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_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)
, getb+-conf
, and check if1
is within this intervalb+-conf
? - Do I use
t = T.INV(0.95,N-4)
, multiply that by thestdev_b
, get the rangeb+-t*stdev_b
and check if1
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?