STS COURSE SYNOPSIS

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STS  203         GENERAL STATISTICS             (2 UNITS)
Analysis and presentation of statistical data.  Measures of locations, dispersion, skewness and kurtosis, coefficient of variation.  Weighted averages and time series.  Demographic measures.  Regression and correlation.  Design of simple experiments.  Analysis of variance and covariance.  Some non-parametric tests.


STS 221          PROBABILITY I              (2 UNITS)

Definition and approaches of probability.  Statistical experiments and generation of events from set theory.  Combinatorial methods.  Simple concept soft probability.  Mutual exclusiveness, independent and conditional events and their probabilities.  Bayes theorem.  Continuous and descrete random variables.  Distribution and density functions.  Rectangular, binomial, poisson,
hypergeometric and normal distributions.  Expectations and moments of random variables.  Probability sampling from tables of random numbers.


STS  212          STATISTICAL INFERENCE I           (2 UNITS)
Sampling from populations, random NUMBERS.  Sampling distributions.  Estimation of parameters, print and interval.  Hypotheses and significance tests, testing equality of means and proportions, use of X2, t and f tests.  Analysis of variance.  Fitting of curves.

STS 242           SOCIO ECONOMIC STATISTICS         (2 UNITS)
Operations and publications of official statistical organization in Nigeria.  Designs for data collection sample, census and administrative data.  Design of questionnaires.  Index number, theoretical construction and problems.  Uses and limitations of index numbers in economic and social measurement s- prices, wages, production, cost and standard of living.  Simple time series analysis – estimation of components.  Additive and multiplicative time series models. 
Methods of moving averages.

STS 292          STATISTICAL INFERENCE LABORATORY I     (I UNIT)
This course assumes that students can write simple programmes using FORTRAN languages.  They will be expected to prepare flow charts, write programmes to compute descriptive statistics like mean, variance, correlation coefficient and estimate, simple regression line and run these programmes with data.  Further application should be based on STS 203 and 212.

STS  321      PROBABILITY II             (3 UNITS)
Review of fundamental concepts of probability.  Random variables, and calculus of expectations,  Moment and probability generating functions.  Further probability distribution and density functions: Bernoulli trials, negative binomial, geometric and multinomial distributions.  Poisson process.

STS  331      DISTRIBUTION THEORY I         (3 UNITS)
Applications of the normal distribution.  Statistical tests and procedures.  Leasts squares.  Analysis of variance and covariance.  Regression and correlation analysis.  Polynomial including orthogonal fittings.  Multiple comparisms.  Elements of non-parametric methods and sequential analysis.

STS  343  SAMPLING TECHNIQUES I            (2 UNITS)
Design of sample surveys.  Procedures and estimation of means, ratios, proportions in simple random, stratified, systematic, cluster, sub-stage and probability proportional to size sampling; sampling and non-sampling errors. Illustration with specific Nigeria sample surveys.  Regression ratio and inference estimation procedures.


STS 391     SAMPLING TECHNIQUES I LABORATORY     (1 UNT)
Introduction to the use of packages in the analysis of sample survey.  Survey analysis should include table planning, questionnaire planning, coding and data entry and other practical applications arising from STS 343.  Available packages at the computer unit or not a micro-computer will be used.  Every student in the Department of Mathematics must undergo an Industrial attachement in a place relevant to the student’s area of interest during the
long vacation of the penultimate year.  Report of the acquire experience will be typed, binded, submitted and present in form of a seminar at a time to be announced during the first semester.

STS 371        STATISTICAL QUALITY CONTROL       (3 UNTIS)
Control charts for means, standard deviations and ranges.  Control charts for numbers of defectives.  Acceptance sampling procedures: single, double and multiple sampling plans. 
Lot-by-lot sampling inspection by attributes and variables.  Continuous sampling plans.


STS 312      STATISTICAL INFERENCE II           (2 UNITS)
Basic principles – type of problems, risk function and loss function, criteria of estimation-consistency, unbiasedness, efficiency, minimum variance and sufficiency.  Method of estimation – maximum likelihood, least squares and method of moments.  Confidence intervals.  Bayesian method and estimation.  Simple and composite hypothesis.  Likelihood ratio tests, sequential tests.

STS 352      EXPERIMENTAL DESIGN I           (2 UNITS)
Basic principles of experimentation.  Randomination, replication and local control.  Randomized blocks and latin square designs.  Factorial experiments with factors at two levels.  Analysis of experimental data.  Confounding and other special problems.  Applications in experimental fields like agriculture, biology and industry.

STS  372  STATISTICAL METHODS            (3 UNITS)
Application of the normal distribution.  Statistical tests and procedures.  Leasts squares.  Analysis of variance and covariance.  Regression and correlation analysis.  Polynomial including orthogonal fittings.  Multiple comparisons.  Elements of non-parametric methods and sequential analysis.  

STS 392    STATISTICAL INFERENCE II LABORATORY     (1 UNT)
Introduction to the use of statistical packages in the analysis of practical applications arising from STS 312.

STS  421  PROBABILITY III            (3 UNITS)
Probability spaces, measures and distribution.  Distribution of random variables as measurable functions.  Product spaces: product of measurable spaces, product probabilities.  Independence and expectation of random variables.  Weak convergence, convergence almost everywhere, convergence in pth mean.  Central Limit Theorem, laws of large numbers.  Characteristic function and Laplace transforms.  Bore-Cantelli Lemmas, Zero-one-law,
Kolmogorov’s and other inequalities.

