Università Roma Tre

The theoretical lessons will focus on the following topics:

Tools and measures. Measurement units - Trigonometry angles and definitions - Sizes and errors - Systematic error and random error - Instrument error - Standard deviation and standard error - Error propagation - Representing data: significant figures, comparison of measurements, tables and graphs, histograms

Descriptive statistics. Indices of central tendency: average, median and mode - Percentiles - Indices of variability: variance and standard deviation - Limit distributions

Correlation between variables. Linear regression, least squares method - Linearization of a function - Verification of the acceptability of a fit: Chi square test and determination coefficient - Pearson r coefficient, Spearman correlation coefficient for ranks

Probability. Definition and fundamental properties - Probability distributions (binomial, Poisson and uniform distribution - Gaussian and error integral, justification of sum in quadrature and standard deviation of the mean, standard normal distribution) - Average and variance of a random variable - Confidence intervals - Standard deviation as acceptability percentage - Applications and verifications: correlation index and chi-square test - Student's t test for comparison between measurements

Inferential statistics. Hypothesis test and significance - The null hypothesis and the alternative hypothesis - Types of studies and sampling - Sample distributions - Criterion of significance and critical values - Errors and decisions of a statistical test - Sign test - Chi square test as test of significance - z-test and t-test - Distribution F - Analysis of variance (ANOVA) with one and two ways

The topics of the laboratory exercises will be chosen from the following list

1) Use of precision instruments (decimal and twentieth caliber, spherometer) for the measurement of quantities. Statistical treatment of the error.
2) Verification of the law of light reflection from a plane mirror.
3) Verification of the law of refraction in a plexiglass plate.
4) Verification of Kepler's law on the reduction of light intensity as a function of distance.
5) Verification of the Lambert-Beer law on the attenuation of luminous intensity on passing through an opaque medium.
6) Determination of the focal distance and dioptric power of a thin lens through an optical measurement.
7) Determination of the focal distance and dioptric power of a lens system with the Bessel method.
8) Determination of the focal distance and dioptric power of an ophthalmic lens by measuring with a spherometer and with a dioptrometer and characterization of an astigmatic lens
9) Verification of Gullstrand's law and search for the main planes of an optical system consisting of two thin lenses.
10) Dispersion of light through a prism: verification of Cauchy's law and determination of the number of Abbe
11) Estimate of the magnification of an optical system: the magnifying lens
12) Use of Student's t test to compare experimental data and the chi-square test to assess how well a theoretical trend reproduces the behavior of experimental data; construction of a histogram and its limit function.

- Lecture notes distributed by the teacher during the course

- D. Halliday, R. Resnick, S. Walker, Fondamenti di Fisica (Casa Editrice Ambrosiana, 2015)

- R. Meyer-Arendt, Introduction to classical and modern optics (Prentice Hall, 1995)

- R. Taylor, Introduzione all’analisi dell’errore (Zanichelli, 2010)

- M. Bland, Statistica medica (Maggioli Editore, 2014)

- M. M. Triola e M. F. Triola, Fondamenti di Statistica (Pearson, 2013)

- J. Welkowitz, B. Cohen e R. Ewen, Statistica per le scienze del comportamento (Apogeo)

- S. A. Glantz, Statistica per Discipline Biomediche (McGraw-Hill, 2007)