The variance function of the difference and the difference of the variance functions between two estimated responses for rotatable designs
Medicinal herbs constitute an important source of raw materials for both the traditional and the conventional medicine. Due to their availability all over the world, they play a key role in world health as complement if not substitute to conventional medicine mainly due to lack of suitable, effective, cheap and reliable drugs at the time they are required and in many cases in the remotest places of the world. Over reliance on herbal drugs whose active ingredients have not been quantified resulting to different herbalist prescribing different concoctions depending on the flora availability, may lead to resistance development, overdose or under dose which may lead to negative repercussion. For these reasons there is need to standardize commonly used herbal drugs, by formulating a mathematical model that can be used to determine the best combination of herbs and best preparation practices in order to achieve the optimal response. By so doing, useful results and conclusions can be drawn by planned and designed experiment. Response surface methodology as a statistical technique is useful in modeling and analysis of problems in which response of interest is influenced by several variables where the objective is to optimize the response. This is equivalent to locating feasible treatment combinations for which the mean response is optimized. This excursion yields interesting patterns of the response surface where ridges are mapped with a view to identifying combinations which give optimal response. It is of interest to note how to discriminate amongst the various points on the response surface which the yield is the same for different combinations of the predictor variables and to isolate the ones which are identified as parsimoniously feasible. This research employs response surface methodology to investigate effectiveness of herbal medicine in reducing the blood sugar level of a diabetic to a level that is acceptable. In this setup, observations are made to investigate effectiveness for particular dosage at reducing the blood sugar level with time. The variance function comes in handy as a tool for discrimination between two points on the identified response surface. The most feasible of all the identified points of equal yield is the one in which the variance function is minimal. In this research we use the variance function of the difference as well as the difference of the variance functions between two points to provide reliable advice on the range around which the dosage is desirable and time required to effectively reduce the blood sugar level to acceptable range. Key words: Response surface; Rotatable design; Variance function ; diabetic; Herbal-Medicine; treatment.