Programme

Teaching program
The course aims to provide the student with the basic knowledge (cultural skills) and the statistical, mathematical and computer tools (methodological skills) needed to:
- conduct an experiment,
- process, process and synthesize experimental data,
- assess the uncertainty and confidence intervals of the experimental results,
- evaluate the statistical parameters of a population starting from a sample (inference),
- quantitatively compare data and models through hypothesis rejection tests.

Detailed plan
1. Tools of a spreadsheet (EXCEL, CALC) for the synthesis and presentation of experimental data and statistical calculation.
0. Import-export of data. Format of numbers,
a. table construction,
b. functions, functions in matrix form,
c. histograms and bar charts,
d. scatter charts.
0.
2. Statistical summary:
to. the main statistical indexes for a set of data also in aggregate form,
b. frequency distributions for a data set,
c. frequency histograms,
d. present the relationship between quantities using scatter plots,
is. evaluate the linear relationship between quantities by evaluating the correlation and / or the parameters of the linear regression.
3. Calculation of probabilities:
to. definitions of probability of an event and symbolism for calculating probabilities,
b. dependent / independent, compatible / incompatible events
c. probability of events: and, or and conditional probabilities,
d. Bayes theorem,
is. model probability distributions (binomial, uniform, Gauss).
4. Evaluation of experimental uncertainties
to. the uncertainty of experimental quantities (data, histogram frequencies, etc.)
b. uncertainties on regression line parameters,
c. uncertainty about linear correlation
d. evaluate the measurement uncertainties on derived quantities
5. Statistical inference
to. Calculate and interpret the confidence intervals for: mean values, distributions, linear correlation, linear regression parameters,
b. hypothesis rejection test (Z, T, and chi ^ 2),
c. test chi ^ 2 for contingency tables or distributions,
d. Calculate a p-value for a hypothesis test,
is. Construct and / or correctly interpret a screening test (Bayes theorem)

Prerequisiti

In order to successfully attend the course, students are expected to possess a basic mathematical background equivalent to the knowledge normally acquired in secondary education, as well as a minimum familiarity with commonly used computer tools. In particular, students should have the following preliminary competencies: * **Basic algebra and elementary linear algebra**: operations with real numbers, fractions, powers, and radicals; manipulation of algebraic expressions; solution of first- and second-degree equations and inequalities; basic concepts of vectors, matrices, and linear systems. * **Elementary functions**: knowledge of the main mathematical functions (linear, polynomial, rational, exponential, and logarithmic), their fundamental properties, and their qualitative behavior. * **Basic differential and integral calculus**: understanding of the concepts of derivative and integral; ability to apply the main differentiation and integration rules to simple functions, particularly polynomials, exponential functions, and logarithms; geometric interpretation of the derivative as a rate of change and of the integral as an area. * **Graphical representation in the Cartesian plane**: ability to plot graphs of simple functions and interpret their main features (increasing or decreasing behavior, maxima and minima, intercepts, and asymptotic behavior). * **Reading and interpretation of graphs and tables**: ability to understand and interpret Cartesian graphs, charts, histograms, and numerical tables, identifying trends, relationships between variables, and possible anomalies in the data. * **Basic numerical skills**: use of percentages, proportions, averages, and orders of magnitude; ability to perform simple approximations and quantitative evaluations. * **Basic computer skills**: even elementary familiarity with the use of a computer and common productivity software (Office suite); basic knowledge of spreadsheet applications (e.g., Excel), including data entry, the use of simple formulas, and the creation of basic charts and graphs. These prerequisites enable students to effectively follow both the theoretical and practical activities of the course, with particular emphasis on the quantitative analysis of biological data and the statistical interpretation of experimental results.

Core Documentation

M. C. WHITLOCK, D. SCHLUTER - ANALISI STATISTICA DEI DATI BIOLOGICI, ZANICHELLI.
Notes and exercises are available at the web site of the course:
https://scienze.el.uniroma3.it/course/view.php?id=2352

Reference Bibliography

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Type of delivery of the course

The course will take place with frontal lessons and practical exercises with the help of PCs and specific programs for the synthesis and analysis of experimental data. (Excel, Calc, Gnuplot) The lessons can be carried out remotely on TEAMS and MOODLE platforms.

Attendance

Attendance at the course is mandatory, in presence or at a distance. A high number of absences may preclude access to the exam. Following the authorisation of the Teaching Board, the lecturer will make streaming and recorded lectures available for those topics and procedures that are more difficult to memorise and follow (algorithms, procedures, etc.).

Type of evaluation

The practical test consists of a multiple-choice test and a test of processing and interpretation of experimental data. The data processing test can be presented in the form of a Thesis (Summer session only). The tests can be carried out in the presence and/or at a distance No in itinere tests are carried out.