![]() ![]() Only then could they announce the discovery of “a Higgs-like particle.” What does it mean when physicists say data has a statistical significance of five sigma?Ī result that has a statistical significance of five sigma means the almost certain likelihood that a bump in the data is caused by a new phenomenon, rather than a statistical fluctuation. In the case of the Higgs boson, physicists needed enough data for the statistical significance to pass the threshold of five sigma. With more and more data, the likelihood of a statistical fluctuation at a specific point gets smaller and smaller. In the same way, this is how physicists determine if an anomaly is indeed a result. The chance of this happening as a fluke is only (1/6) 8 = 0.00006%. There isn’t a particular rule for this, but after around eight times of getting the same number, you’d be pretty certain that it was. At what point can you confirm it is weighted? You roll it twice, three times, or even more, and every time it lands on a three. ![]() There is nothing particularly significant about this – there was a one in six chance of your result – you need more data to determine if it is weighted. Except this time, you are rolling one die, but you do not know if it is weighted. At which point can this anomaly be classified as a new phenomenon? Scientists use statistics to find this out. There is an indication of a new result when there is a larger anomaly. When scientists record data from the LHC, it is natural that there are small bumps and statistical fluctuations, but these are generally close to the expected value. Second image: Animation of the results of 300 dice rolls, where the die has been manipulated to show the number 3 more often than expected. The bump in the graph corresponds to the mass of the Higgs boson. Toews) What has this got to do with physics? First image: Animation of the reconstructed mass from Higgs candidate events in two-photon decays. For data that follows a normal distribution, the probability of a data point being within one standard deviation, or one sigma (σ) of the mean value is 68%, within two σ is 95%, within three σ is even higher (Image: M. Measured by numbers of standard deviations from the mean, statistical significance is how far away a certain data point lies from its expected value. Standard deviation is represented by the Greek letter σ, or sigma. For data that follows a normal distribution, the probability of a data point being within one standard deviation of the mean value is 68%, within two is 95%, within three is even higher. It is symmetrical, its peak is called the mean and the data spread is measured using standard deviation. The normal distribution has some interesting properties. If you were to roll two dice many, many times and record your results, the shape of the graph would follow a bell-curve known as a normal distribution. Now imagine rolling two dice – the probability of getting a certain total number varies – there is only one way to roll a two, and six different ways to roll a seven. There is a one in six probability of getting one number. Scientists look for ways to reduce the impact of these errors to ensure that the claims they make are as accurate as possible. There is also potential for error if there isn’t enough data, or systematic error caused by faulty equipment or small mistakes in calculations. Background noise can cause natural fluctuations in the data resulting in statistical error. Scientists then analyse the filtered data to look for anomalies, which can indicate new physics.Īs with any experiment, there is always a chance of error. In the LHC, millions of particle collisions per second are tracked by the detectors and filtered through trigger systems to identify decays of rare particles. The probabilities of these so-called “decay channels” are predicted by theory. They work like detectives: the end products provide clues to the possible transformations that the particles underwent as they decayed. Instead, they look at the properties of the final particles, such as their charge, mass, spin and velocity. Because they almost immediately decay into further particles, it is impossible for physicists to directly “see” them. Particles produced in collisions in the Large Hadron Collider (LHC) are tiny and extremely short-lived. What does this mean? Why is it so important to talk about sigma when making a claim for a new particle discovery? And why is five sigma in particular so important? Why does particle physics rely on statistics? When a new particle physics discovery is made, you may have heard the term “sigma” being used. Candidate event displays of Higgs boson decaying into two muons as recorded by CMS (left) and ATLAS (right). ![]()
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