DISCUSSION OF STATISTICAL METHODS FOR DATA PROCESSING AND ERROR ANALYSIS.
1. Measurement errors and experimental uncertainties.
a. Inevitability of uncertainty in an experimental measure. Estimation of uncertainties: in reading the scale of a measuring instrument, in repeating a measurement. Better estimate of a size. Significant figures. Comparison of measures. Relative uncertainties. b. Propagation of experimental uncertainties. Direct measurement and indirect evaluation of physical quantities. b. Propagation of errors for measures affected by random and independent uncertainties. Propagation of maximum errors.
2. Statistical analysis of experimental data.
a. Random errors and systematic errors. Average and standard deviation. Standard deviation for a single measurement. Standard deviation of the average. b. The Gauss distribution. Histograms and distributions. Limit distributions. The normal distribution. Standard deviation and confidence limit. The average value as the best estimate of the size of a quantity. Standard deviation of the average. c. Rejection of experimental data. Criterion of Chauvenet. d. The weighted average. The problem of combining different measures for the same size. e. The least squares method. Analysis of the linear dependence of experimental data in a graph: y = A + Bx. Evaluation of the coefficients A and B of the line, and of their uncertainty. Minimum weighted squares. f. Covariance and correlation. New considerations on error propagation. The Pearson linear correlation coefficient r. g. The binomial distribution. Definition and properties. Examples. h. The Poisson distribution. Definition and properties. Examples. i. The chi2 test for a distribution. General definition of chi2. Degrees of freedom and chi2 reduced. The probability for the chi2
INTRODUCTION TO THE EXPERIMENTATION OF CLASSICAL PHYSICS: MECHANICS, THERMODYNAMICS.
Use of the relative instrumentation and measurement methodology.
A series of laboratory experiments will train the student in the use of the equipment and techniques described in the lessons, and in the elaboration of a report of what was obtained during the experiment carried out.
Study and use of statistical methods for data processing and error analysis. Competece in carrying out laboratory experiences in the field of mechanics and thermodynamics.
KNOWLEDGE AND UNDERSTANDING:
Basic knowledge of mechanics and thermodynamics. Ability to perform an experiment in basic physics (mechanics and thermodynamics) and to analyze the results.
APPLYING KNOWLEDGE AND UNDERSTANDING:
Ability in dealing with a physical problem (mechanical or thermodynamic) with the experimental approach, based on the basic knowledge provided by the course and applying the statistical methods described by the teacher
Developing the ability to analyze the results of a laboratory experiment with a critical sense.
Knowing how to describe a laboratory experience, from the experimental apparatus, to the data collection and the analysis of results by discussing the conclusions.
On the base of the activity in the laboratory, knowing how to design laboratory experiences to solve (with an experimental approach) new problems in mechanics and thermodynamics.