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What is the difference between correlation and dependence, and how can the latter be empirically measured from a sample?
Both terms are used in multiple senses. In statistics, “dependence” is usually taken to be the opposite of independence, meaning that knowing something about one variable tells you something about the other. “Correlation” is usually taken as a specific measure of dependence that goes from -1 to +1, and the most common measure is the Pearson product-moment correlation.Because dependence is a general term there is no general measure of it. You can define specific measures of dependence, and people do for specialized purposes, but there are no common ones.If two variables are correlated according to any correlation measure, then they are dependent; but variables can be dependent and still have zero correlation.Just to be confusing, there is an entirely different use of the term “dependent” in statistics, it just means a variable you are trying to predict.
Is there any difference between correlation and correlation coefficient?
correlation tells you that you are naughty or funny in your friends group, and its coefficient tells that how much more naughty or funny are u in friends group if compared to best funny friend.This is the definition to understand now lets move to literature part as cited by wikipedia.In statistics, dependence is any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence. Familiar examples of dependent phenomena include the correlation between the physical statures of parents and their offspring, and the correlation between the demand for a product and its price.mathematically it is given byA correlation coefficient is a coefficient that illustrates a quantitative measure of some type of correlation and dependence, meaning statistical relationships between two or more random variables or observed data values.
What kind of statistical data and tests tend to be used to affirm the discovery of a particle in experimental particle physics?
Each experiment at the LHC roughly records 200 events per second, so there are roughly 2 billion events on tape each year (which is just 1/100,000 of the total number events that occurred).Now only a small fraction of these events are possible Higgs candidate events (about 10,000 or so). Depending on the channel, the signal to background can be large or small (bigger than 1 or as small as 1/100 or even smaller for invisible channels that are currently being ignored).Each experiment uses fairly standard techniques to make statistical inferences for each search (CMS presented 60+ searches at the discovery meeting that were in 5 channels that got combined down to the final result).Here is a recent talk by Kyle Cranmer on the statistical tests used at ATLAS to set a limit on the Higgs boson.http://www-conf.slac.stanford.edu/statisticalissues2012/talks%5Ckyle_cranmer_SLAC_Intro_particles.pdf.Here is the final formula for the measurement of the Higgs mass from the initial input quantities:The little top node is the Higgs mass that comes out, all the lower things are inputs, and the nodes are various combinations take into account correlated systematic effects. (or something like this)
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