A measure of how likely a result is not due to chance, here quantified by a low error probability.Statistical significance is a concept from statistics that indicates how likely an observed effect or difference is real rather than a result of random chance. In physics, it is often quantified by a p-value or by a 'sigma' level — for example, a 5-sigma result means there is less than a 1-in-3.5-million chance the observation is a statistical fluke. This measure is crucial for distinguishing genuine discoveries from noise in experimental data.
The concept was formalized by Ronald Fisher in the 1920s, who introduced the p-value and the 0.05 threshold. Later, in the 1930s, Jerzy Neyman and Egon Pearson developed the framework of hypothesis testing that underpins modern significance analysis.
When physicists collect data, they compare their observations to a null hypothesis — typically that no effect exists. Statistical significance quantifies the probability of obtaining data at least as extreme as what was observed, assuming the null hypothesis is true. If this probability is very low, the result is deemed significant and the null hypothesis is rejected. The threshold for claiming a discovery in particle physics is usually 5 sigma, while softer fields may accept 2 sigma as suggestive.
Statistical significance is used in particle physics to confirm the existence of new particles (like the Higgs boson), in medical trials to validate drug efficacy, and in astronomy to verify detections of exoplanets.
The 5-sigma standard for particle physics discoveries was chosen so that the chance of a false positive is about the same as flipping a fair coin 22 times and getting heads every time.