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Notes > Foundations of Computing > Measures of Association

It is useful to know whether two variables are linked in some way as future predictions can be made based on this relationship. The dependent variable is the variable that is affected in some way by the independent variable. These variables can be plotted on a graph to see if a relationship or "correlation" occurs. The dependent variable is typically plotted on the y-axis.

If the points plotted duster around a straight line then there is a linear relationship. If this line has a positive gradient (i.e. it slopes upwards from left to right) then the variables involved have a positive linear correlation. If the plotted points are randomly scattered on the graph, it can be concluded that there is a very weak correlation between the variables if any at all.

The Product-Moment Correlation Coefficient (r) can be calculated from the values of the variables and it indicates how strong the correlation between two variables is. It takes a value between +1 and -1 where +1 implies a perfect positive correlation and -1 implies a perfect negative correlation. Where r=0 this means that there is no linear correlation.

The Coefficient of Determination is r^2 and describes what percentage of the dependent variable values are directly affected by the independent variable values. The rest of the dependent variable values would therefore have been affected by other factors.

Spearman's Rank Correlation takes into consideration the ranks of each value in the collection of data after it has been sorted.

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