Bias and ErrorsBias and Errors

Some Terms Used to Describe Analytical Methods

Accuracy

Precision

LOD

RDL

LOQ

Selectivity

Sensitivity

Linearity

Ruggedness

Accuracy and Precision...

• Before we can appreciate the term Bias, we must first understand the basic terms “accuracy” and “precision”.

• Accuracy is the closeness of a result to that of an expected value.

• Consider the following example:– 10 µL of each 1 ppm, 5 ppm, 10 ppm, 50 ppm and

100 ppm standards of caffeine standards (USP) are injected into an LC-MS. An external standard calibration curve is generated.

– 10 µL of a “reference” (NIST traceable) sample containing caffeine of a concentration unknown to us is then injected into the LC-MS. The response, once interpolated from the calibration curve, yields 11 ppm in the sample.

– We find out later that the actual concentration of the “reference” caffeine standard is 10 ppm.

– Under what conditions should we be concerned about this result?

– What are some reasons why this occurred?

...Accuracy and Precision...

• We must appreciate that the so-called determination of an analyte concentration in a sample is really, at best, an “estimate” of its actual concentration.

• Associated with every determination is a level of “precision” or “reproducibility”.

• Consider the following continuing with our caffeine determination: (Note, the red bar is the “true” concentration of the target analyte and is 10 ppm.)

5-

10-

15-ppm

• 10 measurements, with an average concentration of 10 ppm, yet the range of concentrations is >20% RSD.

• Accurate Not Precise

...Accuracy and Precision...

5-

10-

15-ppm

• 10 measurements, with an average concentration of 13 ppm and with >20% RSD.

• Not Accurate and Not Precise

5-

10-

15-ppm

• 10 measurements, with an average concentration of 11 ppm, yet with <10% RSD.

• Precise Not Accurate

...Accuracy and Precision

5-

10-

15-ppm

• 10 measurements, with an average concentration of 10.1 ppm, and with <2% RSD.

• ACCURATE and PRECISE

• From this, we can see clues re. BIAS, t-test comparison of means of results using different methods (ANOVA), LOD, LOQ, and even ruggedness.

Bias and ErrorsPage 12-on and A2-A5 Skoog Holler Nieman

• BIAS: The systematic departure of the “measured” value from the “true” or “expected” value.

• There are many sources of BIAS, and they may be additive.

• Accuracy can be assessed quite simply using certified or standard reference materials that “match” your test standards and samples.

– Matrix effects can create artifacts resulting in BIAS, positive or negative.

• SYSTEMATIC ERRORS can result in BIAS.SYSTEMATIC ERRORS can result in BIAS.

• A: No BIAS; B: BIAS +ve

Errors...

• Three basic types:

– Instrumental

– Method

– Personal

Overall:

• Systematic or Determinate

• Random

• Mistakes (human errors, or prejudice)

Instrumental Errors

• “Drift” in electronic circuits (e.g., improper zero)

• Temperature control is unstable is subject to ambient parameters.

• Poor power supplies, e.g., other instruments on the same power grid perturbing the instrument’s power.

• Other systems in the area creating a field that influences detector response, coincidentally while the samples are running, but not the standards.

• Regular calibration is required, the frequency of which is for the most part empirically determined (from actual experiments).

In all cases, accuracy is most likely affected

...Errors...

Method Errors

• Often introduced by non-ideal chemical behaviour.

• Loss of sol’n by evaporation.

• Analyte losses upon unexpected adsorption or absorption.

• Contaminants.

• Interferences (affects selectivity, e.g., electrochemical methods, AA)

• Instability of reagents.

• Difficult to detect the target analytes.

• The solution used to prepare the standards is not the same as the sample matrix. This can be easily accomplished by Standard Addition, Isotope Dilution (deuterated analogues). This is where External Standard Calibration can result in BIAS.

• Use of CRM (certified reference materials), intra- and inter-laboratory method validation, and verification by other analysts really helps here.

...Errors...

Human (Personal) Errors

• Made unknowingly and sometimes knowingly.

• Prejudice w.r.t. reading meniscus, thermometers, pH meters, peak integration (apex determinations), colour end points.

...Errors...

Sources of BIAS and VARIABILITY in the Lab

• Sample storage (contamination, physical or chemical degradation)

• Sample handling (contamination during preparation).

• Sub-sampling

• Weighing and volumetric devices

• Solvent purity

• Extraction yields - low and/or variable

• Analyte concentration following evaporation

• Clean-up steps (analyte losses)

• Quality of reference standards

• Instrument calibration

• Instrumental - injection variability and/or discrimination, matrix effects, changes in detector response during the course of the sample analyses

• Different analysts

• Environmental and electrical conditions in the lab (T, RH).

...Errors

Assessing BIAS and Variability

• Use of reference materials

• Comparison to another method (preferably a standard method)

• Use of representative blank matrices and spikes

• Use of true positive samples and spikes, which have been confirmed by other analysts or lab

• Within-run and between-run variability studies

Comparison to Another Method

Comparison to a Reference Value