2006PASP..118.1716T

In this paper, transformations between Cousins R-I and other indices are considered. New transformations to Cousins V-R and Johnson V-K are derived, a published transformation involving T₁-T₂on the Washington system is rederived, and the basis for a transformation involving b-y is considered. In addition, a statistically rigorous procedure for deriving such transformations is presented and discussed in detail. Highlights of the discussion include (1) the need for statistical analysis when least-squares relations are determined and interpreted, (2) the permitted forms and best forms for such relations, (3) the essential role played by accidental errors, (4) the decision process for selecting terms to appear in the relations, (5) the use of plots of residuals, (6) detection of influential data, (7) a protocol for assessing systematic effects from absorption features and other sources, (8) the reasons for avoiding extrapolation of the relations, (9) a protocol for ensuring uniformity in data used to determine the relations, and (10) the derivation and testing of the accidental errors of those data. To put the last of these subjects in perspective, it is shown that rms errors for VRI photometry have been as small as 6 mmag for more than three decades and that standard errors for quantities derived from such photometry can be as small as 1 mmag or less.