The determination of natural mass independent isotope variations by precise isotopic measurements of elements by multi-collector inductively coupled plasma mass spectrometry (MC-ICP-MS) requires a detailed understanding of the instrumental mass bias. Until recently, the instrumental mass bias in MC-ICP-MS analysis was considered to be entirely mass dependent, most often corrected by an exponential law. Here, we report evidence of an odd–even isotope separation in the tungsten isotopic analysis of the W isotope standard NIST SRM 3163, that is specific to the type of cones used. We also found that mass independent isotope fractionation is a ubiquitous effect in W isotope data reported on NIST SRM 3163 from other laboratories. Nuclear volume isotope effects do not provide an adequate description of this mass bias, unlike for recent reports on Nd isotopes, but a process of odd–even isotope separation is required that may occur in the expansion plume in the interface region of the ICP ion source. Newly available Jet sampler cones combined with X-skimmer cones diminish the odd–even isotope separation, while reducing the mass dependent bias by about half which is corrected adequately with application of the generalized power law. The mass independent effect observed in W is possibly related to its high first ionization potential (FIP, 7.86 eV), implying that other elements with FIP ≥ 8 eV may also exhibit mass independent instrumental bias in MC-ICP-MS analysis.