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RCDS - Further hypothesis testing

Dr. Jesús Urtasun Elizari

Imperial College London - 2024 / 2025

Find the content of the course in GitHub:

https://github.com/ImperialCollegeLondon/rcds_further_hypothesis_testing

This course provides an intermediate level approach to the field of probability and statistical inference. Building on top of the introductiory course rcds_introduction_sampling_hypothesis_testing, the topics covered here will include deeper exploration of hypothesis testing, linear models, and briefly introduce bayesian statistics. The aim of the course is to provide strong foundations at the mathematical and theoretical level, while providing practical exercises to work on real data.

The course is organized in four chapters, covering the topics listed below. All will be followed by a practical session and hands-on coding, both in Python and R. No prior experience on statistics or programming is required for the attendance of this course.

Roadmap of the course

Chapter 1. Parameter estimation & hypothesis testing

  • Parameter estimation. Recap hypothesis testing.
  • Comparing mean values. The t-test.
  • Comparing variances. The F-test.

Chapter 2. Normality & comparing multiple groups

  • The χ2-test for comparing distributions.
  • The χ2-test for testing normality.
  • Comparing more than two groups. ANOVA.

Chapter 3. Multiple hypothesis correction

  • Significance revisited. Interpretation of p-values.
  • Error types in hypothess testing.
  • Adjusted p-values. Bonferroni and BH coffection.

Chapter 4. Introduction to bayesian statstics

  • Bayesian probability. The Bayes' theorem.
  • Prior, likelihood, posterior. Probability as a degree of belief.
  • Bayesian inference and statistics. Posterior distribution and Bayes factor.

Setup

We will be working with Visual Studio Code / RStudio as main editors. Although recommended, they do not need to be installed in your local computers, since we will use Codespaces provided by Github, which already implement an interface ready to program an execute the code. Notebook versions are also useful, such as Jupyter notebooks (for the Python version), or Rmd files (for the R version). If you want to use notebooks for the practical sessions, we recommend install Anaconda from https://www.anaconda.com in advance of the workshop.

Getting Started

  1. Download this repository to your computer as a ZIP file and unpack it.

  2. Open the terminal and navigate to the unpacked directory to work with the .py / .R examples.

  3. Open a Codespace where we will be using either Visual Studio Code / RStudio fro the practical sessions.

  4. Alternatively, you can run the notebooks online using Binder: Binder

Evaluation

Your feedback is very important to the Graduate School as we are continually trying to improve the training we offer. At the end of the course, please help us by completing the evaluation form at http://bit.ly/rcds2021


Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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RCDS Statistics 2 - Advanced statistics & further hypothesis testing

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