of MATH130, 133, 134 or 195.

**Corequisite:** STAT130.

**Aim:** To equip the student with the tools to design and effectively analyze the results of a sample drawn from a finite

population. To introduce the student to nonparametric methods for survey data.

**Content:** Scope of sample surveys. Principles of questionnaire design. Estimation of sample size. Simple random

sampling. Stratified random sampling. Cluster sampling Adaptive sampling. Ratio and regression estimation.

Nonparametric techniques. Single and multiple sample data analysis techniques. Re-sampling techniques. Computerbased

exercises on the above topics.

**Assessment:** Two tests (20%), practical assignments (10%); 3 h exam (70%).

**DP Requirement:** 30% Class mark, 80% attendance at practicals and tutorials. Completion of all assignments.

**Students may not obtain credit for STAT222 and either of BMET210 or BMET222.**

**Experimental Design and Analysis**

STAT222 P2 W2 (39L-18T-18P-0S-63H-13R-0F-0G-9A-13W-16C)

**Prerequisite Requirement:** 40% in one MATH130, 133, 134 or 195.

**Prerequisite Modules:** STAT130.

**Aim: **To provide the skills necessary to analyze & summarize various types of data with an emphasis on experimental

design. Stress will be placed on statistical reasoning & applications, rather than derivation of theoretical details.

**Content:** Analysis of single, two- & multi-sample problems, including z-tests, t-tests and ANOVA. Experimental units.

Error reduction by blocking, including randomized complete blocks & Latin square designs. Use of more than one

square. Split-plot, split-split-plot and split-block designs. Factorial treatment structures. Covariance analysis. General

linear methods. Nonparametric methods. Analysis of binary or count data. Computer-based exercises.

**Assessment:** Two tests (30%); 3 h exam (70%).

**DP Requirement:** 30% Class mark, 80% attendance at tutorials.

**Students may not obtain credit for STAT222 and either of BMET210 or BMET222.**

**Probability Distributions**

STAT230 P1 W1 (39L-36T-0P-0S-65H-13R-0F-0G-7A-13W-16C)

**Prerequisite Modules:** MATH140, STAT140.

**Corequisite:** MATH212.

**Aim:** To introduce the student to univariate and bivariate distributions.

**Content:** Discrete probability distributions. Hypergeometric, Binomial, Poisson, Negative Binomial, Continuous

probability distributions. Normal, Gamma family, Beta, t-distribution, F-distribution. Transformation of random

variables. Moments and generating functions: probability-, moment- and factorial generating functions. Bivariate

distributions: marginal and conditional distributions, moments and correlation. Bivariate Normal distribution.

**Assessment:** Two tests (30%); 3 h exam (70%).

**DP Requirement:** 30% Class mark, 80% attendance at tutorials.

**Statistical Inference**

STAT240 P2 W2 (39L-36T-0P-0S-65H-13R-0F-0G-7A-13W-16C)

**Prerequisite Requirement:** 40% in MATH212.

**Prerequisite Modules:** STAT230.

**Corequisite:** MATH251.

**Aim:** To introduce the student to statistical inference.

**Content: **Sampling distributions. Point estimation: maximum likelihood, method of moments, ordinary least squares.

Properties of estimators. Interval estimation: Hypothesis testing: likelihood ratio test, best critical regions, uniformly

most powerful tests. Least squares estimation and inference for the simple linear regression model. Principles of

Bayesian estimation.

**Assessment:** Two tests (30%); 3 h exam (70%).

**DP Requirement:** 30% Class mark, 80% attendance at tutorials.

**Linear Models**

STAT301 P1 W1 (39L-36T-0P-0S-65H-13R-0F-0G-7A-13W-16C)

**Prerequisite Modules:** MATH212 and 251, (STAT240 or BMET314).

**Aim:** To introduce the student to the theory and application of the general linear model.

**Content:** Topics from linear algebra. The Gauss-Markov Theorem. The general linear model of full rank and less than

full rank. Regression analysis. Analysis of variance and covariance.

Assessment: Two tests (30%); 3 h exam (70%).

**DP Requirement:** 30% Class mark, 80% attendance at tutorials.

**Biostatistics Methods**

STAT305 P2 W2 (39L-36T-0P-0S-65H-13R-0F-0G-7A-13W-16C)

**Prerequisite Modules:** STAT230 and (STAT301 or BMET314).

**Aim:** To provide the student with a thorough understanding of biostatistics and to expose the student to a range of

practical problems in that area.

**Content:** Introduction to epidemiology including the standardization of mortality rates, morbidity studies and clustering

of diseases. Clinical trials. Cohort studies. Survival analysis.

**Practicals:** Computer-based exercises on the above topics.

**Assessment:** Two tests (20%), practicals (10%); 3 h exam (70%).

**DP Requirement:** 30% Class mark, 80% attendance at practicals.

**Applied Statistics**

STAT330 P2 W2 (39L-36T-0P-0S-65H-13R-0F-0G-7A-13W-16C)

**Prerequisite Modules:** STAT301.

**Aim:** To provide the student with practical applications of statistical topics.

**Content:** Applied regression analysis. Analysis of variance and experimental design. Quality control. Acceptance

sampling. Nonparametric methods.

**Assessment:** Two tests (30%); 3 h exam (70%).

**DP Requirement:** 30% Class mark, 80% attendance at tutorials.

**Random Processes**

STAT350 P2 W2 (39L-36T-0P-0S-65H-13R-0F-0G-7A-13W-16C)

**Prerequisite Modules:** STAT360.

**Aim: **To introduce the student to the theory and applications of stochastic models.

**Content:** Broad classification of stochastic processes. Markov chains. Birth and death processes. Queueing theory.

The Poisson process. Conditional expectations and martingales. Branching processes. Renewal theory. Time series.

Loss distributions and risk models.

**Assessment: **Two tests (30%); 3 h exam (70%).

**DP Requirement:** 30% Class mark, 80% attendance at tutorials.

**Applied Probability Theory**

STAT360 P1 W1 (39L-36T-0P-0S-65H-13R-0F-0G-7A-13W-16C)

**Prerequisite Requirement:** 40% in MATH212 and 251.

**Prerequisite Modules:** STAT240.

**Aim:** To expose the student to a range of applications of probability theory and to provide the student with the

necessary techniques for recognizing and solving problems in probability.

**Content:** Combinatorial analysis. Union of events. Conditional probability. Random walks. Generating functions.

Markov chains. Exponential distribution and Poisson process.

**Assessment:** Tests (30%); 3 h exam (70%).

**DP Requirement:** 30% Class mark, 80% attendance at tutorials.

**Engineering Statistics**

STAT370 H1 (18L-13T-5P-0S-33H-5R-0F-0G-6A-13W-8C)

**Prerequisite Requirement:** DP in MATH248.

**Aim:** To introduce engineering students to elementary probability theory and statistical methods.

**Content:** Elementary probability, standard distributions, bivariate distributions. Estimation of parameters and testing of

hypotheses. Regression analysis.

**Assessment:** Tests (30%); 2 h exam (70%).

**DP Requirement:** 30% Class mark, 80% attendance at tutorials.

**Offered only at Howard College to Engineering students. Credit may not be obtained for both STAT370 and
STAT130.**

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