Potential error in single-point-ratio calculations based on linear calibration curves with a significant intercept

Abstract

Calculations based on a single-point standard linear calibration curve which has a finite intercept are a potential source of bias error. The error has been shown to be a function of magnitude of the slope and intercept, and the magnitude of the difference in the standard and sample responses. For maximum accuracy, the ratio of the difference in responses to the standard response should be the lowest possible. For any response curve, a reliable calculation of the percent error resulting from making a single-point-ratio calculation (SPRC) where a finite intercept exists is shown so that a decision as to its proper use or non-use may be made. In most cases, even when an analytically significant intercept is found in a linear calibration curve, the SPRC technique may stili be employed by calculating the sample signal to standard signal, S,/S, ratio range for an acceptable % error bias range. This calculation of the S,/S, ratio constitutes a trade-off between the use of a single standard and a shortened linear dynamic range with its possibility of more reanalyses against the use of the entire linear dynamic range with its mandatory requirement of more standards but the lesser possibility of reanalyses.

An Ion‐Pair High Performance Liquid Chromatographic Method for the Determination of Aspartame and its Decomposition Products

“…All seven compounds have acceptable correlation coefficients, low coefficients of variation and y-intercepts close to zero. The good linearity and small relative y-intercept show that errors in measurement of sample response will remain acceptably small when quantitative analysis is based on singlepoint-ratio calculations using only one standard (Cardone et al, 1980). Finally, the use of ion-pair reagents provides flexibility to the resultant separation when other peaks compete for the same chromatographic space.…”

Analytical Calibrations: Schemes, Manuals, and Metrological Deliberations

“…The real [analyte] can be calculated using the formula: [anal] = [std 1 or 2 ] + k (y unknown -y std 1or2 ), where the brackets express concentrations, k is the reciprocal of slope (sensitivity), and y is the response for the unknown and the standard, respectively [11,12,32]. Examples for this calibration are the pH meter and temperature sensor calibrations.…”

New technique in chemical assay calculations. 1. A survey of calculational practices on a model problem

“…This can be interpreted as meaning that the SB is not favored as the blank correction for the SPRC and the MOSA calculation. Many respondents who ignored the SPRC entirely (51%, 26/51) stated that they did so because of the high SB intercept (10). Even so, the SPRC is apparently unfamiliar to many analysts, since only 49% (25/51) supplied an SPRC result as against the 88% (45/51) who supplied either a MOSA result or a standard curve result.…”

“…In both problems, the sample and standard data each included a pair in which Sx = S,. Only four respondents used these pairs in spite of the published fact that for equal standard and sample responses, the bias error due to a significant standard curve intercept is zero (10).…”