STS  443   SAMPLING TECHNIQUES II           (3 UNITS)
Regression and difference estimation procedures.  Interpenetrating scheme.  Multistage and multiphase sampling.  Cluster sampling with unequal sizes, problems of optimal allocation with more than one item.  Sources of error in surveys.  Double sampling.


STS  461  STOCHASTIC PROCESS          (3 UNITS)
Simple and general random walk with absorbing and reflecting barriers, ruin problems, fluctuations in coin tossing; classification of stages, ergodic properties; generating functions, convolutions, first passage times, recurrent events, Markov processes with finite chains, processes with independent increments; Poisson, branching, birth and death processes; Kolmogorov equations; queuing processes; types and relevant applications

STS  473    TME SERIES ANALYSIS            (3 UNITS)
Components of time series, measurement of trend, seasonal index, cyclic component and random fluctuations.  Fitting parametric models.  Regression and auto-regressive models.  Moving average and auto-regressive moving averages.  Box-Jenlins model; identification, estimation, diagnostic checking and forecasting, spectral analysis, filtering.

STS 431    DISTRIBUTION THEORY II           (3 UNITS)
Distribution of quadratic forms.  Fisher-Cochran theorem.  Multi-variate distribution and elements of multivariate analysis.  Distribution of order statistics from continuous populations.  Characteristic and moment generating  functions.  Uniqueness and inversion theorems.

STS 463     BIOMETRICS               (3 UNITS)

Peller’s theorem and its two analogues.  The Behrens distribution.  Fiducial limits in the strophanthus assay.  Dilution assays.  Adjustments for body weight. Direct assay with covariance.  Efficiency and utility of concomitant measurements.  Design and criticisms of direct assays.  Indirect assays.  The dose-response regression.  The condition for similarity.  Assay validity.  Preliminary regression investigation.  The condition of mentony, linearizing transformations.

STS  471       ECONOMETRIC THEORY           (3 UNITS)
Economic models and econometrics; the regression model and nature of the error term.  Gauss-Markoff theorem; serial correlation, heteroscedasticity and multi-collinearity; errors in variables; nonlinear regression, the specification and identification problem, methods of estimation for simultaneous equation models.

STS 465         THEORY OF GAMES             (3 UNITS)
General history of two-person zero-sum games, symmetric games, theorem of supporting hyperplans, minimax theorem, , the fundamental theorem of matrix games, the primal and dual of the game theoretic problem, matrix games and linear programmes.

STS 412       STATISTICAL INFERENCE III         (2 UNITS)
General linear hypothesis and analysis of linear models.  Further treatment of estimation and hypothesis testing extension of uniparameter results to multiparameter situation.  Basic ideas of distribution free statistics.

STS 414      ANALYSIS OF VARIANCE           (3 UNITS)

Analysis of simple, double and multiple classification of balanced data in crossed and nested arrangements.  Analysis of two-ways, three ways, contingency tables for tests of homogeneity, independence and interactions.  Analysis involving unbalance data.  Multi-variate analysis of variance.  Analysis of multifactor, multi-response of variance such as missing observation .  Non-normality heterogeneity of variance, etc.

STS  452  EXPERIMENTAL DESIGN II           (2 UNITS)
Further confounding and fractional replication.  Analysis of variance of complex nested and crossed classification.  Incomplete block design.  Properties of balanced designs.  Response surface methodology.

STS  494  STATISTICAL INFERENCE III LABORATORY     (1 UNIT)
Use and analysis of statistical data bases.  Data bases and statistical packages.  Analysis of statistical algorithms.  Applications of this course will be based on exercises on STS 412.

STS 496  EXPERIMENTAL DESIGN II LABORATORY     (I UNIT)
The use of SPSS or any other packages in the analysis of practical problems
arising from STS 452.

STS 499      PROJECT                 (6 UNITS)
Independent research work in statistics.

STS 472   SYCHROMETRIX               (3 UNITS)
The foundation of mental measurement theory, measurement in psychology and education.  The construction of true and error scores.  The classical test theory models, fixed length variable length.  Some estimates of parameters of the classical model.  Other weak true-score model, parallel measurements.  Types of reliability coefficients and their estimation.  Some test  theory of equivalent.  Item sampling in test theory and in research designs.

STS 474   NON-PARAMETIRC METHODS           (3 UNITS)
One sample case binomial, chi-square tests for randomized sign test and tests for independence series.  Two sample case medium tests, sign test, Wald-Wolfowtx test and Wilcoxon test, K samples case median test, Kruskal-Wallis H. Test.

STS 476   DECISION THEORY             (3 UNITS)
Principles used in decision making, utility functions and their properties, role of uncertainty, Baye’s strategies with prior and posterior distributions, minimax strategies, statistical inference.

STS  478  DEMOGRAPHY                (3 UNITS)
Sources of population data, vital rates and ratios, the life table, error in population, migration and distribution of population, manpower statistical interpolation and graduation in demographic analysis, construction of life tables and associate problems, techniques of population projection.

STS 482  MUTIVARIATE METHODS           (3 UNITS)
Multivariate normal distribution and related distributions.  The structure of multivariate observations, principles of component analysis, factor analysis, functional relationship, canomical analysis.  Tests of homogeneity, discriminatory analysis.

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