The Statistics in Action course has several objectives.
1. First, we present different data analysis techniques (regressions, principal component analysis, discriminant analysis, factorial correspondence analysis), their uses and interpretations. The relationships between qualitative and quantitative data are shown and the transformation biases between these categories observed. These methods are systematically illustrated by examples taken from real life, where the preparation of data and its difficulties are widely discussed, in particular within the framework of several practical works.
2. Second, we present exact statistical estimation tests, in particular within the framework of the Gaussian model resulting from Fisher’s theorem (Student’s tests, Fisher’s tests), and asymptotic tests. The use of these tests is obviously detailed according to the various cases and approached through numerous examples. But we also show how to create a test, in cases where there is no clear solution, how to calculate confidence intervals and p -values when creating such a new test. We also address the problem of goodness-of-fit tests for discrete and continuous random variables (χ2 and Kolmogorov-Smirnov tests). We also show the limits of these tests. In any case, the problem of the interpretation of these tests is raised, in order to warn the students against hasty or even erroneous conclusions.
3. Third, we extend these tests to the comparison of two populations, both within the framework of the Gaussian model and for the asymptotic tests.
4. Finally, we also present, using numerous simulations, the risks of errors of the first and second kind, their implications in the minimum size of the data to be processed. All of these issues are dealt with numerous labworks where we use appropriate software. These simulations make it possible to verify the properties of classic tests, as well as those of the tests that we have built.
- 教师: ZHANGLiwei