Stats Tutorial - Instrumental Analysis and Calibration

Aim of Statistics in Analytical Chemistry:

Modern analytical chemistry is concerned with the detection, identification, and measurement of the chemical composition of unknown substances using existing instrumental techniques, and the development or application of new techniques and instruments. It is a quantitative science, meaning that the desired result is almost always numeric. We need to know that there is 55 μg of mercury in a sample of water, or 20 mM glucose in a blood sample.

Quantitative results are obtained using devices or instruments that allow us to determine the concentration of a chemical in a sample from an observable signal. There is always some variation in that signal over time due to noise and/or drift within the instrument. We also need to calibrate the response as a function of analyte concentration in order to obtain meaningful quantitative data. As a result, there is always an error, a deviation from the true value, inherent in that measurement. One of the uses of statistics in analytical chemistry is therefore to provide an estimate of the likely value of that error; in other words, to establish the uncertainty associated with the measurement.

Accuracy & Precision:

Two terms of importance in any measurement are accuracy and precision, and it is important to distinguish between them since these terms have highly specific meanings when applied to scientific measurement.

Accuracy:

Accuracy is defined as the closeness of a result to the true value. This can be applied to a single measurement, but is more commonly applied to the mean value of several repeated measurements, or replicates.

Precision:

Precision is defined as the extent to which results agree with one another. In other words, it is a measure of consistency, and is usually evaluated in terms of the range or spread of results. Practically, this means that precision is inherently related to the standard deviation of the repeated measurements.

When referring to the consistency between individual values amongst a set of replicate measurements performed by the same person, at the same time on the same sample, using the same method, this is termed the measurement repeatability.

When referring to the consistency of a method as used by different analysts, laboratories, and/or over an extended time period, this is termed the reproducibility.

Note that accuracy and precision are separate things: while we would prefer to have results that are both accurate and precise (left), it is entirely possible to have results that are accurate but not precise (centre), as well as results that are precise but not accurate (right).

Common Questions:

One way to demonstrate the importance of statistics in analytical chemistry is to look at some of the common questions asked about measurement results, and the statistical techniques we can use to answer them.

When I repeat a measurement, I get different numbers; which do I use?

Calculate the mean and standard deviation of the values; this is the starting point for any statistical evaluation of your data. Remember that the inherent variation associated with any real measurement means you would expect to get somewhat different values for replicate measurements.

One of the values is quite different from the others; can I simply ignore it?

This depends on the range of the values you obtained, how different the suspect value is from all the others, and how close the remaining results are to one another. Use either Dixon's Q test or Grubb's test on the data.

Did I get the ‘right’ answer?

It’s almost impossible to answer this question in any meaningful way for real samples! If you know what the true value is, you can assess whether your result is significantly different using a t-test. If you don’t know the true value (or an accepted true value), you have to determine the range either side of your measurement within which the true value most probably lies. This is called the confidence interval, and is a measure of the uncertainty associated with your measurement.

One sample gives a value of 2.1, the other gives 2.2; these are different values, right?

This depends on the uncertainty associated with each measurement. You will need to perform a significance test in order to determine whether the values can be considered the same or different. You should test whether there is a significant difference in the spread (standard deviation) of replicate measurements for each sample (use the F-test) as well as the mean values themselves (use a pooled t-test).

Continue to Mean & Variance...