Engineering : Mathematics (4 ECTS)

Presentation

Description:
TU "Engineering: Mathematics" aims to provide students with theoretical and practical notions of statistical data analysis.

Objectives:
Summarize and judiciously represent a set of data. Understand the concepts of population, individuals and random samples. Understand the notion of estimation. Know the basic principles of statistical inference via hypothesis testing and confidence intervals. Apply these concepts to discrete and continuous data with one, two or more samples. Master the appropriate R commands.

Hourly volumes :

CM: 19.5 h
TD: 10.5 h
TP: 10.5 h
Field: 0 h

Prerequisites :

L3 in science or health.

Recommended prerequisites :

R.A.S

More information

Assessment of knowledge :

Continuous Integral Control (CCI)

Syllabus :

Introduction to R; different types of data; graphical representations of discrete data: bar chart, camenbert; graphical representations of continuous data: histogram, whisker diagram. Measures of central tendency and dispersion: mean, median standard deviation, interquartile range, quantiles of a data set. Graphical representation of data pairs: the scatterplot. Measures of the strength of a relationship: Pearson's and Spearman's correlation coefficients. Probability and chance, independence of events, random experiments, events; some laws of probability: Bernoulli, binomial, Poisson, uniform, normal, exponential, etc. (6 h CM + 3h TD + 1.5hTP) Populations, samples and sampling laws. The central limit theorem and its uses in estimation. Importance of unbiasedness. Basics of hypothesis testing and confidence intervals. Applications to binary data. Binom.test command (3h CM + 3h TD + 1.5hTP).

Statistical inference (hypothesis testing, confidence intervals) for continuous data. One-sample case, paired and matched samples. Student test (t.test), normality test (shapiro.test), wilcoxon test (wilcox.test). Case of two discrete samples: contingency tables, Pearson and Fisher-Yates dukhi-cdeux tests. Student and Wilcoxon tests for continuous data.

The case of multiple samples: ANOVA and Kruskal-Wallis test. The problem of multiple comparisons, Holm's method and FDR (false discovery rate) applied with 2 x 2 Student and Wilcoxon tests.

Bivariate data: scatterplot, linear, polynomial and multiple regression. Selection of the best regression model. Analysis of covariance (ANCOVA).

Contact

Manager: Gilles Ducharme
Administrative contact(s): Claudie Fabry