Question

1. Come up with an example of a bivariate correlation. It can be the relationship between any 2 numeric variables.
2. Using your example, explain the directionality problem.
3. Come up with a third variable that could likely explain the changes in both of your variables (i.e. identify the potential third-variable problem).
4. Using your example, explain why you can’t determine causality in your (hypothetical) study.

Answer 1

ANSWER:

Consider the variables-poverty and education, where, education is determined as the number of students enrolled for college. The directionality of the correlation is negative, that is rising level of poverty over the years, was followed by decline in number of people enrolled for college.

Now, a third variable is unemployment rate. To establish causality, for the given variables, the level of education and poverty has to be related irrespective of the unemployment rate. If the third variable does not affect the bivariate relationship, it can be concluded that poverty causes low education. But satisfying this criterion requires multivariate analysis and for which partial correlation coefficient has to be computed for poverty (Y) and level of education (X), while controlling unemploment rate (Z). The more the bivariate relationship retains its strength over series of control, the stronger the evidence for direct relationship between X and Y.