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A negative correlation between variables is also called inverse correlation. Negative correlation can be seen geometrically when two normalized random vectors are viewed as points on a sphere, and the correlation between them is the cosine of the circular arc of separation of the points on a great circle of the sphere. [1]
The correlation coefficient is +1 in the case of a perfect direct (increasing) linear relationship (correlation), −1 in the case of a perfect inverse (decreasing) linear relationship (anti-correlation), [5] and some value in the open interval (,) in all other cases, indicating the degree of linear dependence between the variables. As it ...
The reverse correlation technique is a data driven study method used primarily in psychological and neurophysiological research. [1] This method earned its name from its origins in neurophysiology, where cross-correlations between white noise stimuli and sparsely occurring neuronal spikes could be computed quicker when only computing it for segments preceding the spikes.
A correlation coefficient is a numerical measure of some type of linear correlation, meaning a statistical relationship between two variables. [ a ] The variables may be two columns of a given data set of observations, often called a sample , or two components of a multivariate random variable with a known distribution .
Correlation is a valuable type of scientific evidence in fields such as medicine, psychology, and sociology. Correlations must first be confirmed as real, and every possible causative relationship must then be systematically explored.
An illustration of Berkson's Paradox. The top graph represents the actual distribution, in which a positive correlation between quality of burgers and fries is observed. However, an individual who does not eat at any location where both are bad observes only the distribution on the bottom graph, which appears to show a negative correlation.
The negative correlation between fertility and intelligence (as measured by IQ) has been argued to be persistent and systematic in many parts of the modern West in particular. Early studies, however, are sometimes claimed to have been "superficial and illusory" and not clearly supported by the limited data they collected.
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.