Standard addition
Standard addition estimates the native amount in a sample from the responses of its unspiked and spiked aliquots. The Cal group Mode is Standard addition. The native concentration is the x-intercept of a straight line of response against added on-column dose, written as intercept / slope.
Use it when you do not want the reported native amount to be a reading from a separate calibration curve. Spike recovery is the other case: the fortified vial stays on a normal curve and the spike is only a control. SpikeGroup is for spike recovery only. Standard addition does not read it. See Spike recovery.
Spike recovery vs standard addition
| Spike recovery | Standard addition | |
|---|---|---|
| When | A calibration curve already exists. The fortified vial is a control. | The native amount is estimated from the sample’s own unspiked and spiked aliquots. |
| Cal group Mode | Calibration (the normal mode). | Standard addition. |
| Where the fortified vial sits | In the same Cal group as the calibration samples. Pairing is SpikeGroup, not the Cal group. | In the Cal group whose mode is Standard addition, with the unspiked aliquots. |
| Sample type | Sample or QC. A dose marks the spike. | Spiked aliquots are Sample with a Dose. Unspiked aliquots are Sample without a Dose. |
| How the unspiked vial is used | With a SpikeGroup, recovery subtracts the mean Conc of the used unspiked vials in that group. Without a SpikeGroup, it is not subtracted. | Samples that share the Cal group are pooled into one addition for that quant. |
| Conc | Read from the external curve. SpikeGroup does not change it. | Read from the external curve when that group also has calibration samples. Otherwise replaced from the addition. |
| NConc | A Sample with a dose, and a QC with a dose in a SpikeGroup, subtract the on-column dose. Other QC, Calibration, and CCV keep the curve concentration. | One shared native on Sample and Solvent in that Cal group and quant. Calibration, QC, CCV, and Blank keep the native from quantitation. |
| RecPct | With a SpikeGroup: 100 × (curve concentration − unspiked reference) / on-column dose. Without a SpikeGroup: 100 × curve concentration / on-column dose. | On Sample and Solvent: 100 × (Conc − NConc) / on-column dose. |
What to set
- Put the aliquots that belong to one addition in one Cal group. In Cal groups, set that group’s Mode to Standard addition. A different Cal group is a different addition. The sample key is not used to split the group.
- Set each unspiked aliquot to type Sample and leave Dose empty.
- Set each spiked aliquot to type Sample and set Dose to the amount added (the spike), not the total amount you expect in the vial. Do not mark those aliquots as Calibration.
- Enter level names under View → Doses. Enter the added concentration for each analyte under View → Analyte doses. Use off on a level keeps that level out of the dose lookup.
- Set Dil on each aliquot. The added amount on the line is the analyte dose concentration divided by Dil. A dilution of 0 or below is treated as 1.
- The reserved dose name IS is the spike for ISTD and Surrogate analytes. On a target, IS is not an added dose.
- Calibration samples are optional. If this Cal group also contains type Calibration, those injections still build the external curve (by the method’s Initial, Partial, Bracket, or Bracket with borrow mode). The addition then writes a shared native beside that curve. If the group has no calibration samples, Conc is replaced from the addition, as below.
Quantitate reads any external curve first, then runs standard addition, then spike recovery, then blank-concentration correction. Spike recovery does not change a Standard addition group.
How the native concentration is calculated
For each Standard addition Cal group, and for each quant, Analyze builds one addition line from the Sample and Solvent injections in that group. Calibration, QC, CCV, and Blank injections stay off the addition line, and the addition does not write NConc, RecPct, or FConc onto them.
- Spiked: x is the on-column dose (the result Dose). y is the response. When this quant’s ISTD result is ready, y is the response divided by the ISTD response. x is not divided by the ISTD amount.
- Unspiked: x is 0. y follows the same response rule. A response of 0 is a real point.
- A response that is missing or not a valid number is left off the line. An ISTD that is assigned but not ready leaves that injection off the line.
- A point is left out of the fit when its bracket Use is off, its response Use is off, the result or sample is rejected, or the dose level’s Use is off. A stored dose does not put the vial on the line when that level’s Use is off. Turning Use back on, the same way as on a normal calibration point, refits the line and recomputes NConc, RecPct, and FConc.
The line is linear with a fitted intercept. The quant’s Weight is applied. The quant’s curve type and origin are not. The fit runs when at least two included points have different added doses and the slope is a valid non-zero number. One unspiked aliquot plus one spike is enough when those two x values differ. NConc = intercept / slope, then kept at or above 0.
That native is written onto the Sample and Solvent results for that quant. It is not written onto Calibration, QC, CCV, or Blank.
When fewer than two included points have different added doses, or the weight cannot accept a point (for example 1/x with an undosed aliquot at x = 0), the line is not fitted. Conc and NConc stay as quantitation left them. Warnings contains: Standard addition could not resolve a shared native concentration.
Conc on Sample and Solvent depends on whether the group contains a calibration sample:
- No calibration sample in the group, and the line was fitted: an unspiked result’s Conc is set to the native, and a spiked result’s Conc is set to native + on-column dose. Both are kept at or above 0.
- Any calibration sample in the group: Conc stays the external-curve reading.
RecPct, on Sample and Solvent only, is then 100 × (Conc − NConc) / on-column dose. It is empty when the dose is missing or 0. DevPct = RecPct − 100. Calibration and QC keep the recovery written from the curve, 100 × Conc / dose.
