Most simulations of stellar N-body systems are done for the purpose of observing global evolution or for taking statistics of global measurements. The microscopic details of which star goes where are rarely of interest. On this basis, a sufficient condition for simulation reliability is that all global measurements of interest from the real system should be reproduced by the simulation. In fact, the assumption that macroscopic measurements are valid (the MMV assumption), even though the microscopic details are possibly wrong, is a necessary working assumption for practicing N-body researchers. It is difficult to see how this assumption could be verified conclusively without an understanding of how the simulation treats microscopic details (for example, a set of self-consistent simulations may contain systematic errors such that they are all wrong in the same way), but most practitioners of stellar N-body simulation take the MMV hypothesis as a working assumption anyway. Heggie  states that this assumption ``is little better than an article of faith.'' Nonetheless, we are led to the question of what accuracy level is necessary in order for us to collect undistorted statistics.
When measuring statistical quantities, we must keep in mind that even if we had a perfect N-body simulator, we could only run it a finite number of times, so there would still be the fundamental noise that is present in any finite-sized statistical sample. Thus, there is little use in attempting to measure statistics any more accurately than this limit dictates [74, 73, 35, 38]. Also, a disadvantage of using direct N-body simulation to collect statistics is that only a small amount of the wealth of information in a full N-body simulation is ever extracted. Thus direct N-body simulation is not a particularly information-efficient method of gathering statistics .
Smith  used a 2nd order variable timestep predictor/corrector with no regularization and double precision arithmetic to test the hypothesis that some statistics are relatively insensitive to integration accuracy. The statistics he measured in globular cluster simulations were the first and third quartic mean stellar density, energy, and radius, as well as the median radius. He compared simulations with varying degrees of accuracy using various statistical tests and found the statistics to disagree at only the 10% level, i.e., there was little evidence to conclude that the simulations gave different results according to integration accuracy. He concluded that the statistics taken are reliable unless energy conservation is grossly violated. However, Lecar  chose to measure different statistics, and found them to vary widely depending on which machine or algorithm was used to integrate the problem. This will be further discussed below.