Statistical methods

Gradiance combines an AI assistant with scientific Python tools. The method used depends on the analysis path and the instructions in your run. Confirm the model and processing in the completed result before reporting them.

Statistical analyses

Select the analysis that matches the experimental question and independent sampling unit. Each method returns its calculated quantities, assumptions, and relevant tables or plots.

• Association: Pearson or Spearman correlation, or single-predictor ordinary least-squares regression.
• Group comparisons: Welch or paired t-tests, one-way ANOVA, or Kruskal-Wallis. Optional multi-group pairwise comparisons use Holm adjustment.
• Distribution checks: descriptive statistics, a histogram and normal Q-Q coordinates, and Shapiro-Wilk normality testing.
• Discrimination and agreement: empirical ROC with DeLong AUC uncertainty, or Bland-Altman bias and limits of agreement.
• Repeated or nested observations: time-course comparison using one AUC per subject, or comparison of independent cluster means. These methods do not fit mixed models.
• Survival: Kaplan-Meier curves, at-risk tables, and log-rank comparison for right-censored independent subjects.
• Outlier review: a single-point Grubbs test or IQR flags. All supplied observations remain in the result.

Pairing, censoring codes, control roles, and the selected test must match the study design. The library reports an explicit outcome when required information or an estimable result is missing. Statistical intervals named 95% remain 95% intervals; a configurable significance threshold changes decisions, not their coverage.

Supported four-parameter logistic fits

The supported dose-response methods are unweighted 4PL, 5PL, and 3PL with lower plateau fixed at zero, fitted with SciPy’s curve_fit using bounded trust-region reflective optimization (method="trf"). This is distinct from an unconstrained Levenberg–Marquardt fit. Other fixed parameters and weighting are unsupported. For 5PL, the primary endpoint is the relative half-response concentration; its interval uses the full covariance and a Student-t delta method on log(midpoint), with n − 5 degrees of freedom. Unidentified or boundary fits do not receive covariance intervals.

Response = Bottom + (Top − Bottom) / (1 + (Concentration / IC50)^HillSlope)

In this 4PL convention, IC₅₀ is the concentration halfway between the fitted asymptotes. The sign of the Hill slope determines curve direction; its value alone does not establish binding stoichiometry or cooperativity. State whether the response is activity, viability, or inhibition, and retain concentration units.

Relative and absolute IC₅₀

A fitted midpoint is a relative IC₅₀. An absolute IC₅₀ refers to the concentration at a specified 50% response on a defined normalization scale. They coincide only under appropriate asymptotes and normalization. State which value you report and how it was calculated. A crossing outside the observed range is an extrapolation, and a crossing may not exist.

Weighting and replicates

The supported 4PL, linear or quadratic calibration, and Michaelis-Menten methods use unweighted least squares. Weighting is not an option in the supported launch contract.

Technical replicates describe measurement variability; independent biological replicates support biological inference. Identify the experimental unit and preserve the replicate structure. The executed-method record states whether observations were fitted individually or averaged by x value; the calculator does not infer biological independence or partition replicate variance.

Confidence intervals

When estimable, the supported 4PL reports local covariance-based 95% Student-t intervals for IC₅₀ and Hill, and Michaelis-Menten reports them for Vmax and Km. Top, Bottom, linear or quadratic calibration coefficients, and back-calculated unknown concentrations do not receive intervals. An interval can be unavailable when there are too few residual degrees of freedom or the covariance is near-singular. These are local fit approximations and do not quantify biological or across-experiment uncertainty.

The built-in IC₅₀ is fitted on the concentration scale. Do not describe its interval as back-transformed from log space unless your run actually used a log-parameter fit. Parameter intervals, confidence bands for a mean curve, and prediction intervals for new observations answer different questions.

Diagnostics and exclusions

Inspect residuals, the measured concentration range, plateau coverage, parameter bounds, and uncertainty. R² describes agreement with the observed responses; a high value alone does not establish the model or experiment’s validity. Fewer data points than needed to characterize the curve can produce a visually convincing but poorly identified fit.

Record missing values and exclusion decisions explicitly. Trusted raw-source execution does not silently discard invalid mapped values: it records empty unused roles, refuses selected rows with partial, nonnumeric, or nonfinite required values, and retains declared exclusions with their reasons. Preserve the original input and review which observations entered the fit.

Evidence and example figures

The figures currently shown on the landing page are illustrations generated from simulated measurements. They are not independent validation, instrument measurements, or evidence of agreement with a paper. Validation claims require traceable inputs, recorded execution, a stated reference method, and numerical comparisons.

When reproducing a published experiment, retain the source dataset and license, any digitization or transformation steps, the complete run outputs, and a comparison with the reference values. Agreement on one dataset does not establish performance across assay types.

Further reading

See the SciPy curve_fit reference for optimizer, covariance, and weighting semantics. Continue with quality control and reporting and reproducibility.