Several comments:

The terminology used in the original question is troubling, " When to use ...". This phrase implies that we make this decision based on the instrument or sample, BEFORE we have analyzed it. This is counter to how samples are measured.

We do not select a data-point fit (formula type) until after we have collected all of the data, for each sample (or standard). Response is calculated from measured data. Once the data has been collected, then you can plot the data and let it SHOW YOU what the best formula is to describe it accurately. In general, the more data points, the better to describe it.

For most chromatography data sets that were collected using a method which followed proper chromatography guidelines and fundamentals, a linear fit is appropriate.

• Note: The number one reason why I am called in as a consultant to troubleshoot Quant or calibration results that are unreliable are due to the use of poor quality methods, not poor quality curve fits.

This data collection process requires that the data collected be within the range of the method (dynamic range, column load capacity, detector range etc).

• Some types of chromatography detectors are known for providing both linear AND non-linear outputs within their dynamic range, esp over more than one order of magnitude (i.e. CAD, ELSD...) so finding the best formula that accurately describes the data is very important. I have run many methods with these types of detectors where different curve fit formulas were needed to correctly describe EACH and every Sample / Standard set accurately. Fortunately, use of these types of specialized detectors is rare, so many will not have the experience of dealing with this additional complexity.

Perhaps this is a good time to point out that if you have a mixture of compounds, each one must be calibrated separately, in multiple levels, to acquire enough sample points to allow it to SHOW YOU what the best formula is to describe it.

It is not specifically technique or chemistry based. Let the actual data show you which formula is best suited to describe it.

If you read my initial post again, you'll find that I requested that our preferences be supported with references so that we are not misleading this discussion to non-disputed opinions.

I understand that you have extensive experience, but without putting your experience into peer-reviewed publications, your experience is just your own preference.

Going back to the topic. You assumed that I would pick my fitting formula before even I did the calibration curve points injection and observed their responses. This assumption might apply to a first timer, not me my friend.

If you give the discussion thread another thought, you would understand that I didn't start this discussion out of the blue, but after several years of chromatography and multiple projects involving different compounds with numerous chemistries. So, if you have an advice, state it please without a prejudice.

If you are experienced in chromatography, you would know that most of the analyses involve multiple analytes, not a single one or a couple of them. Because not all analytes are the same, not necessary that all of them can be fitted with the same order of equation. I have several examples of assays whereby there are more than 20 analytes being detected simultaneously. A linear fit would be ideal, but my initial question was about the cases whereby there is a need for quadratic fit. If you believe a quadratic fit isn't needed, why would equipment manufacturers put it in the software!?

It caught my attention that you raised a point about calibrating the mixtures as individuals. So let me pick it from there, if you have a mixture of say 5 proteins that come in one standard vial from the manufacturer at a similar concentration, would you make a serial dilution from this vial to make a calibration curve, or you would purchase them individually to make five different calibration curves and then apply these individual curves to the mixtures of proteins in the real samples? This is one constructive topic we may discuss.

Finally, what about the weighing power?

Please read my responses again. No opinion(s) are given except that your question does not address the features available in most research grade chromatography software. Curve fits can not be categorized into just two types, linear and quadratic. You make it sound like we must choose only between these two choices. Are you using a software package that limits you to only 2 types of curve fits? If so, that may pose a problem for some sample types. Why do you limit this to just two curve fit types when in fact, several types may be needed for some sample types (e.g. the n-polynomial fits are useful too)? Some real world samples require far more than 2 (proof can be found from experience using many types of specialized detectors and different compounds. The literature is filled with examples, but the easiest way to see examples would be to search for HPLC-ELSD based methods). To ask 'why' instrument vendors include various curve fit options in their software does not address an actual need, but a perceived one. IN the case of curve fits, the DATA determines which fits are appropriate (not the vendor) and we are fortunate that so many chromatography software vendors have continued to include and offer many different types, similar to what is found in good quality statistical software packages.

I never stated that Linear output should always be used. I stated that you should use the best fit, the best formula that describes the data. This is not an opinion, but the mathematical model used to describe a data set.

Regarding calibration of mixtures. This has nothing to do with them all coming in the same vial. It is about measuring the response obtained from EACH sample or standard (which is not related to them being in the same vial. That is concentration, not response). We calibrate and fit points based on response. Two different proteins with the same concentration in solution can have two different responses (e.g. depending on the detector used), and this is why we measure it, record it and then plot it for each compound.