Zero Intercept and residual plots

[mijnadarian]

Hey Guys

Hello guys
Question is the following

We know that R square gives the value of 0.99 or higher value we are taking in parameter in order to see if this is a good curve.
My question is the following
How would you catch mistakes of a "perfect" curve?

Let me elaborate

How would you perform a Zero-Intercept test?
How would you calculate residual plots in your curve to determine whether the results are the True values?

Thank you

[aceto_81]

First of all: R^2 > 0.99 doesn't guarantee a good fit!!
You could have a logaritmic model, but if you keep your range narrow enough, you can have a R^2 0.99.

As a zero-intercept test, you could do a t-test to see whether the confidence interval of the intercept include 0.

I'm not sure how to interpret your residual plots question.


Ace

[lmh]

I'm inclined to think that zero-intercept is (or ought to be) a bit of a red herring.

Ideally we should always be defining a range over which our measurement works; the limits of quantification. Between these limits, the error (difference between measured value and real, known value) must be less than a certain predefined value (with a certain, predefined confidence). If the assay is good between the limits, does it matter what it does outside the limits? I don't care what my calibration curve looks like outside the regions in which I am using it.

Zero intercepts are really most relevant if you suddenly try to quantify samples way below the lowest point on your calibration curve. But none of us has ever done that, have we???

The more interesting question is looking for systematic errors between the measurements and the calibration curve, and this is where looking at residuals can come in.

[mijnadarian]

Ace and Imh
Thanks for responding

My concern is following

If I get an intercept in calibration curve-
Have I made a systematic error?

I have a curve that I have an intercept with; and I'm looking to see where I have made a mistake?

Thanks guys

[aceto_81]

...
Zero intercepts are really most relevant if you suddenly try to quantify samples way below the lowest point on your calibration curve. But none of us has ever done that, have we???...

Or if you want to use a single point calibration...

If you have an intercept, there can be various reasons: systematic error, carryover, some co-elution with your matrix, ...

Ace

[HW Mueller]

The statements of Imh are quite confusing to someone, like me, who has been "shaky" with some aspects of statistics. In my understanding residuals have more to do with randomness (precision) rather than systematic error. Also, it seems that if the curve does not go through zero, then at least the lowest calibration point must have a systematic error in it? Neglecting the zero intercept would then be "licence"?
Isn´t here anybody who can straighten out this mess? Googling doesn´t help much. you just see the usual formulars, which are fairly easy to undestand, but not their consequences. For instance the r and r^2 discussion in the other threat is also typical of the blind helping the blind. In the internet the r apparently goes by different names, residual being the more common? r^2 is also called the coefficient of determination. It is all confusing, in my case already because I have always had trouble distinguishing the independent from the dependent variable. Mathematically it js all more or less understandable, but the "handle" is missing.

[aceto_81]

The statements of Imh are quite confusing to someone, like me, who has been "shaky" with some aspects of statistics. In my understanding residuals have more to do with randomness (precision) rather than systematic error. Also, it seems that if the curve does not go through zero, then at least the lowest calibration point must have a systematic error in it? Neglecting the zero intercept would then be "licence"?
Isn´t here anybody who can straighten out this mess? Googling doesn´t help much. you just see the usual formulars, which are fairly easy to undestand, but not their consequences. For instance the r and r^2 discussion in the other threat is also typical of the blind helping the blind. In the internet the r apparently goes by different names, residual being the more common? r^2 is also called the coefficient of determination. It is all confusing, in my case already because I have always had trouble distinguishing the independent from the dependent variable. Mathematically it js all more or less understandable, but the "handle" is missing.

I will give it a try, if not clear, just ask.

The residuals are due to randomness and precision, as you point out, in an ideal world!
If you take a look at your residual plot, and don't see an even spread, you might think about a systematic error (take a look at http://images.google.be/imgres?imgurl=h ... jAfh1uDgBg)

This gives you an idea about how it should NOT be.
So non linearity can be determined from a residual plot.
If on the other hand, the residuals are normal spread across the entire calibration line, but still no intercept through zero, then you have another problem, like coelution, dilution errors, ...

If you can use a calibration line not going through zero depends on your application or in house protocols.

I hope I clarified a bit?

Ace

[HW Mueller]

Not really, I am thinking of a mistake in the analytical process when I consider "systematic error", not of an intrinsic nonlinear response. If one tries to force a straight line through a curving one, then one can indeed provoke a systematic error.
In my experience, an inspection of the data reveals faults in the method much more quickly than all this jazz, as I mentioned before I have used ANOVA more for fun, and mostly because one has to "standardize" evaluations of ones data when publishing.

[tom jupille]

For anyone who seriously wants to understand all of this, there is a great series of articles written by David Coleman and Lynn Vanetta in "American Laboratory" magazine. You can download the series (34 of them as I recall) from their web site, but you will have to register with them to access the content. The series is extremely well-written, and actually uses chromatography as examples. Here's a link that will redirect you to the appropriate place on their site:
http://www.lcresources.com/sandbox/amla ... stics.html

[lmh]

aceto_81 and HW mueller, you've put much more clearly than I could have, what I think I was trying to get at, and sorry to have been confusing.

Like HW Mueller, I hope I can judge when my straight line fit is not a good model for a calibration curve by looking at it, but I've heard many others use plots of residuals for the purpose, which is why I mentioned the concept.

All I was trying to suggest with the intercept problem is that if the method gives the right answer over the whole range where I use it, then I am happy with the method.

Aceto_81, yes, sorry to have forgotten single-point calibration.

Thanks Tom for the useful reference.

[orcicdejan]

There is one more nice article:

M.M. Kiser, J.W.Dolan, Selecting the Best Curve Fit, LC Troubleshooting, LC-GC Europe, 17(3) 138-143 (2004))

[HW Mueller]

American Laboratory doesn´t process my registration, so I have not been able to look into these articles, the titels are already overwhelming, though.