A memory in a sensor is used to store multiple coefficients for a physiological parameter. In one embodiment, not only are the sensor's specific calibration coefficients stored in a memory in the sensor for the formula to determine oxygen saturation, but multiple sets of coefficients are stored. The multiple sets apply to different ranges of saturation values to provide a better fit to occur by breaking the R to SpO2 relationship up into different pieces, each described by a different function. The different functions can also be according to different formulas for determining oxygen saturation.