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:


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), 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?
Define the angular coefficients of the two resulting lines and evaluate the parallelism between them. Perform the statistical evaluation of the data.
For the parallelism test between the curves, considering the equations of the lines to be compared as: $y_1 = a_1 + b_1x + \varepsilon$ and $y_2 = a_2 + b_2x + \varepsilon$, the hypothesis for comparison of the lines slopes is given by:
$$H_0 : b_1 = b_2$$
$$H_1 : b_1 \neq b_2$$
When the null hypothesis ($H_0$) is true, the regression lines become: $$y_1 = a_1 + b_3x + \varepsilon$$
$$y_2 = a_2 + b_3x + \varepsilon$$
Considering a significance level of $5\ \%$, the null hypothesis will be true when the test returns a P-Value above $0.05$.

More information in the link:
http://www.real-statistics.com/regression/hypothesis-testing-significance-regression-line-slope/comparing-slopes-two-independent-samples/