Statistical Metrics: R-squared, %CV, %RE Explained
Numbers without context can be misleading. A reported concentration of 50 ng/mL means little unless you also know how well the calibration curve fits the data, how reproducible the measurement is, and how closely the back-calculated standard values agree with their nominal concentrations. Three statistical metrics — R-squared (R²), percent coefficient of variation (%CV), and percent relative error (%RE) — answer exactly these questions and are reported by the K LAB MRX A2000 microplate reader for every run.
R-squared: Goodness of Fit
R-squared, or the coefficient of determination, quantifies how well the fitted curve describes the observed standard data. It ranges from 0 to 1: an R² of 1.000 means the curve passes through every standard point exactly; an R² of 0.900 means 10% of the variance in the response is unexplained by the model. For quantitative bioanalytical work, regulatory guidance typically requires R² ≥ 0.99 (linear) or, for ligand-binding assays, that back-calculated standard concentrations fall within ±20% of nominal (±25% at the LLOQ) rather than relying on R² alone. The K LAB Alpha and POP UV-Vis instruments regularly achieve R² up to 0.9999 in well-optimised linear assays.
An important caution: a high R² does not guarantee a correct model. A curved dataset can yield R² > 0.99 with a linear fit if the curvature is subtle and standards are sparse. Always inspect the residual plot alongside R².
%CV: Precision and Reproducibility
The percent coefficient of variation (%CV) is the standard deviation of replicate measurements expressed as a percentage of their mean:
%CV = (SD / Mean) × 100
%CV captures the random variability (imprecision) in your assay. A %CV of 5% means the standard deviation is 5% of the mean value — acceptable for most research-grade assays. For regulated bioanalytical methods (e.g., FDA Bioanalytical Method Validation), intra-run and inter-run %CV are typically required to be ≤15% (or ≤20% at the LLOQ). Sources of high %CV include inconsistent pipetting, reagent instability, temperature fluctuations during incubation, and edge effects on microplates.
- %CV < 5% — excellent precision, typical of well-optimised automated assays.
- %CV 5-15% — acceptable for most quantitative biological assays.
- %CV > 15% — investigate sources of variability before reporting results.
%RE: Accuracy of Back-Calculated Standards
Percent relative error (%RE) — sometimes called percent relative difference or, in recovery contexts, percent recovery — compares the back-calculated concentration of a standard (obtained by reading its absorbance off the fitted curve) to its known nominal concentration:
%RE = ((Back-calculated − Nominal) / Nominal) × 100
A %RE of +8% means the curve overestimates that standard by 8%. %RE diagnoses systematic errors (bias) in individual calibration points: a single standard with a large %RE often indicates a preparation error for that point. Accepted thresholds are typically ±15% (%RE magnitude), or ±20% at the lower limit of quantification (LLOQ).
Using the Three Metrics Together
No single metric tells the whole story. Consider this decision workflow:
- High R² + low %CV + low %RE across all standards: the curve is fit for purpose — proceed with unknown quantitation.
- High R² but one standard with %RE > 20%: likely a preparation error for that standard; rerun or exclude with documentation.
- Low %RE but high %CV: the curve is accurate on average but imprecise — check for random process variation (pipetting, temperature).
- Low R² with a non-random residual pattern: the wrong curve model has been chosen; switch from linear to 4PL/5PL or cubic spline as appropriate.
The MRX A2000 displays all three metrics per run and flags points that exceed user-defined thresholds, giving analysts an immediate, objective basis for accepting or re-running a plate. Documenting these acceptance criteria before the run — as required by GLP and GCP guidelines — ensures that pass/fail decisions are prospective rather than post-hoc.