# Method: qPCR ΔΔCt Calculator (method version 1.0.0)

## Calculation

1. **Replicates.** For each sample and gene, replicate Ct values with three or more replicates are screened with Tukey fences: quartiles by linear interpolation, IQR = Q3 − Q1, and values below Q1 − k·IQR or above Q3 + k·IQR are dropped (k = 1.5 by default, adjustable). The mean and sample SD use the remaining values. Screening is skipped when the IQR is 0.
2. **ΔCt** = mean Ct of the target gene − mean Ct of the reference gene. With several reference genes, their mean Ct values are averaged first.
3. **ΔΔCt** = ΔCt of the sample − mean ΔCt of the samples marked control, per target gene.
4. **Fold change** = 2^−ΔΔCt; **log2 fold change** = −ΔΔCt.

The 2^−ΔΔCt method assumes about 100% amplification efficiency (E = 2) for the target and reference genes. No efficiency correction is applied; genes outside 90–110% efficiency need an efficiency-corrected method (Pfaffl 2001).

## Conventions

- Blank, zero and non-numeric Ct entries (for example "Undetermined") are excluded when the data are read.
- A sample not marked as control is treated.
- A control sample compared with the control mean has ΔΔCt 0 and fold change 1.

## Worked examples

Three cases in `cases.json`, each with the arithmetic written out: a fourfold induction, the control against itself, and a stray replicate removed by the fence (edge case).

## References

- Livak KJ, Schmittgen TD. Analysis of relative gene expression data using real-time quantitative PCR and the 2^−ΔΔCT method. Methods. 2001;25(4):402-408. https://doi.org/10.1006/meth.2001.1262
- Pfaffl MW. A new mathematical model for relative quantification in real-time RT-PCR. Nucleic Acids Research. 2001;29(9):e45. https://doi.org/10.1093/nar/29.9.e45
- Bustin SA, et al. The MIQE guidelines: minimum information for publication of quantitative real-time PCR experiments. Clinical Chemistry. 2009;55(4):611-622. https://doi.org/10.1373/clinchem.2008.112797
- Tukey JW. Exploratory Data Analysis. Addison-Wesley; 1977. ISBN 0-201-07616-0.

## Changes from the page before this record

- The page described an optional Pfaffl efficiency correction. The page never passed efficiencies to the calculation, and the correction code ignored the reference gene's efficiency. The claim and the code were removed; the page now says no correction is applied.
- The page offered "Set to max Ct" for missing values. The file readers already drop blank and undetermined values, so the option never took effect. It was removed.
- Fold changes for the default settings are unchanged.