Statistics (2009-2010)

Anno Accademico: 
Matilde Trevisani
Graham Crocker
The course provides a basic grounding in the theory and concepts of statistical reasoning, both descriptive and inferential. The first part discusses techniques for exploratory data analysis including organizing, displaying and summarizing data. This will include the formation of appropriate scientific questions. The second part presents the basics of probability theory and random variables to help in understanding the techniques of statistical inference. The fundamentals of statistical inference are then covered including the primary tools of estimation and hypothesis testing. Students are also introduced to the descriptive and inferential aspects of simple linear regression models.
Exploratory data analysis (Instructor: Matilde Trevisani) Introduction: statistics, scientific method and science; from the world of information to knowledge; descriptive statistics and inferential statistics. Data collection: variables, units and population; census and sample surveys, designed experiments and observational studies; categorical and quantitative variables. Displaying univariate distributions: frequency tables; graphical displays (histogram, stem-and-leaf display, quantile plot, pie chart, bar graph). Summarizing univariate distributions: measures of location (measures of central tendency, quantiles), spread (range, interquartile range, standard deviation) and shape (symmetry, kurtosis); boxplots; measures of homogeneity; moments. Analyzing the relationship between two variables: two-way contingency tables (joint, conditional, and marginal frequencies), and measures of association (X2, ?, odds ratio); grouped data and mean difference across groups; scatterplot, covariance and linear correlation, regression line (computation, interpretation, properties, and prediction). Elements of probability and statistical inference (Instructor: Graham Crocker) Elements of probability: Events. Probability (notes on different definitions), axioms, the multiplication and addition rules. Conditional probability, independent events. The total probability theorem, Bayes theorem. Univariate discrete and continuous random variables. Density and distribution functions. Joint, marginal and conditional probability distributions. Expected values and variance. Chebyshev’s inequality. Probability models for discrete and continuous variables: Binomial, Poisson, Geometric, Uniform (discrete and continuous), Exponential, Normal (use of tables). Moments of random variables. Introduction to transformations of random variables. Additivity of random variables and linear combinations of random variables. The Law of Large Numbers and the Central Limit Theorem. Introduction to statistical inference: Probabilistic sampling in statistical inference. Simple random sampling. Sample statistics. Sampling distribution of mean and variance of samples from normal populations. Sampling distribution of mean for large samples. Sampling distribution of a proportion. Chi-squared, Student-t and Snedecor-F probability models. Point estimation: Mean squared error. Properties of an estimator (unbiasedness, consistency, efficiency). Brief description of estimation methods: method of moments, least squares criterion, maximum likelihood. Interval estimation: Interpretation and construction of confidence intervals. Confidence intervals for the mean of a normal population with known or unknown variance. Confidence interval for a proportion. Confidence intervals for large samples. Hypothesis testing: Null and alternative hypotheses. Type I and type II errors. Levels of significance. Observed significance probability (p-value). Hypothesis tests on the mean, variance and proportion from one population. Hypothesis tests to compare the means, variances and proportions from two populations. Chi-squared goodness of fit test, Chi-squared test of independence. Estimation and hypothesis testing in simple linear regression.
Testi consigliati: 
P. Newbold, W.L. Carlson, B. Thorne, Statistics for Business and Economics, Pearson/Prentice Hall, 2007, 6th ed.David S. Moore, The Basic Practice of Statistics, 4th Edition (2006), 5th Edition (2009), W.H. Freeman PublishersFreedman, Pisani, and Purves, Statistics (3rd edition) W. W. Norton & Company, Inc.
Ultimo aggiornamento: 11-12-2013 - 16:27