CalcFConc = NConc × Dil × the limit group’s Final Conc multiplier (empty multiplier = 1). FConc is ManFConc when set, otherwise CalcFConc. Standard addition updates CalcFConc on Sample and Solvent only.
When Blank corr is on and the origin is not Blank offset, Sample then subtracts BConc from the shared NConc only. QC subtracts BConc from its own on-curve NConc, not from the shared native. Conc and RecPct are not recalculated. Blank, Calibration, and Solvent do not get that subtraction.
For a Sample or Solvent in a Standard addition group, concentration flags compare NConc (not CalcFConc) with the too-low and too-high limits. The recovery flag still compares RecPct with the limit group’s recovery window. The result R² flag uses this addition bracket’s R², the same way an external bracket’s R² is used. A missing R² counts as below the minimum.
How spiked aliquots relate to the unspiked aliquot
Quanto does not pair one spiked file with one unspiked file, and it does not use the sample key. Every live Sample and Solvent in the Cal group is part of the same addition for that quant. Two physical samples that share the group share one native.
Calibration, QC, CCV, and Blank vials in the group stay off the line and do not receive that shared NConc.
A second Cal group, or a group left on Mode Calibration, is a separate calculation.
Where the values show up
On the result grid:
| Column | What it shows |
|---|---|
| Conc | External-curve concentration, or native / native + dose when the group has no calibration samples. |
| Dose | On-column added dose. |
| NConc | The shared native on Sample and Solvent (intercept / slope when the line was fitted). |
| RecPct | 100 × (Conc − NConc) / dose on Sample and Solvent. |
| DevPct | RecPct − 100. |
| CalcFConc | NConc × Dil × Final Conc multiplier. |
| FConc | ManFConc when set, otherwise CalcFConc. |
| BConc | Blank concentration subtracted from NConc when Blank corr ran. |
| R² flag | Too low when this addition bracket’s R² is missing or below the limit group’s minimum curve R². |
| Warnings | The standard-addition failure note, and any blank-correction notes. |
The addition line is stored as a calibration bracket. The bracket grid lists its points. Use on a point works the same way as on a normal calibration point: off leaves that point out of the fit, and the line, NConc, RecPct, and FConc are computed again. Unused points are drawn the same way as unused points on a normal curve.
In Calibration / Curves, the addition bracket is its own column. The chart title is Standard addition · the Cal group name. The x-axis title is Added dose. The fitted line is drawn through the points and out to the x-intercept. That intercept is marked NConc with the reported value.
Report names for the bracket are the usual curve fields: Bracket.Coeff0, Bracket.Coeff1, Bracket.CurveR, Bracket.CurveR2, Bracket.CurveFormula, Bracket.MaxRelativeResidual. Result formulas stay Result.Concentration, Result.Dose (also Result.DosedConcentration), Result.NativeConcentration, Result.RecPct, Result.DevPct, Result.CalcFConc, Result.FConc, Result.BlankConcentration, Result.R2Flag, Result.Warnings.
Example
These numbers are an illustration. Responses follow y = 10 + 5x. Dilution is 1. No calibration samples are in the group, and blank correction is off.
| Vial | Type | Added dose | Response |
|---|---|---|---|
| Unspiked | Sample | (none) → x = 0 | 10 |
| Spike A | Sample | 1 | 15 |
| Spike B | Sample | 5 | 35 |
The unspiked aliquot and the two spikes are three distinct added doses, so the line is used. Slope 5, intercept 10, NConc = 10 / 5 = 2. With no calibration samples in the group, Conc is replaced:
| Vial | Conc | NConc | RecPct | FConc |
|---|---|---|---|---|
| Unspiked | 2 | 2 | (empty) | 2 |
| Spike A | 3 (2 + 1) | 2 | 100 | 2 |
| Spike B | 7 (2 + 5) | 2 | 100 | 2 |
RecPct is 100 because Conc was set to native + dose. A second Cal group with different responses gets its own native and does not change this one.
A different illustration, with calibration samples in the same group (slope 10 through the origin) and one spike plus one unspiked aliquot. Those two added doses differ, so the addition line is fitted. Responses are y = 30 − 15x, so intercept / slope = −2, and NConc is kept at 0. Conc stays the curve reading. The calibration results keep the native quantitation gave them. The spike’s RecPct is 100 × (1.5 − 0) / 1 = 150.
| Vial | Type | Dose | Response | Conc from the curve | NConc |
|---|---|---|---|---|---|
| Cal 1 | Calibration | 1 | 10 | 1 | (unchanged) |
| Cal 2 | Calibration | 2 | 20 | 2 | (unchanged) |
| Spike | Sample | 1 | 15 | 1.5 | 0 |
| Unspiked | Sample | (none) | 30 | 3 | 0 |
If that spike were the only Sample, the line would not be fitted. Conc and NConc would stay the curve values, and Warnings would contain Standard addition could not resolve a shared native concentration.
Limitations
- x is the added on-column dose. It is not an ISTD ratio, and it is not corrected by a spike volume.
- Aliquots that share a Cal group share one native even when their dilutions differ. FConc then multiplies that native by each sample’s own Dil.
- With no calibration samples in the group, a successful line sets spiked RecPct to 100, because Conc is defined as native + dose.
- Weight 1/x, 1/x², or Log cannot use the undosed point at x = 0. The line is then not fitted and the failure note is written.
- NConc is kept at or above 0, including after blank subtraction.
- Blank correction changes NConc and does not update RecPct, so the recovery no longer matches Conc − NConc after a non-zero blank.
The standard-addition example batch is described in Example batches.