Engineering: Mathematics (4 ECTS)

Overview

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

Objectives:
Be able to summarize and appropriately represent a dataset. Understand the concepts of population, individuals, and randomly selected samples. Understand the concept of estimation. Be familiar with the basic principles of statistical inference through hypothesis testing and confidence intervals. Be able to apply these concepts to discrete and continuous data with one, two, or multiple samples. Master the relevant R commands.

Hourly volumes:

Lectures: 19.5 hours
Tutorials: 10.5 hours
Lab Sessions: 10.5 hours
Fieldwork: 0 hours

Required prerequisites:

A bachelor's degree in science or health sciences.

Recommended prerequisites:

All is well

More information

Knowledge Assessment:

Continuous Integral Control (CCI)

Course Outline:

Introduction to R; different types of data; graphical representations of discrete data: bar charts, Camembert charts; graphical representations of continuous data: histograms, box-and-whisker plots. Measures of central tendency and dispersion: mean, median, standard deviation, interquartile range, and quantiles of a dataset. 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 probability distributions: Bernoulli, binomial, Poisson, uniform, normal, exponential… (6 hours of lectures + 3 hours of tutorials + 1.5 hours of lab work) Populations, samples, and sampling distributions. The central limit theorem and its applications in estimation. Importance of unbiased estimation. Basic concepts of hypothesis testing and confidence intervals. Applications to binary data. The `binom.test` command in R (3 hours of lectures + 3 hours of tutorials + 1.5 hours of lab).

Statistical inference (hypothesis testing, confidence intervals) for continuous data. Single-sample, paired, and matched-sample cases. Student’s t-test (t.test), normality test (shapiro.test), Wilcoxon test (wilcox.test). Cases involving two discrete samples: contingency tables, Pearson’s chi-square test, and Fisher-Yates’ chi-square test. Student’s t-test and Wilcoxon test for continuous data.

The case of multiple samples: ANOVA and the Kruskal-Wallis test. The problem of multiple comparisons; the Holm method and FDR (false discovery rate) applied to 2×2 Student’s and Wilcoxon tests.

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

Contacts

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