Mathematical Studies for the IB Diploma © Hodder Education Pearson’s product–moment correlation coefficient

Mathematical Studies for the IB Diploma © Hodder Education 2010 Pearson’s product–moment correlation coefficient When the relationship between two variables needs to be studied, a good way of representing the data graphically is to use a scatter diagram. With a scatter diagram, a series of points is plotted. The x- and y-coordinates of each point are taken from the values of the variables. The data and scatter diagram below show the height of young children (cm) plotted against their mass (kg). HeightMassHeightMass

Mathematical Studies for the IB Diploma © Hodder Education 2010 Pearson’s product–moment correlation coefficient From the graph it is clear that there is a relationship between the two variables. Generally, as height increases so does mass. This can be emphasized by plotting a line of best fit. This should pass through the point which represents the mean values of the height and mass. To see how strong a correlation there is between the two variables, Pearson’s product–moment correlation coefficient can be calculated.

Mathematical Studies for the IB Diploma © Hodder Education 2010 Pearson’s product–moment correlation coefficient The value of Pearson’s product–moment coefficient (r ) gives an indication of the level of correlation between two variables. It has a value in the range –1 ≤ r ≤ 1. The value of r is calculated using the formula where is the standard deviation of x, is the standard deviation of y and is the covariance of x and y A value of r near –1 implies a strong negative correlation between the two variables. A value of r near +1 implies a strong positive correlation between the two variables. A value of r near 0 implies there is little or no correlation between the two variables.

Mathematical Studies for the IB Diploma © Hodder Education 2010 Pearson’s product–moment correlation coefficient For the data given earlier, the results can be entered in a GDC calculator and the value of r calculated. r = This value of r shows that there is a moderate positive correlation between a child’s height and mass.