Instant Notes: Analytical Chemistry

Section B – Assessment of data

B3 SIGNIFICANCE TESTING

Significance tests involve a comparison between a calculated experimental

factor and a tabulated factor determined by the number of values in the set(s) of

experimental data and a selected probability level that the conclusion is correct.

They are used for several purposes, such as:

● to check individual values in a set of data for the presence of determinate

errors (bias);

● to compare the precision of two or more sets of data using their variances;

● to compare the means of two or more sets of data with one another or with

known values to establish levels of accuracy.

Tests are based on a null hypothesis -an assumption that there is no signifi-

cant differencebetween the values being compared. The hypothesis is accepted

if the calculated experimental factor is less than the corresponding tabulated

factor, otherwise it is rejected and there is said to be a significant difference

between the values at the selected probability level. The conclusion should

always be stated clearly and unambiguously.

Probability levels of 90%, 95% and 99% are generally considered appropriate

for most purposes, but it should be remembered that there are also corre-

sponding 10%, 5% or 1% probabilities, respectively, of the opposite conclusion

being valid. For example, if a test indicates that the null hypothesis is correct

and that there is no significant difference between two values at the 95% proba-

bility level, it also allows the possibility that there is a significant difference at

the 5% level.

Significance
tests

Key Notes

These are statistical tests used to compare individual values or sets of

values for significant differences.

A measurement or result that appears to differ significantly from others

in the same set of replicates is described as an outlier.

The Q-test is used to determine whether to reject or retain a suspected

outlier.

The F-test enables the precisions of two sets of data to be compared using

their variances.

The t-test is used to compare two experimental means, an experimental

mean with a known value or sets of pairs of experimental values.

F-tests can be applied to several sets of data to assess and compare

different sources of variability.

Related topic Assessment of accuracy and precision (B2)

Significance tests

Outliers

Q-test

F-test

t-test

Analysis of variance