Sociology Index

# CORRELATION ZERO ORDER AND ZERO ORDER CORRELATION

Correlation is a measure of association between two variables and zero order correlation indicates there is no relationship between the two variables. Age and sex are the two strongest correlates of crime. A correlation of zero order means the same that there is no relationship between the two variables. The variables are not designated as dependent variable or independent variable.

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. 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. 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.

Criminologists from an empiricist perspective tend to look at the social world in terms of variables. Everyone in your class is a student so that is a constant, however, there is a great deal of variation by factors like sex, age, income, program, GPA, religion, ethnic heritage. If one gathers information from the whole class on these variables we might begin to see that some variables vary in patterned ways. People with a particular ethnic heritage may tend to be more religious than those from other heritages. This would suggest a correlation; as one variable varies, so does the other. If there were more students of that particular ethnic heritage in the class then religiosity for the group would also increase. As one goes up, so does the other. This is referred to as a positive correlation. If one variable goes up and the other down, this is called a negative relationship. As age goes up, the crime rate goes down, is a negative correlation. A correlation does not mean that one variable causes the other.

CORRELATION ZERO ORDER
A correlation between two variables which does not include a control variable. A first-order correlation, then, would include one control variable as well as the independent variable and dependent variable.

What is the meaning of correlation of zero order 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 that we can sharply discriminate between phenomena.
I should point out that there are two ways of viewing independent variation. One is that the more distinct and unrelated the covariation, the greater the independence. Then, a zero correlation represents complete independence and -1.00 or 1.00 indicates complete dependence. Independence viewed in this way is called statistical independence. Two variables are then statistically independent if their correlation is zero.

"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. The example I use in class is the equation I've been developing over the years to predict the greatness assessments of US presidents. It turns out that one of the best predictors in a 6-variable multiple regression equation is whether or not a president was assassinated while in office. Yet assassination does not have a significant zero-order correlation.

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.