  Visible colors (BVRI) are a reasonable proxy for real spectra of Centaurs and
Kuiper Belt Objects, which are rather linear in this range. Colors provide
limited information but remain the best tool to study the bulk surface
properties. We explore recurrent effects in the study of visible colors: i) how
a correlation could be missed or weakened as a result of the data error bars,
ii) the "risk" of missing an existing trend because of low sampling, and the
possibility of making quantified predictions on the sample size needed to
detect a trend at a given significance level, iii) the use of partial
correlations to distinguish the mutual effect of two or more parameters, and
iv) the sensitivity of the "reddening line" tool to the central wavelength of
the filters used. We have compiled the visible colors of about 370 objects
available in the literature and carried out an analysis per dynamical family.
Our results show how a) data error bars impose a limit on the detectable
correlations regardless of sample size and that therefore, once that limit is
achieved, it is important to diminish the error bars, but it is pointless to
enlarge the sampling with the same or larger errors; b) almost all dynamical
families still require larger samplings to ensure the detection of correlations
stronger than 0.5; c) the correlation strength between (V-R) vs. (R-I) is
systematically lower than the one between (B-V) vs. (V-R) and is not related
with error-bar differences between these colors; d) it is statistically
equivalent to use any of the different flavors of orbital excitation or
collisional velocity parameters regarding the color-inclination correlation of
classical KBOs whereas the inclination and Tisserand parameter relative to
Neptune cannot be separated from one another; and e) classical KBOs are the
only dynamical family that shows neither (B-V) vs. (V-R) nor (V-R) vs. (R-I)
correlations.
