The precision of electron microprobe analyses has been investigated as a function of elemental concentration and a rigorous derivation is presented for the K-factor equation K = S/C (where S is the measured standard deviation and C the element oxide concentration). It is shown that K is not a constant, but is dependent on element sensitivity and counting times. If counting times for each element are adjusted, for example, such that 50,000 counts would be accumulated at the 10% oxide level, then it is shown that for a homogeneous material, Poisson counting errors in any element at any concentration level will fall within the limits of 0.014 C< or =S< or =0.042 C. This relationship has been tested by the analysis of homogeneous minerals. Data are presented to show that this expression can be used to discriminate inhomogeneous mineral phases and that it is fully compatible in this respect with Boyd's homogeneity index. The equations apply equally to X-ray fluorescence analytical data where counting errors are also controlled by Poisson counting statistics.--Modified journal abstract.