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Correlating Fluorescence Intensity Fluctuations

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What is Correlation?

Correlation results when the relationship between two measurements is not random.

See these sections below for more information on correlation:

Correlation: A Fluorescence Exampleback to top

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.

Intensity Measurement

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)
901227949412
2122840118064
2990353778554
4194858158092
4522373078194
6113178939647
6824594759390
7811698528634
83310118379900
90254131838069

Relationships Between Measurements

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.

Figure 1
Figure 1: Correlation Between Intensities

Degree of Correlation

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.

High Correlation

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.

Low Correlation

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.

Figure 1
Figure 2: The Correlation Between Two Intensities. The lines indicate the linear least squares fit or regression lines.

Correlation Mathematicsback to top

The correlation coefficient, R, is determined from paired data sets by the equation

Figure 1

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).