The Modified Arcsine-Logarithm Methodology for Analyzing Soil Test - Relative Yield Relationships.

The main question when developing models for diagnosing fertilization based on soil test values (STV) may be: which is the critical value (or range) of a soil fertility variable for a specific crop response level? This article discusses the arcsine-logarithm calibration curve (ALCC), an alternative methodology developed for answering this question. This technique has two main differences as compared with usual methodologies: i) transformation of the variables – ln for STV and arcsine for relative yield (RY)-; and ii) estimation of a confidence interval (CI) of the critical soil test value (CSTV). Despite the latter advantage, the authors noticed that the CI_95% of the original method resulted in too wide ranges and decided to reduce the confidence level (CI_70%) to get narrower ranges for recommendations. However, more accurate ranges are possible by modifying specific steps that avoid reductions in the confidence level. For this purpose, a STV:RY dataset of 103 experiments of phosphorus fertilization in wheat (Triticum aestivum L.) performed in Argentina during the last two decades was used. While the best fitted least squares (LS) regression model (non-linear) did not accomplish the assumptions -normality and homoscedasticity-, the ALLC did it. For RY=90%, the estimated CSTV was lower (17.2 mg kg^-1 Bray-1 P) with the ALCC compared to the LS method (23.8 mg kg^-1). On the other hand, the CI_95% for the modified ALCC (15.2 to 19.6 mg kg^-1) was 30% and 67% more accurate compared to the original ALLC (14.1 to 20.2 mg kg^-1) and to the LS regression (18.5 to 31.7 mg kg^-1), respectively. Moreover, a predictive model such as LS regression may have risks of misuse since the explanatory variable is not fixed. The modified ALCC instead, based on a bivariate approach, describes a structural relationship between variables and may represent a more reliable alternative.