Case studies in turning data into
clear, defensible decisions.

A client used three different test methods that measure related but not identical aspects of a product. Each method reported results in different units and on different scales, making direct comparison difficult.

• Setting: Three analytical methods with different units
• Core question: Do the readings move together, and can one test help predict another?

• We first visualized the data using standardized scales, correlation plots, and simple regression fits, so trends were visible without requiring the client to think in transformed units.
• We then fit regression models where each method in turn was treated as a “response” and the other methods as predictors, checking linearity, residual patterns, and uncertainty in the estimated relationships.
• The final report focused on plain-language conclusions: where readings tended to agree, where they diverged, and in what ranges it was reasonable (or not) to treat one method as a proxy for another.

Due to a procedural error, a suspect autoclave load (potentially over-processed) was accidentally mixed with correctly processed loads of the same product. All units were now indistinguishable.

• Setting: One suspect subgroup mixed into a larger batch
• Core question: How many units must be sampled so that, with high probability, the sample contains at least a small number of units from the suspect group?

• We represented the situation with a finite-population model: a known number of “suspect” units and a known number of “non-suspect” units combined into a single pool.
• Using the hypergeometric distribution, we computed the probability of capturing at least a target number of suspect units for different sample sizes.
• From this, we recommended a minimum sample size that achieved roughly a 95% chance of including at least the desired number of suspect units, along with a simple table the client could use in similar situations.

A client used a 4-Parameter Logistic (4PL) model in their plate reader software to analyze dose–response curves for reference and test materials. The software produced chi-squared, F-tests, p-values, R², and relative potency estimates — but the practical meaning of these numbers was unclear to non-statistical stakeholders.

• Setting: 4PL dose–response curves (reference + tests)
• Core question: How do we interpret the parallelism tests and relative potency estimates in a way that guides pass/fail decisions?

• We explained the idea of “parallel” 4PL curves: if the shapes (slope and upper/lower levels) are statistically compatible, their difference can be summarized as a horizontal shift — which is exactly what relative potency captures.
• We reviewed the chi-squared and F-test outputs from the software, defining what it means when a test supports the parallelism assumption versus when the data suggest meaningful shape differences.
• Instead of prescribing rigid universal cutoffs, we provided example ranges for “clearly good,” “borderline,” and “problematic” results (e.g., high R², p-values that do not signal strong lack of fit), emphasizing that these thresholds should be embedded in the client’s broader assay strategy and regulatory context.
• Finally, we showed how to interpret the relative potency estimate and its confidence interval in simple language: when a test batch is effectively similar to the reference, and when the data suggest meaningfully higher or lower potency.