Instant Notes: Analytical Chemistry

Separate tabular values for some significance test factors have been compiled

for what are described as one-tailedand two-tailedtests. The exact purpose of

the comparison that is to be made determines which table to use.

● Theone-tailed test is used EITHER to establish whether one experimental

value is significantly greater than the other OR the other way around.

● Thetwo-tailed test is used to establish whether there is a significant differ-

encebetween the two values being compared, whether one is higher or

lower than the other not being specified.

The two-tailed test is by far the most widely used. Examples are given below.

Outliers Inspection of a set of replicate measurements or results may reveal that one or
more is considerably higher or lower than the remainder and appears to be outside
the range expected from the inherent effects of indeterminate (random) errors
alone. Such values are termed outliers, or suspect values, because it is possible
that they may have a bias due to a determinate error. On occasions, the source of
error may already be known or it is discovered on investigation, and the outlier(s)
can be rejected without recourse to a statistical test. Frequently, however, this is
not the case, and a test of significance such as the Q-test should be applied to a
suspect value to determine whether it should be rejected and therefore not included
in any further computations and statistical assessments of the data.

Q-test Also known as Dixon’s Q-test, this is one of several that have been devised to
test suspected outliersin a set of replicates. It involves the calculation of a ratio,
Qexptl, defined as the absolute difference between a suspect value and the value
closest to it divided by the spread of all the values in the set:

Qexptl=suspect value −nearest value/(largest value −smallest value)

Qexptlis then compared with a tabulated value, Qtab, at a selected level of proba-

bility, usually 90% or 95%, for a set of nvalues (Table 1). If Qexptlis lessthan Qtab,

then the null hypothesis that there is no significant differencebetween the

suspect value and the other values in the set is accepted, and the suspect value

is retained for further data processing. However, if Qexptlis greaterthan Qtab, then

the suspect value is regarded as an outlier and is rejected. A rejected value

should NOT be used in the remaining calculations.

Table 1. Critical values of Q at the 95% (P=0.05) level for a two-tailed test

Sample size Critical value

4 0.831

5 0.717

6 0.621

7 0.570

8 0.524

Example 1

Four replicate values were obtained for the determination of a pesticide in river

water

0.403, 0.410, 0.401, 0.380 mg dm-^3

B3 – Significance testing 35