A foundational assumption in paleomagnetism is that the Earth's magnetic field behaves as a geocentric axial dipole (GAD) when averaged over sufficient timescales. Compilations of directional data averaged over the past 5 Ma yield a distribution largely compatible with GAD, but the distribution of paleointensity data over this timescale is incompatible. Reasons for the failure of GAD include: (a) Arbitrary “selection criteria” to eliminate “unreliable” data vary among studies, so the paleointensity database may include biased results. (b) The age distribution of existing paleointensity data varies with latitude, so different latitudinal averages represent different time periods. (c) The time‐averaged field could be truly non‐dipolar. Here, we present a consistent methodology for analyzing paleointensity results and comparing time‐averaged paleointensities from different studies. We apply it to data from Plio/Pleistocene Hawai'ian igneous rocks, sampled from fine‐grained, quickly cooled material (lava flow tops, dike margins and scoria cones) and subjected to the IZZI‐Thellier technique; the data were analyzed using the Bias Corrected Estimation of Paleointensity method of Cych et al. (2021, https://doi.org/10.1029/2021GC009755), which produces accurate paleointensity estimates without arbitrarily excluding specimens from the analysis. We constructed a paleointensity curve for Hawai'i over the Plio/Pleistocene using the method of Livermore et al. (2018, https://doi.org/10.1093/gji/ggy383), which accounts for the age distribution of data. We demonstrate that even with the large uncertainties associated with obtaining a mean field from temporally sparse data, our average paleointensities obtained from Hawai'i and Antarctica (reanalyzed from Asefaw et al., 2021, https://doi.org/10.1029/2020JB020834) are not GAD‐like from 0 to 1.5 Ma but may be prior to that.