Introduction to Statistics

Introduction to critical thinking and handling of data. Students will conduct experiments, collect and describe data. Data analysis and valid inference. Types of variables and measurement scales. Frequency tables and graphs. Measures of central tendency. Techniques of sampling, time series, probability, random variables, statistical inference. Analysis of variance. Regression and correlation. Non-parametric methods. Experimental design, hypotheses. Variance analysis.

Students will do projects related to their field of study.

Note: Course may be adapted for particular groups to reflect needs of their fields of study.

Statistical Methods

Applications of various types of distributions. Statistical inference. Parameter estimation and test of hypotheses. Errors. Significance and p-values. Variances, power curves. Analysis of linear regression. Regression coefficients, correlation. Outliers. Analysis of data. Bartlett Test, Chi-square. Fisher's test. Non-parametric methods. Sign test. Wilcoxon rank test, Mann Whitney U test. Tests of fit, randomness. Kruskal-Wallis Test, Friedman test.

Probability and Probability Distributions

Probability as a set function. Baye's theorem. Random variables, distributions. Stochastic independence. Expectations. Moments and distributions. Probability distributions: Hypergeometric, binomial, geometric, Poisson, uniform, exponential, gamma, beta, Laplace, normal, Cauchy, Weibull, Pareto, Rayleigh. Random variables, Chi square, t and F. Chebyshev's inequality. Order statistics, sample range.

Sampling and Survey Methods

Methods, requirements of sampling. Planning census and sample surveys. Selection and estimation. Estimation of variances, standard errors and confidence limit. Stratified random sampling. Ratio and regression estimates. Cluster sampling. Subsampling, PPS sampling, Double sampling, Multistage and Multiphase sampling. Study of sample Pastian surveys:

Econometrics and Regression Analysis

Data Processing and Statistical Computing: Introduction to hardware and software. Computer programming. Languages: Visual, Basic, Fortran, C++ and Java. Use of some statistical packages such as SPSS, MINITAB, MSTAT-C, GENSTAT, SAS, BMDP, GLIM, STATGRAPHIC

Multivariate Analysis

Matrix algebra, meaning of multivariate analysis. Distributions. Estimation of mean vector and covariance matrix. Sample mean vector and covariance matrix. MANOVA. Factor, Discriminant, Canonical and Cluster analysis. Multidimensional scaling.

Population Studies

Demographic data, census. Housing and demographic surveys. Population growth, composition and vital events. Testing accuracy. Errors. Demographic measures: fertility, mortality measures rates. Estimation from incomplete data. Life tables. Stationary population model. Population estimates and projections. Models and theories. Malthusian and post Malthusian theories. Consequences of world population growth and explosion. State of population demographics in Pakistan.

Statistical Quality Control and Reliability

Concept of control and total quality management (TQM). Statistical process. Shewhart charts. CUSUM and moving average control charts. Process capability analysis, experiments, improvements. Acceptance sampling plans. ISO 9000 and ISO 14000 series. Reliability structures. Lifetime distributions, hazard rates, fatigue rate models. Testing reliability hypothesis. Failure models. New-better-than used models. Accelerated life testing.

Time Series Analysis and Forecasting

Concepts and importance of good forecasts. Classifications and frameworks. Regression and exponential methods. Stochastic and Econometric time series models. Spectral analysis, feed forward/feed backward control schemes.

Statistical Inference

Estimation of parameters. Estimator properties. Cramer-Rao inequality, Rao Blackwell and Lehman-Scheffe theorems. Estimation methods. Tests of hypotheses: simple and composite, Neyman-Pearson Lemma, power functions. Randomized tests. Likelihood ratio tests and asymptotic properties. Interval estimation, and confidence intervals. Baytes' interval estimation. Sequential Tests. SPRT, ASN and OC functions.

Design and Analysis of Experiments

Design principles of experiments. Cochran's theorem. Violation of assumptions and transformations. Randomized, block, Latin square and crossover designs. Efficiency of designs. Mean squares and expectations. Factorial experiments. Confounding complete and partial. Split plot, split bock and nested design. Incomplete block designs. Response surface methods first and second order. Analysis of covariance in CR, \RCB and LS designs. Estimation of missing values by analysis of covariance.

Decision Theory

Nature and concept of loss functions, parameters, decisions and sample spaces. Risk and average loss. Admissibility. Mini-max principle. A prior distributions. Baye's decision procedures. Posterior analysis. Sufficiency in decision making. Randomization. Optimum sample size.

Statistics and Information Technology

Statistics and data bases. Problems of obtaining, collection and production. Errors in statistical indicators. Common social indicators. Modes of dissemination of statistical information, print and electronic media. Computers in dissemination. Modern Information transfer. Internet, intranet, Email, websites. IT in daily life. Computer graphics and interactive learning of statistical concepts.

Additional Statistics courses are presented in various departments, and introductory concepts are included in core Research Methods and Information Technology course.