1 sigma 2 sigma 3 sigma 6 sigma12/13/2023 ![]() ![]() ![]() Where is the variable, is the mean of the distribution, and is the standard deviation of the distribution. The mathematical formula for the normal distribution is given by something called the Gaussian function (and so another name for a normal distribution is a “Gaussian distribution”) and has the form In this plot, the x-axis represents the variable being measured, the y-axis is the frequency with which that variable occurs. The normal distribution looks like a “bell curve”. The curve is often referred to as a bell curve for obvious reasons. Normal distributions are usually normalised so that the total probability (the area under the curve) is unity (1), as the sum of all probabilities is always equal to one. This distribution looks like the following, where on the x-axis we have some variable (such as the the background noise in a signal), and the y-axis represents the frequency with which that variable occurs. If you have a large number of independent measurements, then their distribution will tend towards something called the normal distribution. Read more about it by following this link. My book “The Cosmic Microwave Background – how it changed our understanding of the Universe” is published by Springer. You can read more about the BICEP2 result, and how its conclusions were withdrawn, in my book “The Cosmic Microwave Background – How it Changed Our Understanding of the Universe”. In order to fully understand why scientists quote results to a particular, and what it means in detail, the first step is to understand something called the normal distribution. What does a phrase like “with significance” actually mean? It is the significance with which scientists believe a result to be real as opposed to a random fluctuation in the background signal (the noise). In the abstract to their paper, the BICEP2 team sayĬross correlating BICEP2 against 100 GHz maps from the BICEP1 experiment, the excess signal is confirmed with significance and its spectral index is found to be consistent with that of the CMB, disfavoring dust at. ![]() As Peter Coles’ blog mentions, their paper has now been published in Physical Review Letters. A few days ago, I blogged about the controversy over the BICEP2 result, and the possibility that their measured signal may actually be dominated by contamination from foreground Galactic dust. ![]()
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