CORRELATE, CORRELATION - ZERO ORDER
Any variable which is correlated (the relationship between the two variables is one of correlation) with another variable. Age and sex are the two strongest correlates of crime.
Correlation is a measure of association between two variables. The variables are not designated as dependent or independent. The value of a correlation coefficient can vary from minus one to plus one. A minus one indicates a perfect negative correlation, while a plus one indicates a perfect positive correlation. A correlation of zero means there is no relationship between the two variables.
When there is a negative correlation between two variables, as the value of one variable increases, the value of the other variable decreases, and vise versa. In other words, for a negative correlation, the variables work opposite each other. When there is a positive correlation between two variables, as the value of one variable increases, the value of the other variable also increases. The variables move together.
The two most popular correlation coefficients are: Spearman's correlation coefficient rho and Pearson's product-moment correlation coefficient.
The standard error of a correlation coefficient is used to determine the confidence intervals around a true correlation of zero. If your correlation coefficient falls outside of this range, then it is significantly different than zero. The standard error can be calculated for interval or ratio-type data (i.e., only for Pearson's product-moment correlation).
The significance (probability) of the correlation
coefficient is determined from the t-statistic. The probability of the t-statistic
indicates whether the observed correlation coefficient occurred by chance if the true
correlation is zero. In other words, it asks if the correlation is significantly different
than zero. When the t-statistic is calculated for Spearman's rank-difference correlation
coefficient, there must be at least 30 cases before the t-distribution can be used to
determine the probability. If there are fewer than 30 cases, you must refer to a special
table to find the probability of the correlation coefficient.
CORRELATION - ZERO ORDER
What is the meaning of zero or near zero
correlation? It means simply that two things vary separately. That is, when the magnitudes
of one thing are high; the other's magnitudes are sometimes high, and sometimes low. It is
through such uncorrelated variation--such independence of things--that we can sharply
discriminate between phenomena.
"Two variables can have a causal relation even
in the absence of a non-zero correlation. Zero-order correlations can be spuriously small
as well as spuriously large. This outcome is especially likely in the complex causal
networks that likely underlie real-world phenomena. Hence, the three conditions for causal
inference from correlational data are misspecified. They probably reduce to two: temporal
priority and a non-zero correlation after controlling for all reasonable third
variables." Alan & Bo's Correlation & Causality Blog -
Zero-order correlation matrices are used as the starting point in the analysis of causal structure inherent to the data.
Theory of correlation - Zero-Order, Partial and Multiple Correlation
Coefficients;. Correlation Ratios; Weighted Correlations