The use of statistical methods to analyze data and test hypotheses.Statistical analysis is the application of mathematical methods to collect, summarize, and interpret data, allowing researchers to test hypotheses and draw conclusions from observations. In physics, it is indispensable for extracting signals from noisy measurements, such as detecting a faint particle signal in a detector or identifying patterns in cosmic microwave background radiation. It bridges the gap between raw data and physical laws, enabling scientists to quantify uncertainties and make predictions.
The foundations were laid by Carl Friedrich Gauss (method of least squares, 1809) and later formalized by Ronald Fisher in the 1920s, who introduced concepts like p-values and analysis of variance.
Statistical analysis involves choosing a model for the data, estimating parameters (e.g., mean, variance), and using probability distributions to assess how likely the observed data are under different hypotheses. Techniques like maximum likelihood estimation, Bayesian inference, and hypothesis testing (e.g., chi-squared tests) are used to determine whether a result is statistically significant or just a fluctuation. In complex systems, methods like Monte Carlo simulations help model uncertainties and compare theoretical predictions with data.
Statistical analysis is used in particle physics to confirm discoveries (e.g., the Higgs boson), in epidemiology to model disease spread, and in machine learning for data-driven predictions.
The discovery of the Higgs boson in 2012 required a statistical significance of 5 sigma, meaning the chance of a false positive was less than one in a million.
