Università Roma Tre

Experimentation in Physics 1
Physical quantities. Intensive and Extensive physical quantities. Direct and indirect measurements. Base and Derivatives quantities .
Unit of measure. Systems of measurements units. The International System and the cgs systems. Changing units of measure.
Physical dimensions and dimensional analysis.

Measurement Instruments. Analog and Digital Instruments. Counters. Measurement instruments features:
Linearity, Sensitivity and Accuracy. Uncertainty in measurements. Errors and uncertainties. Causes of uncertainty.
Type A and Type B uncertainties. Random errors and systematic effect.

Presentation and graphic analysis of data. Charts for Data Representation and Analysis. Linear, semi-logarithmic, double-logarithmic graphs.
Methods of linearization of mathematical relations. Histograms.

Probability. Definitions of probability: Classical, Frequentist and subjective. Probability of the Sum of Events. Probability of the Product of Events.
Conditional Probability. Bayes Theorem. Probability distributions. Discrete and continuous distributions. Cumulative probability distribution.
Binomial and Poisson distribution. Continuous distributions. Probability density distribution. Definition of expected value.
Moments of distributions. Central moments of distributions. Mean value and Variance. Skewness and Kurtosis.
Average value and variance of Binomial, Poisson, Uniform, Gaussian, Exponential, t-Student and Cauchy distributions. Multivariate Distributions.

Statistical tools.
Tchebicheff's Inequality. The Law of the Great Numbers. The central limit theorem. Sample average and sample variance.
Estimation of the mean sample value and formula for estimating sampling variance.

Uncertainty in indirect measurements. Propagation of uncertainties. Independent variables.
Propagation of uncertainties in the case of monomous formulas. Related random variables. Definition of correlation coefficient.
Composition of type A and type B uncertainties.

Estimation of parameters. Least square method. Maximum Likelihood method. High likelihood stimuli.
Examples of applications of Least square and Maximum Likelihood methods.
The concept of confidence interval and level.


Chi square test. Chi square test for functional relations. Pearson square square test for histograms.

Experiments: Measurements of Lengths. Measurement of Density. Verification of Boyle-Mariotte law.
direct method. Experiment for the determination of the spring constant.
The pendulum. Measurement of gravitational acceleration with a reversible pendulum.

C. Bini - Lezioni di Statistica per la Fisica Sperimentale - Edizioni Nuova Cultura. Roma 2011