Understand the relationship
The reasoning behind the result
A spillover coefficient is a background-centered control slope
SOVi→j = (Pj−Nj)/(Pi−Ni)
For one single-stain source i, the positive-minus-negative change in secondary detector j is divided by the corresponding change in the source's primary detector i.
The arithmetic relies on the entered summaries. It cannot establish that the positive and negative populations have matched autofluorescence, that the signal is within the detector's linear range or that the gates identify suitable controls.
The spillover matrix maps source-signal space into detector space
y = cS
This workbench follows the displayed row-source/column-detector convention: each row describes how one source signal contributes to every observed detector, and the diagonal is one.
Matrix orientation is part of the result because software exports and prose may use different layouts. Transposing a matrix silently changes the calculation.
Compensation applies the inverse relation
c = yS⁻¹
The inverse is applied to the complete entered detector vector. Pair-by-pair subtraction is not equivalent when several source signals contribute across several detectors.
A singular matrix has no unique inverse. An ill-conditioned matrix can amplify small coefficient or signal changes, so the workbench rejects matrices beyond its stated numerical condition limit.
Negative corrected values remain numerical observations
Compensation is a linear operation and can produce signed corrected values. Clamping them to zero would change the matrix result and hide the entered-model residual.
A negative corrected value does not by itself establish overcompensation, a failed control, biological absence or an invalid experiment.
Spillover spreading is a different quantity
A spillover-spreading matrix describes additional variance or signal spread associated with spillover and measurement statistics. Its entries are not the conventional spillover fractions used here.
This workbench therefore does not accept robust standard deviations or calculate a spreading-error matrix, panel score or fluorochrome ranking.
Follow the numbers
Resolve and apply a two-channel control-derived matrix
- For the FITC-A single-stain row, the entered FITC-A difference is 10,000 and the PE-A difference is 1,000, so FITC-A→PE-A spillover is 0.10.
- For the PE-A single-stain row, the FITC-A difference is 2,000 and the PE-A difference is 10,000, so PE-A→FITC-A spillover is 0.20.
- The row-source/column-detector matrix is [[1, 0.10], [0.20, 1]].
- The observed Tube 1 vector is [3,340, 4,450]. Multiplication by the inverse matrix gives [2,500, 4,200].
- Reapplying the spillover matrix to [2,500, 4,200] reconstructs [3,340, 4,450], leaving only floating-point roundoff in the displayed reconciliation column.
The control deltas, normalized spillover coefficients, inverse and corrected signals remain independently inspectable.
Quick guide
How to use this calculator
- Use the pairwise mode to audit one entered positive-minus-negative control slope without constructing a full matrix.
- Use the control-derived mode only when every declared source has an entered single-stain positive and negative summary in every detector, all under the same acquisition configuration.
- When applying a matrix, preserve the displayed row-source/column-detector orientation and declare whether coefficients are fractions or percentages.
- Review the spillover matrix, its computed inverse, the reconstruction difference and any retained negative corrected signals before using the record elsewhere.
Calculation method
Calculation and interpretation
Keep control differences, spillover coefficients, matrix orientation, inverse compensation and corrected signals visible as separate quantities.
Pairwise SOVsource→detector = (positive secondary − negative secondary)/(positive primary − negative primary). For a row-source/column-detector spillover matrix S: observed row y = corrected row c × S, so c = y × S⁻¹.
Worked example
Resolve and apply a two-channel control-derived matrix
The control deltas, normalized spillover coefficients, inverse and corrected signals remain independently inspectable.
Pairwise SOVsource→detector = (positive secondary − negative secondary)/(positive primary − negative primary). For a row-source/column-detector spillover matrix S: observed row y = corrected row c × S, so c = y × S⁻¹.
Supported inputs
Precision and limits
Entered summaries and matrices only
The workbench does not read FCS files, select populations, fit event clouds, identify fluorochromes, import instrument metadata or modify analysis files.
Conventional compensation only
It does not perform spectral unmixing, autofluorescence extraction, AutoSpill-style regression, nonlinear correction or time-dependent compensation.
Control validity remains external
Matching fluorochromes and tandem lots, comparable autofluorescence, positive/negative gating, detector linearity, voltage settings, treatment compatibility and sufficient events require experimental review.
No spreading-error calculation
Spillover spreading, measurement variance, stain index, panel optimization and resolution are separate analyses and are not inferred from coefficient magnitude.
Numerical conditioning is not assay quality
The reported infinity-norm condition estimate describes only matrix inversion sensitivity. The workbench rejects estimates above 1e+10 but supplies no experimental pass/fail threshold.
No biological or clinical interpretation
Corrected signals do not define gates, identify cell populations, establish positivity, diagnose a sample or validate an assay.
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