Inflammatory biological markers are clinically useful in a number of different ways, one being the assessment of disease activity in conditions such as systemic lupus erythematosus (SLE). A new inflammatory marker is being investigated in patients with active SLE flares. When the blood level of the new marker (in mg/L) is plotted against the C-reactive protein (CRP) level (also in mg/L), the following plot is obtained: Based on the plot, the correlation coefficient between the 2 variables is closest to which of the following values?

Question

Inflammatory biological markers are clinically useful in a number of different ways, one being the assessment of disease activity in conditions such as systemic lupus erythematosus (SLE).  A new inflammatory marker is being investigated in patients with active SLE flares.  When the blood level of the new marker (in mg/L) is plotted against the C-reactive protein (CRP) level (also in mg/L), the following plot is obtained:  Based on the plot, the correlation coefficient between the 2 variables is closest to which of the following values?

Quizplus · Accepted Answer

11ec160b_3703_f412_9249_3f8a8847d0af_MD0001_00 Scatter plots are useful for crude data analysis. If a linear association is present between 2 variables, a correlation coefficient (r) mathematically describes how well a "line of best fit" (blue line in Figure) would correspond to the data points plotted. The value of r ranges from −1 to +1 and describes 2 important characteristics of an association: the strength and the polarity. The closer the r value is to its margins [−1, 1], the stronger the association. An increase in C-reactive protein (CRP) level is associated with a decrease in the new marker's level; therefore, r <0. Although the scatter plot does not demonstrate a perfect linear arrangement, it does show a reasonably strong linear association as there is minimal variation along the line of best fit (points are relatively close to the line). Therefore, the most appropriate answer among the options given is r = −0.8. (Choices A and B) In this example, r cannot be >0 as an increase in CRP level is associated with a decrease in the new marker's level. (Choice C) An r = 0 indicates that there is no association (ie, a random distribution). (Choice D) An r = −0.2 would also indicate a negative association; however, there would be more variation along the line of best fit (as seen in the Figure). The value of r is not the slope of the line of best fit. For instance, assuming a data set with a maximum positive association (ie, all data points forming a straight line with a positive slope), the line of best fit will always have r = +1, even if its actual slope is 0.2, 5.5, or any other positive value (as seen in the Figure). Educational objective: The correlation coefficient (r) ranges from −1 to +1 and describes the strength and polarity of a linear association.

Inflammatory Biological Markers Are Clinically Useful in a Number of Different