This course is aimed to provide statistical, mathematical and computer competences needed to collect experimental data, synthesizing the quantitative information, compare the results and make previsions evaluating the risk of failure.
Practicals will mainly addressed to biological phenomena also concerning day-life aspects lessons (9 cfu) and practicals (3 cfu) describe:
- the principal methods for statistical synthesis: indexes, histograms, scatter plots (xy plots);
- the statistical laws that govern the experimental observations and cause the uncertainties associated with measurements and data processing.
- basic knowledge about probability and probability distribution functions, namely: binomial, poisson, uniform, gauss.
- use of “rejection tests” to understand and compare the experimental results.
- use of the bayes theorem, especially to understand the diagnostic tests.
The course will provide the following abilities
- to use statistical methods to synthesize the quantitative information in an experimental data set.
- to evaluate the uncertainty on direct and indirect measurements
- to evaluate the experimental results applying statistical tests
- to apply the bayes theorem in order to quantitatively understand the probability of a cause
Activities will use basic software (spreadsheets) for statistical data analysis
Practicals will mainly addressed to biological phenomena also concerning day-life aspects lessons (9 cfu) and practicals (3 cfu) describe:
- the principal methods for statistical synthesis: indexes, histograms, scatter plots (xy plots);
- the statistical laws that govern the experimental observations and cause the uncertainties associated with measurements and data processing.
- basic knowledge about probability and probability distribution functions, namely: binomial, poisson, uniform, gauss.
- use of “rejection tests” to understand and compare the experimental results.
- use of the bayes theorem, especially to understand the diagnostic tests.
The course will provide the following abilities
- to use statistical methods to synthesize the quantitative information in an experimental data set.
- to evaluate the uncertainty on direct and indirect measurements
- to evaluate the experimental results applying statistical tests
- to apply the bayes theorem in order to quantitatively understand the probability of a cause
Activities will use basic software (spreadsheets) for statistical data analysis
teacher profile teaching materials
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.
a. table construction,
b. functions, functions in matrix form,
c. histograms and bar charts,
d. scatter charts.
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)
Notes and exercises are available at the web site of the course:
https://sites.google.com/a/personale.uniroma3.it/meneghini-did/statistica
Programme
Teaching programThe 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.
a. table construction,
b. functions, functions in matrix form,
c. histograms and bar charts,
d. scatter charts.
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)
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://sites.google.com/a/personale.uniroma3.it/meneghini-did/statistica
Reference Bibliography
.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.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.