The Meaning Behind the Measures of Association

The strength of an association is expressed in numbers between -1 and +1.
And the minus sign makes a difference, tells us that the direction of the data is negative, that there’s a negative association between the variables. More of one variable indicates less of another.

The Pearson r is the statistic we use for interval and ratio data, so you will see it in much of the literature you read.

The r, a measure between -1 and 1, shows the direction the variables are taking when they present together in a sample, and the correlation. The r predicts, too, meaning once you know the r, if you know the value of one variable, you can figure out the value of another.



Any association close to -1 or +1 is a strong association. So a negative correlation, like a -.95 is a strong correlation, stronger than a positive correlation of only .13.

95% of the variance is associated with the two variables, as opposed to thirteen percent. _.95 tells us that when you see one of the variables, you'll probably find the other variable. The direction doesn't matter, they're still strongly associated.

Whereas an r of .13 means that if you find one variable, there's only a thirteen percent probability that you'll find the other.

To find out what portion of variation is explained by another variable, you square the correlation. So a Pearson r of .80, a strong relationship between variables, when squared, indicates to us that .64 or 64 percent of the variation is explained by that relationship.

Something else, some other variables are explaining the rest of the variation.

Now you're into multivariate data analysis. Adding a third variable, we can partial out which variables affected the others by taking them two at a time. The computations are complex, but ultimately give us information about how much each variable contributed to the results of our statistical enterprises.

We ask our computers to spit out what are called correlation matrices. Below is a correlation matrix. The study in question looked for reasons parents had for visiting their foster children. Very low correlations between the reasons on the left and the amount of parent contact indicate that those variables didn't contribute very much to a parent's reasons for visiting.

In this table only three of the reasons on the left showed any contribution at all, Years in Care r = .256
Reason placed (child's behavior) r = .265,
and the parent's discharge objective, (wanting to take the child home), r = .387.

The little note under the table about dichotomous variables tells us that these were nominal variables "dummy" coded with 0's and 1's.

It is the magnitude, not the significance that matters to us in regression, one way to analyze multivariate data. Regression helps us parse out the contributions of independent variables to the dependent variable(s).



The "beta" is called a beta weight, a standard partial regression coefficient, sometimes called a standardized regression coefficient.

The b weights are standardized (this discussion isn't finished)