which a wide range of dilution assays can be modelled. Estimates of may describe satisfactorily over the range of doses tested, but they do not necessarily have to describe beyond that range. However, this does not mean that dissimilar curves can be restricted to an interval where they happen to be similar. In practice, itself is rarely of interest. More of interest is an estimate of or an estimate of the dose that induces a specific response. These estimates involve taking ratios of statistically dependent parameter estimates. Fieller's theorem can be used to compute confidence intervals of these ratios. Some special cases deserve particular mention because of their widespread use: If is linear and this is known as a slope-ratio model. If is linear and this is known as a parallel line model. Another commonly applied model is the probit model where is the cumulative normal distribution function, and follows a binomial distribution. Example: Microbiological assay of antibiotics An antibiotic standard (shown in red) and test preparation (shown in blue) are applied at three dose levels to sensitive microorganisms on a layer of agar in petri dishes. The stronger the dose the larger the zone of inhibition of growth of the microorganisms. The biological response is in this case the zone of inhibition and the diameter of this zone can be used as the measurable response. The doses are transformed to logarithms and the method of least squares is used to fit two parallel lines to the data. The horizontal distance between the two lines (shown in green) serves as an estimate of the potency of the test preparation relative to the standard. Software The major statistical software packages do not cover dilution assays although a statistician should not have difficulties to write suitable scripts or macros to that end. Several special purpose software packages for dilution assays exist. References Finney, D.J. (1971). Probit Analysis, 3rd Ed. Cambridge University Press, Cambridge. Finney, D.J. (1978). Statistical Method in Biological Assay, 3rd Ed. Griffin, London. Govindarajulu, Z. (2001). Statistical Techniques in Bioassay, 2nd revised and enlarged edition, Karger, New York. External links Software for dilution assays: PLA CombiStats Unistat BioAssay Pharmaceutical industry Drug discovery Biostatistics