Everyone has a sense about what the term correlation means. It means that the measurements of two properties are co-related. Let's explore this a little more closely.
Suppose that we measure fluorescence signals at three wavelengths and call them I1, I2, and I3. Suppose that we get the following set of measurements of these three intensities.
|I1 (Counts per Second)||I2 (Counts per Second)||I3 (Counts per Second)|
In Figure 1 we plot I2 and I3 versus I1. When we see this kind of data our intuition says that, yes, I2 and I1 are correlated because from a given value of I2 we can predict an approximate value of I1. I3 and I1 are not well correlated because the value of I3 is not a good predictor of the value of I1.
Typically, to assess the degree of correlation between two measurements we would next perform a linear regression, as shown in Figure 2, and calculate the regression coefficient.
The black line in Figure 2 shows the linear fit between I2 and I1. The coefficient of correlation, R, of this fit is 0.98. Perfect correlation has an R value of 1.00 (See Correlation Mathematics, below, for the equation used to calculate R). So our intuition is confirmed the two intensities are indeed highly correlated.
The red line shows the linear fit between I3 and I1. The low R value of 0.18 confirms that these two intensities are not highly correlated.
The correlation coefficient, R, is determined from paired data sets by the equation
where <I1> and <I2> are the average values of I1 and I2 respectively and SD1 and SD2 are their standard deviations. M is the total number of measurements (in this case of the example above, ten).