Geary showed how the correlated ratio formula_97 could be transformed into a near-Gaussian form and developed an approximation for formula_98 dependent on the probability of negative denominator values formula_99 being vanishingly small. Fieller's later correlated ratio analysis is exact but care is needed when used with modern math packages and similar problems may occur in some of Marsaglia's equations. Pham-Ghia has exhaustively discussed these methods. Hinkley's correlated results are exact but it is shown below that the correlated ratio condition can be transformed simply into an uncorrelated one so only the simplified Hinkley equations above are required, not the full correlated ratio version.