What is linearity?

Linearity is the ability of a method to give, within the measurement range selected, results proportional to the concentration of the compound sought in the wine.

It is studied for a given field.

What is the principle of the linearity study?

Verifying the linearity of a method consists in validating that the mathematical function linking the instrumental signal to the analytical result is indeed a straight line for a defined range of values. This study is carried out by comparing the deviations between experimental points and the value assigned to TITRIVIN standards with a maximum accepted deviation defined by each laboratory in coherence with its various requirements.

How to study or verify the linearity of a method using TITRIVIN standards?

Explanation by example... 

Evaluation of linearity for the determination of TAV by Infrared Reflectance using TITRIVIN AA series standards.

Step 1:

I analyze each TITRIVIN under conditions of intermediate fidelity (i.e. different days) and construct the table of instrumental values obtained (see below: table n°1).

Step 2:

For each range, using the method of least squares, I determine the regression line whose function will be y = a0 + a1x with:

• a0 represents the intersection of the regression line with the y-axis,

• a1 is the slope of the regression line.

Step 3:

Using the equation of the lines, I calculate the values found. Then I plot them against the TITRIVIN theoretical values.

This graph(Graph #2)helps to show - or not - that linearity is good in the chosen measurement range.

Step 4:

I plot the biases, i.e. the difference between the values found and the TITRIVIN value, on a graph (Graph no. 3) with the maximum acceptable deviation (MAD) I've set myself, here in the example 0.15% vol.

If the biases are less than the MAE for each level, then the linearity of the calibration is considered acceptable.

If this is not the case:

• You can redo the calculations with values within TITRIVIN confidence intervals,

• You can reduce the scope of the study,

• You must study a model other than the linear model.

 CAUTION !

In the case of alinear calibration model, the biases of each level must oscillate around zero randomly and between the bounds of the defined EMA.
If you observe biases always on the same side of zero, and on both sides for each level, it's likely that there's a linearity problem with the calibration function.

What is the maximum acceptable deviation?

The maximum acceptable deviation (MAD) is the acceptance criterion for the linearity study.

It's up to each laboratory to set this MAD according to the expected uncertainty of the method or analysis, a regulatory requirement.

Bibliographical sources for this page:

• Support for the training course " How to use TITRIVIN ? " Philippe Caillaud

• Validation protocol - compendium of International Methods of Analysis - OIV