LEARNING TO MAKE DECISIONS BY MEANS OF EXPERIMENTAL DATA
Evidences about a decline in mathematical skills among chemistry students have been reported [Yates, Anal Bional Chem 404 (2012) 2787], problem that in fact is not confined to chemistry. This work presents a strategy that has proven to be successful to deal with this so-called “mathematical problem”. Instead of giving theoretical lectures about the basic elements of statistics for interpretation of experimental data [Ortiz et al., Anal Chim Acta 674 (2010) 123], the learning of hypothesis tests and data analysis is made along a sequence of laboratory practices. These practices, further to work the necessary experimental skills, give the students their own experimental data to analyse, reflect about, interpret and draw conclusions.
There are seven practices for a third semester in a degree of Chemistry or similar. Each practice is planned for a session of three hours in a laboratory with no more than 16 students working in pairs. After a brief lecture about the basic statistical elements, students should obtain the experimental data by properly doing the corresponding experiments and write a report about the experiments and the conclusions from the experimental results. In a third step the results are shared in a common session (all the students, all the teachers), where the possible interpretations are discussed, and mistakes and misconceptions found in the reports are also discussed and corrected. Finally, after these activities of continuous feedback, each student should pass an individual test that consists of questions similar to the ones already discussed during the practices and with data also similar to those obtained.
The seven practices (24 ECTS in laboratory + 6 ECTS in seminars) can be summarized as follows ('Stats' refers to the statistical methodology involved):
1) With fixed probabilities of false noncompliance and false compliance and a reference value, students should determine the number of measurements needed, then doing them, and decide whether the sample is compliant or not. Stats: hypothesis testing.
2) By gathering together the experimental data from the 8 groups, four of them are picked at random and students should ‘simulate’ an interlaboratory comparison, explicitly evaluating repeatability and reproducibility of the method according to norm ISO 5725. Stats: Analysis of Variance (ANOVA).
3) Evaluation of the sources of variability in the analysis of the homogeneity of a mixture of solids. Stats: ANOVA.
4) Calibration of two analytes (food dyes) and comparison of analytical sensitivities. Stats: univariate regression.
5) Determination, by the standard addition method, of a food dye in a commercial sample. Stats: univariate regression, estimation of uncertainty in analytical determinations.
6) Capability of detection according to ISO 11843. Stats: hypothesis testing with univariate regression models.
7) Separation of spectral overlap in mixtures of food dyes. Stats: Principal Component Analysis (PCA).
This schedule has been put into practice for three consecutive years in academic degrees adapted to the European Higher Education Area with remarkable success despite the initial reluctance of students. Largely, these good results can be attributed to the coordination between statistical and analytical chemistry teachers handling the same chemical language to raise statistical methodology.