The idea of correlation
In analysing the scatterplot we look for a pattern in the way the points lie. Certain patterns tell us that certain relationships exist between the two variables. This is referred to as a correlation.
Bob and Jim work for the same company. Bob drives a Porsche, costing $200000, and Jim drives an Austin Allegro, costing $9000. Which man has the greater salary?
In this case, we can reasonably assume that it must be Bob who earns more, as he drives the more expensive car. As he earns a larger salary, the chances are that he can afford a more expensive car. We can’t be absolutely certain, of course. It could be that Bob’s Porsche was a gift from a friend, or part of the divorce settlement from his wife – or he could have stolen it! However, most of the time, an expensive car means a larger salary.
So we say that there is a correlation between someone’s salary and the cost of the car that he/she drives. This means that as one figure change, we can expect the other to change in a fairly regular way.
The q-correlation coefficient is a measure of the strength of the association between two variables. The calculation of the q-correlation coefficient aids us considerably in making that judgment.
To calculate the q-correlation coefficient:
The value of the q-correlation coefficient in the above example indicates a strong correlation. The diagram below gives a rough guide to the strength of the correlation suggested by the value of q.
a. Calculate the q-correlation coefficient for your scatter plot of height vs arm span.
b. Write down what type of relationship exists between the pair of variables and comment on this relationship.