How to determine if two calibration curves are parallel, within 5%
I have complex matrices and I need to make sure the matrix does not affect the measurement of my analyte. To do that, I need to prepare samples of my analyte in a solvent and of the matrix reinforced with my analyte. Both curves are going to have 5 concentration points, each done 3 times and, for sake of argument, let's assume both have comparable levels of precision. Then, I linearize these two calibration curves and check if they are parallel, which is where my question lies.
How do I prove that both curves are parallel (meaning no matrix effects are present), within a margin of 5%?
I have found the following method:
1. 870
Get the y-data of the matrix data and apply them to the calibration function of the solvent and get an "apparent concentration" of the matrix.
2. Perform a linear regression of the concentration values of the solvent with the apparent concentrations of the matrix.
Then, I have an intercept a and a slope b. A value of b different from 1 indicates a concentration dependent bias. I have both standard deviations of the fit, stdev_a, stdev_b, so I have to determine the confidence interval (95%) of b and check if their values are withing these confidence intervals.
I have found two ways to do that in Excel and I am unsure which one is correct. For example, the slope:
* Do I use the conf = CONFIDENCE.T(0.05, stdev_b, N-4), get b+-conf, and check if 1 is within this interval b+-conf?
* Do I use t = T.INV(0.95,N-4), multiply that by the stdev_b, get the range b+-t*stdev_b and check if 1 is within this range?
I have used N-4 for the degrees of freedom, since it's two linear regressions, each consuming one degree of freedom, correct? In this case, N-4 == 11.
In summary:
* Which function do I use to calculate the confidence intervals for this example in Excel, and
* Is this method of checking parallelism correct?
* Is there an easier/simpler or more correct way of doing this parallelism check? 1021