Comparing two quadratic calibration curves

[rblue2]

Hello,

In order to check for matrix effects I constructed two calibration curves, one made up with solvents, the other using my matrix. The two curves both fit quadratic equations best (y = -2.7484E-07x2 + 1.5453E-03x + 7.1982E-02 and y = -3.7290E-07x2 + 1.6799E-03x + 5.8039E-03), both also have R2 values >0.999.

I was wondering if anyone could offer some advice on what is the best way to go about comparing these two quadratic calibration curves to see if matrix effects are an issue or not? Are there any stats test I can apply to these curves, or am I best just simply to quote the two equations? I am happy using R, SPSS or Excel for any analysis.

Thanks

[MaryCarson]

Is there justification to fit to a quadratic curve? It looks like the x2 values are 4 orders of magnitude less than the x values--i.e., they are not really significant contributors. I would just do linear calibrations then test whether slopes and intercepts are statistically different.

You don't mention the range of the calibration curves or the number of levels used. You may need to use weighting if your range is more than 1 order of magnitude. Residuals are a better indicator of good fit than R^2.

For matrix effects, your best comparator is slope. If the intercepts are different, especially if the matrix curve intercept is significantly higher, you probably have an endogeneous peak in the matrix underlying your analyte. Your slopes look similar to me, but the intercept in your first curve seems pretty high. If your residuals are good, I would go back and look at blank matrix (if the first equation came from your matrix curve).

[lmh]

whether you need a quadratic curve in this instance depends on the range of "x". I agree with Mary, you should consider whether you need it, and she's right you can do that by looking at residuals.

If your values of x are in the range 0-200, you'll probably find that a straight line will be almost identical to the quadratic line, but you'll have a dreadful y-axis intercept.

If your values of x are in the range 0-2000 then the curve is strong, and you definitely need a quadratic fit or your residuals will have huge systematic errors.

Incidentally, any set of data will always fit a quadratic curve at least as well as a straight line, and any data with random errors will fit a quadratic curve better than a straight line. The more parameters you give the fitting line, the better it will fit...

It's much easier to test whether two straight lines are the same, because many chromatography packages will estimate the error on the intercept and gradient of a straight line, and if they won't, Excel's "linest" function will do it for you. I'm as interested as you are in any comments on how to do this with a quadratic line!

[rblue2]

Thank you both for your replies.

Just looking at the data it seems fairly apparent that the relationship is not best described by a linear relationship. I tried fitting linear, quadratic and cubic models to both calibrations curves and compared the three models fits using an anova. There was significant change in the R2 value between the linear and quadratic model, but no significant change for the cubic model.

I already know that my matrix contains the analyte of interest, I took this into account by determining the mean concentrations in my 'blanks' before hand and then spiked this matrix with methanolic standards.

My calibration curve uses the concentrations 0, 10, 200, 400, 600, 800 and 1000 and 363, 373, 563, 763, 963, 1163 for the matrix matched samples. I have four replicates at each concentration (although one replicate is missing for one of the matrix matched concentrations).

I have also looked at the residuals and seem to get slightly more even scatter around 0 when quadratic or cubic models are fitted. Although at the lowest concentrations (0, 10) there is little spread in the residuals I would not say that my data is heteroscedastic.

Do you still think I am best to try and use a linear equation?

Many thanks again for all you help.

[Peter Apps]

If you have multiple points at each level of each calibration then you can get a standard deviation for each parameter of the curve, then do a t-test for significance.

Peter

[MaryCarson]

What concentration range are you interested in for your analyte, and why does your matrix curve start so much higher than your solvent curve?

You are not using the origin as point in either curve, are you?

What are the residuals? linear vs. weighted (1/x and 1/x2) vs. quadratic?

[Alexandre]

Or anova of 3 parameters a, b and c of ax2+bx+c of each curve.