Physics, Physics Lab, Lab of Mathematical and Statistical Methodologies

Descriptive statistics.
1) Population sampling. Types of data and variables.
2) Subdivision of data into classes and creation of frequency tables. Histogram and histogram/bars.
3) Centrality indexes (mean, mode, median, midrange), dispersion indexes (range, standard deviation, variance), percentiles, quartiles. Outliers. Boxplots.
Probability and random variables.
4) Sample space, events, probability of events.
5) Probability of union and intersection of events. Complementary events. Independent events. Conditional probability. Bayes theorem. Factorial and binomial coefficients.
6) Random variables. Expected value, variance and standard deviation of discrete random variables.
7) Discrete random variables: binomial and Poisson. Continuous random variables: uniform and normal.
8) Standardization and calculations with the normal distribution. Percentiles. Normal approximation of binomial distribution.
Inferential statistics.
9) Fundamental concepts: population, sample, parameters, statistics, estimators. Sample mean behavior: large number law and central limit theorem.
10) Confidence interval: general concepts. Confidence interval for a proportion.
11) Confidence interval for the mean, both with known and unknown standard deviation. Student's distribution.
12) Hypothesis test. General concepts: null and alternative hypothesis, first and second kind errors, significativity level, power function, p-value, statistics of the test, critical region.
13) Test on the proportion. Test on the mean (both with known and unknown variance).
14) Inference on two samples. Inference on two proportions. Inference on two means, both for independent and paired samples.
Linear regression and non-parametric precedures.
15) Covariance and correlation. Simple linear regression. Test on regression coefficients and model validation.
16) Test of independence and good adaptation. Chi-square distribution.
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Reference material
Reference text:
Sheldon Ross, Probabilità e statistica per l'ingegneria e le scienze (terza edizione), Maggioli Editore (2015).

The course is delivered in the form of lectures and exercises in the classroom where it will be easy to take notes. The latter are necessary to integrate and at the same time efficiently summarize the contents of the course. So course attendance is strongly recommended. Other material is available on the Ariel website of the course.

Prerequisites and examination procedures

The student needs the basic concepts of elementary algebra and it is necessary he have attended the basic course in calculus.
To take part to the examination, you must register with the official procedures set by the Teaching Board of Biological Sciences. The student has to register, through SIFA, ONLY to the module itself. The verbalization is possible only for the overall exam; separate verbalization of individual modules are not allowed. Once different modules are passed, the student must contact the professor responsible for the Physics module and communicate to him/her, via e-mail, name, grade, date, teacher of the modules passed, in order to allow a preliminary verification.

The examination of the module Laboratory of mathematical and statistical methods consists of a written test. The exam is passed when the score obtained is at least 18/30. The written test consists of two parts: the first requires the resolution of some exercises and the second the formulation of open answers to theoretical questions.
The two parties have the same weight as regards the evaluation of the test and the final grade assigned for the aforementioned module will be unique.
The type and level of the exercises are similar to those solved during the course. The knowledges required are described in the course program and the skills necessary for the resolution of the exercises have been previously detailed.
In order to participate to the written test the student must have an identification document. During the test the following material is allowed: writing material, calculator, statistical tables (also available on the Ariel website of the course).
It is possible to consult an A4 sheet that students can prepare for their own use (also printed and written on both sides). Notes, collections of exercises or other material are not allowed.
The duration of the test is 2 hours.
The results of the exam will be communicated on the Ariel website of the course.

Recommended prerequisites:
Basic concepts of elementary algebra and calculus.

Teaching methods
The course is held through lectures mainly on the blackboard.
The student is encouraged to ask questions, to participate actively in the class discussion to improve his / her logical-analytical reasoning skills, to take a scientific and critical attitude to problems with uncertainty aspects, to use the precise technical language of the matter as well as its specific methodologies for solving statistical problems.

Language
Italian

Program information
For any information please contact the teachers of the course.



WEB site
http://ariel.unim.it