Stats Tutorial - Limits of Detection:


Basics of Excel™

Basic Statistics

Linear Regression:



Linear Portions

Regression Equation

Regression Errors

Using the Calibration

Limits of Detection

Outliers in Regression

Data Evaluation & Comparison


As mentioned above, there is always some error associated with any instrumental measurement. This also applies to the baseline (or background or blank) measurement, i.e. the signal obtained when no analyte is present. An important determination that must be made is how large a signal must be for it can be distinguishable from the background noise of the instrument. Various criteria have been applied to this determination, however the generally accepted rule in analytical chemistry is that the signal must be at least three times greater than the backgound noise.

Formally, the limit-of-detection (lod) is defined as the concentration of analyte required to give a signal equal to the background (blank) plus three times the standard deviation of the blank. So, before any calibration or sample measurement is performed, you must evaluate the blank. That is, we first calculate the instrument response obtained with no analyte. The lod is then determined by :

This gives the minimum signal that can be interpreted as a meaningful measurement. To find the associated concentration, you must use the calibration curve to convert the signal to a concentration, ylod, → xlod.

Where no blank has been measured, we can use the calibration data and regression statistics instead. In this case, we would use the y-intercept and standard deviation of the regression:

The lod represents the level below which we cannot be confident whether or not the analyte is actually present. It follows from this that no analytical method can ever conclusively prove that a particular chemical substance is not present in a sample, only that it cannot be detected. In other words, there is no such thing as zero concentration!

When performing a calibration, you should always determine and report the lod from your calibration data, in addition to the regression statistics outlined above.

The following image shows a graphical definition of the limit of detection, as well as the regression line and the error in x0:

Finally, in the last part of this section, we begin to explore the concept of outliers, and how you decide when to include them and when to ignore them. This involves the Q-test, which will be covered in greater detail in the next section on Data Evaluation and Comparison.

© 2006 Dr. David C. Stone & Jon Ellis, Chemistry, University of Toronto
Last updated: September 26th, 2006