Learning outcomes of the course unit
As regards Statistics, the course intends to introduce the basic concepts at a level which may consent simple but already significant applications both in Bio-medical and in social problems. Once the course is completed, students should possess the principal notions regarding: probability and related properties, measurement process of an aleatory quantity, treatment of a set of data and deduction of its relevant statistic significance, the most usual random variables and their characteristic distribution, use of statistic numerical tables, the sampling problem and inference of the parameters of a population, structure of a hypothesis test, several important tests (parametric and non-parametric) with applications.
Course contents summary
Probability, frequency and the ''law of large numbers''. The union of events e its probability (disjoint and non-disjoint single events). Compound events and the conditional probability (independent and non-independent single events). Bayes’s theorem.
2. Treatment of experimental data:
Arithmetic mean of a set of data. Deviations from the mean and averaged square deviation. Covariance of two data sets. Pearson’s correlation coefficient. Fitting experimental points with mathematical curves. The Least Squares method. Regression line. Best fit with parabolas, and power or exponential curves.
3. Random variables and probability distributions:
Discrete and continuous random variables. Statistical population and its representation by histograms. Probability density function. Expected value, variance and standard deviation for a population. Cumulative distribution of frequency. Median and quantiles. Standardized variable. Aspects about other important functions of r.v. (cost, cost´x, x1+x2+.., x2, x´y, x12+x22+...). Some important statistical distributions: Uniform, Triangular, Binomial, Multinomial, Poisson, Normal, Standardized-Normal, t-Student, Chi-square, and F distributions. Numerical tables of the various distributions and use of them. The central limit theorem and consequences for the sample mean.
4. Sampling and inference problem:
Random sampling. Random numbers and randomization processes. Inference from sample data of the population parameters ''mu'' and ''sigma'' and confidence intervals. Minimal dimension of a sample. The test of hypothesis and its procedure. One- and two-tailed test. Critical values and significance level. The most usual tests about ''mu'' e ''sigma'' for one sample. Test for comparing the means of two samples (non-paired and paired). Analysis of variance and test F. ''Alfa'' e ''beta'' errors and the notion of ''power'' of a test.
5. Physical measurements and errors:
A physical quantity and its measurement process. Convention about the estimated error. Repeated evaluations with different precision of the same physical variable (“weighted” mean and variance). Physical value dependent on several measured quantities and “propagation of errors”.
E.Buluggiu, Elementi di Statistica e teoria della misura, Edizioni Santa Croce, Parma (2002).
Other useful textbooks:
Peter Armitage, Statistica Medica, Feltrinelli, Milano (1989).
Glantz A. Stanton, Statistica per Discipline Bio-mediche, McGraw-Hill, Milano, 1994
Siegel Sidney, Statistica non parametrica per le scienze del comportamento, OS Ed. Firenze, 1985