## Training and consultancy for testing laboratories. ### Recall basic ideas of ANOVA (Analysis of Variance)

There is a growing interest in sampling and sampling uncertainty amongst laboratory analysts.  This is mainly because the newly revised ISO/IEC 17025 accreditation standards to be implemented soon has added in new requirements for sampling and estimating its uncertainty, as the standard reckons that the test result is as good as the sample that is based on, and hence the importance of representative sampling cannot be over emphasized.

Like measurement uncertainty, appropriate statistical methods involving the analysis of variance (frequently abbreviated to ANOVA) have to be applied to estimate the sampling uncertainty. Strictly speaking, the uncertainty of a measurement result has two contributing components, i.e. sampling uncertainty and analysis uncertainty.  We have been long ignoring this important contributor for all these years.

ANOVA indeed is a very powerful statistical technique which can be used to separate and estimate the different causes of variation.

It is simple to compare two mean values obtained from two samples upon testing to see whether they differ significantly by a Student’s t-test.  But in analytical work, we are often confronted with more than two means for comparison. For example, we may wish to compare the mean concentrations of protein in a sample solution stored under different temperature and holding time; we may also want to compare the concentration of an analyte by several test methods.

In the above examples, we have two possible sources of variation. The first, which is always present, is due to the inherent random error in measurement.  This within-sample variation can be estimated through series of repeated testing.

The second possible source of variation is due to what is known as controlled or fixed-effect and random-fixed factors: in the above example on protein analysis, the controlled factors are respectively the temperature, holding time and the method of analysis used for comparing test results.  ANOVA then statistically analyzes the between-sample variation.

If there is one factor, either controlled or random, the type of statistical analysis is known as one-way ANOVA.  When there are two or more factors involved, there is a possibility of interaction between variables.  In this case, we conduct two-way ANOVA or multi-way ANOVA.

On this blog site, several short articles on ANOVA have been previously presented.  Valuable comments are always welcome.

https://consultglp.com/2017/04/04/anova-variance-testing-an-important-statistical-tool-to-know/