Bivariate+association

Bivariate association:

When two variables are associated together, this means that they vary with each other. Which means that a change to one variable in turn changes the variable associated with it. When we test for bivariate association, we test to see if we can detect "non-random" relationships. This test can be used to look for causality: cause and effect. However, causality can never be entirely proved; we can look to see the strength of relationship between the variables.

Bivariate association can be tested by asking three questions:
 * 1) Is there an association?
 * 2) How strong is the association?
 * 3) What is the pattern or direction of the association?

The table below shows the relationship between the authoritarianism of bosses (X) and efficiency of workers (Y) for 44 workplaces (from Healey, Ch 12)

Authortarianism (X)
 * Efficiency (Y) || Low || High ||  ||
 * Low || 10 || 12 || 22 ||
 * High || 17 || 5 || 22 ||
 * Total || 27 || 17 || 44 ||

This table shows the higher the authortarianism of the bosses, the lower the efficiency of the workers, and vice versa.

An association exists if the conditional distribution of one variable changes along across the values of another variable. With bivariate tables, column percentages are the //conditional distributions// of Y for each value of X. If the column percentage changes, the variables are associated.