Instant Notes: Analytical Chemistry

between-runs variability. It may also be important to establish the precision of

individual steps in an analysis.

This is the most widely used measure of precisionand is a parameter of the

normal erroror Gaussian curve(Topic B1, Fig. 4). Figure 2shows two curves for

the frequency distribution of two theoretical sets of data, each having an infinite

number of values and known as a statistical population.

Standard
deviation

28 Section B – Assessment of data

Deviation from mean

Frequency of occurrence

of each deviation

sd = s 2

sd = s 1

s 1 > s 2

• m +

Fig. 2. Normal error or Gaussian curves for the frequency distributions of two statistical

populations with differing spreads.

The maximum in each curve corresponds to the population mean, which for

these examples has the same value, m. However, the spread of values for the

two sets is quite different, and this is reflected in the half-widths of the two

curves at the points of inflection, which, by definition, is the population stan-

dard deviation,s. As s 2 is much less than s 1 , the precisionof the second set is

much better than that of the first. The abscissa scale can be calibrated in

absolute units or, more commonly, as positive and negative deviations from the

mean, m.

In general, the smaller the spread of values or deviations, the smaller the

value of sand hence the better the precision. In practice, the true values of m

and scan never be known because they relate to a population of infinite size.

However, an assumption is made that a small number of experimental values or

a statistical sample drawn from a statistical population is also distributed

normally or approximately so. The experimental mean, x

_

, of a set of values x 1 ,

x 2 , x 3 ,.......xnis therefore considered to be an estimateof the true or population

mean, m, and the experimental standard deviation,s, is an estimateof the true

or population standard deviation, s.

A useful property of the normal error curve is that, regardless of the magni-

tude of mand s, the area under the curve within defined limits on either side of

m(usually expressed in multiples of ±s) is a constant proportion of the total

area. Expressed as a percentage of the total area, this indicates that a particular

percentage of the population will be found between those limits.

Thus, approximately 68% of the area, and therefore of the population, will be