Publisher Summary In the comparison of several procedures, each may be subject to systematic error; the procedures then constitute a (controlled) factor. Moreover, the results of the analytical determinations are subject to random errors. The analysis of variance compares both causes of variation with the purpose of deciding whether or not the controlled factor has a significant effect. An example relates to the work of official or public analysts and concerns the statistical analysis of a collaborative test of a procedure considered for official adoption. In such a test, several laboratories are asked to analyze a number of samples with the same procedure using a predetermined number of replicate determinations. The analysis serves to distinguish between sources of variation between laboratories, between samples, and between replicates. Therefore, there are two controlled factors (laboratories and samples), the variance between replicates being considered to be the effect of chance.