All examples · Example 17 of 34
Scatter Plot: qPCR Standard Curve
Threshold cycle (Ct) against log10 template copy number for a 7-point, 10-fold dilution series in triplicate, with the least-squares line.
Key findings
- Pearson r = -0.99976 (r² = 0.99952): Ct is almost perfectly linear in log copy number.
- Slope -3.354 cycles per 10-fold dilution → amplification efficiency 98.7%, inside the accepted 90–110% window.
Replicate Ct at each dilution
Three technical replicates per dilution. A tight SD within each dilution is what makes a standard curve usable.
| Group | n | Mean | SD | SEM | Median | Q1 – Q3 | Min – Max | Skewness | Excess kurtosis |
|---|---|---|---|---|---|---|---|---|---|
| 10^1 copies | 3 | 34.83 | 0.1709 | 0.09866 | 34.85 | 34.75 – 34.92 | 34.65 – 34.99 | -0.519 | — |
| 10^2 copies | 3 | 31.54 | 0.1664 | 0.09609 | 31.47 | 31.45 – 31.6 | 31.42 – 31.73 | 1.56 | — |
| 10^3 copies | 3 | 28.16 | 0.1115 | 0.06438 | 28.2 | 28.12 – 28.22 | 28.03 – 28.24 | -1.48 | — |
| 10^4 copies | 3 | 24.82 | 0.1513 | 0.08737 | 24.87 | 24.76 – 24.91 | 24.65 – 24.94 | -1.32 | — |
| 10^5 copies | 3 | 21.43 | 0.04619 | 0.02667 | 21.46 | 21.42 – 21.46 | 21.38 – 21.46 | -1.73 | — |
| 10^6 copies | 3 | 18.05 | 0.1552 | 0.08963 | 18.04 | 17.97 – 18.12 | 17.9 – 18.21 | 0.289 | — |
| 10^7 copies | 3 | 14.76 | 0.3153 | 0.1821 | 14.69 | 14.59 – 14.89 | 14.48 – 15.1 | 0.909 | — |
LabTools call
stats.describelabtools stats describe --groups @groups.json
The same method is available as an MCP tool (stats_describe) and from the desktop app's statistics panel.
Linearity of the curve
A standard curve is only usable if Ct falls linearly with log copy number. All three coefficients should be close to −1.
| Coefficient | Estimate | r² | n | p |
|---|---|---|---|---|
| Pearson r (linear) | -0.9998 | 0.9995 | 21 | 4.9 × 10⁻³³ |
| Spearman ρ (monotonic, rank) | -0.9912 | — | 21 | 3.8 × 10⁻¹⁸ |
| Kendall τ (rank, tie-robust; normal-approximation p) | -0.9429 | — | 21 | 2.2 × 10⁻⁹ |
LabTools calls (3)
stats.correlationlabtools stats correlation --a @log10_copies.json --b @Ct.json --method pearson
stats.correlationlabtools stats correlation --a @log10_copies.json --b @Ct.json --method spearman
stats.correlationlabtools stats correlation --a @log10_copies.json --b @Ct.json --method kendall
The same method is available as an MCP tool (stats_correlation) and from the desktop app's statistics panel.
LabTools notes
- Pearson's r measures LINEAR association only, and is sensitive to outliers. A scatter plot (plot.create kind='scatter') is worth a look before reporting it; use method='spearman' if the relationship is monotonic but curved.
Methods paragraph
Written to go straight into a manuscript.
The standard curve (Ct = −3.354·log10 copies + 38.22) was linear over seven orders of magnitude (R² = 0.9995; Pearson r = −1.000, p < 0.0001), giving an amplification efficiency of 98.7%.
Every number on this page was computed by the LabTools statistics engine (version 0.14.3) from the example's CSV on 2026-09-23. Where a value was derived before the data reached LabTools (replicate means, paired differences, log odds ratios), the text says so. The data are simulated from a fixed random seed.
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