Correlation

Correlation indicates the relationship between two variables. If you ask such questions as:

• Is there a relationship between writing ability and grammar competence?
• Is there a relationship between reading ability and vocabulary size?

...actually you want to know whether the two variables (writing ability & grammar competence, reading ability & vocabulary size) are correlated. You could get the answers to these questions by drawing a scattergram or computing the correlation coefficient.

Scattergram

A scattergram is a graph which shows the relationship between two variables. If you have two sets of data in the form of scores and plot them in the graph, it will look like the following:


The dots form an oval which leans to the right. It means there's a positive, high relationship between the two variables. If, however, the dots form an oval which leans to the left, there's a negative, high relationship between the variables.


The problem with scattergram is the ambiguity in interpreting the strength of the correlation. How high is high? And how low is low? To get a precise results, it is better to use statistical formulas.

Formulas

There are two formulas that you can use to compute the correlation coefficient.

1. Pearson Product Moment. Use this formula if you have two sets of data which are interval or ratio.
2. Spearman Rank. Use this formula if you have two sets of data which are different types, eg. interval and nominal. Convert both sets of data into ordinal by changing the interval/ratio/nominal numbers into ranks.