9780521516358book.pdf

Comparison of two competitive analytical methods – pairedt-test

A variant of the previous type of comparison of two analytical methods based upon

the analysis of a common standard sample, is the case in which a series of test samples

is analysed once by the two different analytical methods. In this case there is no

replication of analysis of any test sample by either method. Thet-test is applied to the

Example 8COMPARISON OF TWO ANALYTICAL METHODS USING REPLICATED
ANALYSIS OF A SINGLE TEST SAMPLE

Question A sample of fasting serum was used to evaluate the performance of the glucose
oxidase and hexokinase methods for the quantification of serum glucose
concentrations (for details see Section 15.3.5). The following replicated values
were obtained: for the glucose oxidase method 2.3, 2.5, 2.2, 2.6 and 2.5 mM and for
the hexokinase method 2.1, 2.7, 2.4, 2.4 and 2.2 mM.
Establish whether or not the two methods gave the same results at the 95%
confidence level.

Answer Using the standard formulae we can calculate the mean, standard deviation and

variance for each data set.

Glucose oxidase method

x¼ 2 : 42 mM;s¼ 0 : 16 mM;s^2 ¼ 0 : 026 ðmMÞ^2

Hexokinase method

x¼ 2 : 36 mM;s¼ 0 : 23 mM;s^2 ¼ 0 : 053 ðmMÞ^2

We can then apply theF-test to the two variances to establish whether or not they

are the same:

Fcalc¼

0 : 053

0 : 026

¼ 2 : 04

Ftablefor the two sets of data each with four degrees of freedom and for the 95%

confidence level is 6.39 (Table 1.11).

SinceFcalcis less thanFtablewe can conclude that the two variances are not

significantly different. Therefore using equations 1.17 and 1.18 we can calculate that:

spooled¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ð 0 : 16 Þ^2 ð 4 Þþð 0 : 23 Þ^24

8

s

¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

0 : 102 þ 0 : 212

8

r

¼

ffiffiffiffiffiffiffiffiffiffiffiffi

0 : 039

p

¼ 0 : 198

tcalc¼^2 :^42 ^2 :^36

0 : 198

ffiffiffiffiffiffiffiffiffiffiffiffiffi

ð 5 Þð 5 Þ

10

r

¼ð 0 : 303 Þð 1 : 58 Þ¼ 0 : 48

Using Table 1.10 at the 95% confidence level and for eight degrees of freedomttableis

2.306. Thustcalcis far less thanttableand so the two sets of data are not significantly

different, i.e. the two methods have given the same result at the 95% confidence level.

31 1.4 Quantitative biochemical measurements