When determining what is statistically significant, you always want to pay close attention to your variables. Find out what determines what is statistically significant with help from an applied physics professional in this free video clip.

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When determining what is statistically significant, you always want to pay close attention to your variables. Find out what determines what is statistically significant with help from an applied physics professional in this free video clip.

Part of the Video Series: Such Great Physics

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Hello, my name is Walter Unglaub, and this is "what determines what is statistically significant?" In statistics, we'll have a distribution of a given random variable. If we have multiple random variables, then our distribution will be embedded in higher dimensions. In this case, I'm examining a normal distribution, or a distribution of a bell shaped curve that is described mathematically by a Galician distribution function, and the average value is typically denoted by the Greek letter, mu, and then, we have another variable called sigma, which essentially represents the spread in our distribution. So, if I were to plot this, my Y axis would be probability, and my X axis would be the different types of events that can occur. I can bend this if I have a discrete set of data, or i can examine this function continuously. But, the point is as I go further out away from the mean, I have a greater number of sigma's. So, to the right, I would have positive sigma, positive two, positive three, so on and so forth. And, then, I would have sigma going away in the other direction. Here, I'm assuming a symmetric distribution, but a distribution naturally doesn't have to be symmetric. If it was asymmetric, it wouldn't be Galician. But, the point is we would be using sigma to characterize or quantify uncertainty in the system, enhance whether an event can be deemed statistically significant. Sigma, as a measure of uncertainty, is mathematically given as the square root of the average value of a random variable minus the average mu squared. I can manipulate this function and get the uncertainty sigma, in terms of a square of the variable, taking an average of that minus square of the average. So, it depends, of course, on what field we're discussing. In particle physics, for example, an event or a detection of a particle that must be deemed statistically significant, has to have some event or probability greater or equal to five sigma. So, the greater this sigma value, the more one can deem an event to be statistically significant. If it occurred in the area or region of the distribution, by the mean, then there's no differentiating such an event from a certain type of noise, or some random event. If it occurs beyond a certain sigma threshold, then we can deem it to be statistically significant in this probabilistic manner. Naturally, this threshold depends, again, on what field we're discussing, and it can be entirely described, or defined by the experimenter, or experimenting group. My name is Walter Unglaub, and this is "what determines what is statistically significant."