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tokens: a non-zero slope for either half. Similarly, if we split the sample into smaller ranges of group mass, as in Section 4.2 , we are not able to distinguish the slope from zero slope for either half. For our sample, the halfway point at r = 2.06 is at or beyond R 200 (up to almost seven times beyond; see Table 1 ). Therefore, it is not surprising that the gradient in galaxy properties is primarily within this radius. Ideally, with a larger sample, one could find a specific (not necessarily linear) function to describe the change in H i content within R 200 as function of group-centric distance. So far, this has proven to be a challenge; for example, Yoon Rosenberg ( 2015 ) do not detect a radial gradient in H i mass ratio within R 200 at all, using a slightly larger sample (but not including upper limits for galaxies not detected in H i ). 5. CONCLUSIONS AND DISCUSSION In this paper, we take the approach of comparing the H i content at fixed galaxy type and stellar mass in the centers of groups and clusters over a wide range of masses with the H i content in galaxies in control regions out to 4 Mpc surrounding each group or cluster. This process allows us to statistically test for pre-processing in the central systems themselves, including in isolated groups, an approach that complements environmental tests based on local density. Our H i data is from the new catalog, and we use statistical tests from survival analysis in order to include information on upper limits for galaxies not detected in H i . Our primary results are the following. (1) Late-type galaxies in groups lack H i at fixed stellar mass relative to galaxies in a control region extending to 4.0 Mpc surrounding each group. Most of the gradient in galaxy properties out to 4.0 Mpc occurs in the inner 2.0 Mpc. Although this effect is stronger in clusters and large groups (), it is also detectable in groups with . This shows pre-processing of H i gas, not simply at intermediate densities, but in intermediate-density isolated groups. (2) The gradient in H i content for fixed stellar mass is stronger in larger groups, but the gradient in stellar mass and color does not follow this trend; stellar masses increase and galaxies become bluer with r at similar rates across our four bins of group mass. These difference between H i and optical properties might reflect an additional, rapid mechanism for the removal of gas in the inner regions of larger groups and clusters. Our statistics are insufficient to address whether this is truly a threshold effect, or a gradual change with group mass. (3) Comparing six different environment variables, we find that local density is the best predictor of galaxy properties (including H i content at fixed stellar mass), followed by group-centric radius r and . Considering all combinations of two variables together, we find that fits are improved (higher adjusted R 2 ) only for the addition of group mass M 200 to local density, r , or . We note that