Introduction to Statistical tests
Objectives
Know how to accurately describe data, model it, and rigorously introduce the test problem to be solved. ; Recognize the type of problem in question (parametric or non-parametric, single or multiple hypotheses). ; Understand what a test statistic, a test, and the associated concepts are. ; Know classic tests and their application frameworks. ; Know how to decide and quantify decision errors.
Course outline
Introduction to the theory of hypothesis testing: test statistics, test or decision rule, rejection zone, type 1 and type 2 error, p-value ; Mean and variance tests for one or two Gaussian populations, asymptotic approximations to generalize to the non-Gaussian case ; Goodness-of-fit and homogeneity tests (Chi-square, ANOVA) ; Independence tests (Pearson correlation, Chi-square, Wilcoxon)
Prerequisites
Integration and probability: notion of probability space and measurement, convergence in the law of random variables, density of a real random variable, vector of random variables ; Inferential statistics: maximum likelihood estimator, confidence intervals