Context. To increase cereal production, primary producers want to know the amount of fertiliser that needs to be applied to achieve high yield. To calculate the critical soil test value (CSTV) especially in Colwell-P, several models were found in the literature. The arcsine-log calibration curve has been commonly used in Australia to estimate the CSTV. However, this method has some mathematical weaknesses, which tend to give underestimated values for CSTV.
Aim. In this paper, we describe the mathematical issues and propose a model to overcome these issues. The simplified model proposed allows us to estimate the CSTV and its standard error.
Method. We have applied the regression and the delta method to the data used in the arcsine-log calibration curve (ALCC) method.
Key results. Based on the given data, a soil test value of 31.5 mg P kg−1 soil is required to achieve 90% relative yield of wheat, which is the middle ground of previously published critical values between the underestimate (21.4 mg kg−1) generated by the ALCC algorithm and the overestimate (40 mg kg−1) generated by the conventional Mitscherlich method.
Conclusions. Advantages of this method are: (1) simple to apply to any data sets; and (2) easy to incorporate other covariates into the models. This method should be applied for computing estimates of CSTV and its standard error because it overcomes the contentious issue of the division of the y-axis by the correlation coefficient.
Implication. The proposed method should replace the ALCC algorithm and the current P values used in farming may need to be updated.
