In short
This project closes the mathematics course. Choose one three-component accord, and study it as a scientist would: a mixture design to map how it responds to its proportions, an uncertainty budget for the blends you weigh, a discrimination test of whether your best blend differs from your starting point, and a model reported with its limits. The plan is written and dated before any blend is made.
What you will learn
- Plan a study whose design, sample size and analysis are fixed before data are collected
- Combine a mixture design, an uncertainty budget and panel statistics in one analysis
- Report a model with its uncertainty and its limits, so that someone else could check it
Before this lesson: A Formula as a Linear System, Optimization Under Constraints: Cost and Composition, Mixture Designs for Accords, Discrimination Tests and Thurstonian d′, Measurement Uncertainty in Weighing and Dilution, Regression and Principal Component Analysis of Panel Data
The plan (written first)
- Question. One sentence, such as "Where in the triangle of these three components does the accord read most clearly as intended, at one hour?"
- Design. A simplex-centroid with at least two replicate centroids and one further checkpoint.
- Response. One defined rating, its scale, its reference smells and its time point.
- Panel. Who, how many, how briefed, and how samples are coded and randomized.
- Analysis. The Scheffé model you will fit, how you will judge adequacy at the checkpoints, and the triangle or directional test you will run between the model's optimum and your starting blend, with the d′ you care about and the sample size that implies.
- Uncertainty. Your balance's budget for the smallest weighing in the design.
The report
- The plan, unedited, with any deviation listed and explained.
- Raw data and the spreadsheet or script that analyzes them.
- The fitted coefficients, with what the replicate centroids say about noise.
- The optimum the model predicts, and whether a confirmation blend there behaved as predicted.
- The discrimination test: count, exact p-value, pd and d′.
- Limitations: panel size and training, single time point, single dose, the uncertainty of the smallest weighing.
A realistic schedule
Week one: write the plan, make the stock dilutions and weigh the ten blends (seven design points, two replicate centroids, one checkpoint) in one session, with the uncertainty budget for the smallest weighing. Let them rest for the maceration time you specified. Week three: run the rating session at the stated time after dipping. Week four: fit the model, make the confirmation blend at its predicted optimum and a fresh starting blend, rest them, and run the discrimination test. Write up as you go; a report assembled from memory after a month is where details are lost.
What would make it research
A study like this becomes a contribution when its question is one someone else cares about and its data are published in a reusable form. Two examples worth pursuing: whether a fitted optimum at one hour remains the optimum at six hours (time as a second response), and whether two independent panels, given the same blends, agree on the coefficients. Either is within reach of an independent perfumer with patient volunteers.
How it connects
This is the Research and Innovation project raised one level: the same insistence on a checkable report, now with a model and explicit uncertainty. The computational course that follows shows how to keep such a study reproducible as data and code.
Practical exercise: The mathematics course project
Carry out the study and write the report.
Assess yourself against these criteria:
- The plan is dated before the first blend, and every deviation is listed.
- Someone else could rerun your analysis from your data and script and get your numbers.
- Model adequacy is judged at checkpoints against replicate noise, not by its fit to its own points.
- The discrimination result is reported as count, exact p-value and d′, with power stated.
- Conclusions do not exceed what the panel size supports.
Common mistakes
- Changing the question after seeing the data. Report the planned question; add others as exploratory.
- Omitting replicates to save time. Without them there is no estimate of noise.
- Reporting only the optimum. The whole map, with its uncertainty, is the result.
Safety
All evaluation is on strips. Brief assessors as in the ethics lesson, keep personal data out of what you publish, and follow the safe handling lesson.
Knowledge check
Written and reviewed by the RUŌOD Lab team. This is general education, not legal, regulatory, medical or safety advice. Example dilutions and exercises are for learning, are not validated products, and have not been safety-assessed. Completing a lesson confers no qualification. How we check these lessons.