FCSXpert Solutions: Fluorescence Correlation Spectroscopy Simplified!.
## FCS Classroom

#### What is Correlation?

### Correlation: A Fluorescence Exampleback to top

#### Intensity Measurement

#### Relationships Between Measurements

#### Degree of Correlation

##### High Correlation

##### Low Correlation

### Correlation Mathematicsback to top

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

See these sections below for more information on correlation:

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 I_{1}, I_{2}, and I_{3}. Suppose that we get the following
set of measurements of these three intensities.

I_{1} (Counts per Second) | I_{2} (Counts per Second) | I_{3} (Counts per Second) |
---|---|---|

9012 | 2794 | 9412 |

21228 | 4011 | 8064 |

29903 | 5377 | 8554 |

41948 | 5815 | 8092 |

45223 | 7307 | 8194 |

61131 | 7893 | 9647 |

68245 | 9475 | 9390 |

78116 | 9852 | 8634 |

83310 | 11837 | 9900 |

90254 | 13183 | 8069 |

In Figure 1 we plot I_{2} and I_{3} versus I_{1}. When we see this kind of data our intuition says
that, yes, I_{2} and I_{1} are correlated because from a given value of I_{2} we can predict an
approximate value of I_{1}. I_{3} and I_{1} are not well correlated because the value of I_{3} is
not a good predictor of the value of I_{1}.

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 I_{2} and I_{1}. 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 I_{3} and I_{1}. 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 <I_{1}> and <I_{2}> are the average values of I_{1} and I_{2} respectively
and SD_{1} and SD_{2} are their standard deviations. M is the total number of
measurements (in this case of the example above, ten).