Statistics

Information

Aim and objective

Introduction to the basic statistical methods concerning both descriptive statistics and statistical inference. Reasoning with uncertain data that is subject to random variation.

Outcome learning

• INSA reference data :
  • Obtenir une description statistique d'un ensemble de données [3P]
  • Diagnostiquer des erreurs dans des données [3P]
• CNISF reference data :
  • J10C [3P]
  • N40T [2I]

Course description

Descriptive statistics

Univariate analysis to describe the distribution of a single variable

• Central tendency (mean, median, and mode),
• Dispersion (range and quantiles of the data-set, and measures of spread such as the variance and standard deviation),
• Shape of the distribution (skewness and kurtosis),
• Graphical or tabular format (histogram and stem-and-leaf).

Bivariate analysis to describe the relationship between pairs of variables

• Cross-tabulations and contingency tables,
• Graphical representation via scatterplots,
• Quantitative measures of dependence (correlation and covariance)
• Regression analysis to reflect the relationship between variables.

Statistical inference

To make statistical propositions about populations using data provided with random sampling.

• Characterizing an estimate and the Cramer-Rao theorem
• Building an estimate (maximum likelihood and moment methods)
• Building a confidence interval
• Rejection of a hypothesis with parametric and non parametric testing methods

Prerequisites

Some backgrounds in probabilities.

Bibliography

• Probabilités, analyse des données et statistique - Gilbert Saporta, Technip, 1990
• Méthodes statistiques, Philippe Tassi, Economica, 1992.

Assessment

• Oral exam (40%) : Project presentation
• Written exam (60%) : Max (Mean (Mid exam, Final exam), Final exam)