I have generated several data sets under varying experimental conditions, that are plotted as hyperbolic curves. I have two experiments that were done under identical conditions, but the curve is not the same. I'll call experiment A the "ideal". The equation for this line is: y=(435.6*S)/(0.333*S). In experiment B, I would expect the same result but instead the equation I get is: y=(390.1S)/(0.3176+S)
I'd like to generate a correction factor to shift equation B to match equation A, and then apply that correction factor to other data sets within experiment B. Is this possible? How would I go about finding the correction factor?
First, to answer your question of how you shift a function like the one you've written, think of the function as a general function $f(x)$. You can shift this function to the right by writing a new function $f(y)$ where $y=x+a$. For your function this substitution is on the variable $S$. If $a>0$ the shift is to the left; conversely, if $a<0$ the shift is to the right. To shift up and down, write a new function $g(x)=f(x)+b$, where $b>0$ will shift up and $b<0$ will shift down. You can also apply a gain factor so that $h(x)=c\cdot f(x)$. This will generally distort your curve, so rather than shifting, it will flare open.
That said, from a statistics/experimental standpoint, warping data B to fit data A gives me pause. It sounds like there was some scaling difference between experiment A and experiment B that you are trying to eliminate (e.g., someone bumped a knob and all the data are off by a similar amount). That is a calibration question, and you can fit a nonlinear calibration curve between sets A and B that essentially provides a mapping from B to A. To do that you would want to plug your S-values from B into your fit from A. This would give you what you "should" have measured based on your A data. Plot the A-model predicted values versus your B measurements and do a nonlinear curve fit on that data set. The resulting equation converts a B measurement into the A measurement that it "should" have been.