Search results
Results from the WOW.Com Content Network
Also confidence coefficient. A number indicating the probability that the confidence interval (range) captures the true population mean. For example, a confidence interval with a 95% confidence level has a 95% chance of capturing the population mean. Technically, this means that, if the experiment were repeated many times, 95% of the CIs computed at this level would contain the true population ...
Exchangeable sequences have some basic covariance and correlation properties which mean that they are generally positively correlated. For infinite sequences of exchangeable random variables, the covariance between the random variables is equal to the variance of the mean of the underlying distribution function. [10]
If two variables are uncorrelated, there is no linear relationship between them. Uncorrelated random variables have a Pearson correlation coefficient, when it exists, of zero, except in the trivial case when either variable has zero variance (is a constant). In this case the correlation is undefined.
The two variables are said to be correlated; however, they may or may not be the cause of one another. The correlation phenomena could be caused by a third, previously unconsidered phenomenon, called a lurking variable or confounding variable .
For example, in an exchangeable correlation matrix, all pairs of variables are modeled as having the same correlation, so all non-diagonal elements of the matrix are equal to each other. On the other hand, an autoregressive matrix is often used when variables represent a time series, since correlations are likely to be greater when measurements ...
In this case, the relationship between and is non-linear, while correlation and covariance are measures of linear dependence between two random variables. This example shows that if two random variables are uncorrelated, that does not in general imply that they are independent.
In particular, it is possible to have serial dependence but no (linear) correlation. In some fields however, the two terms are used as synonyms. A time series of a random variable has serial dependence if the value at some time in the series is statistically dependent on the value at another time . A series is serially independent if there is ...
In other words, the two variables are not independent. If there is no contingency, it is said that the two variables are independent. The example above is the simplest kind of contingency table, a table in which each variable has only two levels; this is called a 2 × 2 contingency table. In principle, any number of rows and columns may be used ...