The process of data selection in paleointensity studies is an essential step to ensure data fidelity. There is, however, no consensus as to the best approach to consistently select data with most studies using arbitrarily defined thresholds for selection. We present a new numerical model that simulates the variability of paleointensity data from hypothetical ideal samples acquiring a thermoremanent magnetization (TRM) by incorporating experimental noise, which has been constrained using over 75,000 data measurements. Using Monte Carlo analyses, we investigate the behavior of simulated data and characterize the distributions of parameters typically used to select paleointensity data. We use the 95th percentiles of the distributions to define thresholds for the maximum likely parameter values that can result from experimental noise. These represent values below which we cannot distinguish non-ideal behavior from noise. We find that a number of parameters are highly sensitive to noise and laboratory field strength (e.g., partial TRM, pTRM, checkCDRAT and pTRM tail check δt*); this sensitivity may diminish their ability to identify non-ideal behavior. The fractional (f) dependence of some parameters and the proportion of inaccurate results provide justification for f≥ 0.35 when selecting data from both Thellier-Thellier and Coe protocol experiments. The manifestation of noise in the original Thellier method, however, is different to that of methods that use zero-field heating steps. This suggests that the data selection procedure for the Thellier method should be different, but it also suggests that, contrary to previous analyses, the accuracy and scatter of results from this method are more sensitive to noise than methods that use zero-field heating steps. The general approach taken here is shown to be a powerful means of understanding the behavior of selection parameters and has the potential to be extended to models incorporating non-ideal behavior resulting from alteration and multidomain grains.