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:
- 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.
- 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_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
1is within this interval
- Do I use
t = T.INV(0.95,N-4), multiply that by the
stdev_b, get the range
b+-t*stdev_band check if
1is 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.
- 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?