Instant Notes: Analytical Chemistry

As texptlis greaterthan ttabat both the 95 and 99% probability levels, there is a

significant difference between the means of the two methods.

Example 2

A new high performance liquid chromatographic method for the determination

of pseudoephedrine in a pharmaceutical product at two different levels was

compared with an established method with the following results:

Pseudoephedrine per dose (mg)

Method 1 Method 2

59.9 58.6

59.3 58.3

60.4 60.5

30.7 29.4

30.2 30.4

30.1 28.9

Do the means of the two methods differ significantly?

Because the two levels of pseudoephedrine differ considerably, equation (3)

for a paired t-test is used to calculate texptl. The differences between the pairs of

values are 1.3, 1.0, -0.1, 1.3, -0.2 and 1.2 mg per dose, and the estimated

standard deviation of the differences from their mean of 0.750 mg per dose is

0.706 mg per dose. Substitution of these values into the equation gives

texptl=
x

s

_

d

d×N^1 ⁄^2 =(0.750/0.706) ¥ 61 ⁄^2 =2.60

For 5 degrees of freedom, the two-tailed value of ttabat the 95% probability level

is 2.57. As texptlis greaterthan ttab, there is a significant difference between the

means of the two methods. (Note: using equation (1) would give a texptlvalue of

0.08 and an incorrect conclusion.)

Example 3

A method for the determination of mercury by atomic absorption spectrometry

gave values of 400, 385 and 382 ppm for a standard known to contain 400 ppm.

Does the mean value differ significantly from the true value, or is there any

evidence of systematic error (bias)?

x

_

=389 ppm s=9.64 ppm m=400 ppm

Using equation (4) to evaluate texptl

texptl= ×N

(^1) ⁄ 2
= × 3
(^1) ⁄ 2
=1.98
For 2 degrees of freedom, the two-tailed ttabvalue is 4.30 at the 95% probability
level. As texptlis lessthan the two-tailed value of ttab, the mean is not significantly
different from the true value. There is, therefore, no evidence of a systematic
error, or bias.
Analysis of variance, also known as ANOVA, is a statistical technique for inves-
tigating different sources of variability associated with a series of results. It
enables the effect of each source to be assessed separately and compared with
the other(s) using F-tests. Indeterminate or random errors affect all measure-
ments, but additional sources of variability may also arise. The additional
sources can be divided into two types:
Analysis of
variance


(389 −400)
9.64
(x
_

−m)
s
B3 – Significance testing 39