Practical statistics excerpts from 2023 European School of High Energy Physics

Abstract

These lecture notes provide an overview of fundamental statistical concepts used in high-energy physics research. The discussion begins with the philosophy of statistics, emphasizing its role in analyzing experimental data, correcting biases, and ensuring precision. Key estimators such as mean, standard deviation, skewness, and kurtosis, which help summarize datasets, are introduced. Various probability density functions (PDFs), including Binomial, Poisson, and Gaussian distributions, are explored to demonstrate their relevance in data modeling. Methods for analyzing data, such as maximum likelihood estimation and ChiSquare tests, are presented, offering techniques for extracting meaningful insights from observations. The notes also cover hypothesis testing, explaining concepts like false positive rates, p-values, and significance levels for evaluating scientific claims. Practical applications include setting observational limits and improving statistical methodology. By applying these techniques, researchers can ensure rigorous data analysis, enabling reliable conclusions and impactful discoveries in physics.