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Bootstrapping e-tools for simulating laboratory works

15 一月, 2016 - 09:46

Laboratory works play a fundamental role in learning environments, allowing learners tooperate on experiments with real world items. Practice is ess ential in learning activities, because learning by doing increases substantially the effectiveness of the learning processes. Practical exercises are designed to prompt conceptual reasoning and critical thinking which prompts the application of science to everyday situations. Heavy emphasis is put on detailed laboratory reports, written answers to exercises, completed homework assignments, tests and group work. Often we must repeat the same laboratory experiment many times, to make our utmost for all the students to participate and watch it. Students learn to ask questions, design experiments and analyze data, facts and theories. Also, statistical methods play a fundamental role in our university’s didactic and research activities. Both the students and the teaching staff use traditional statistical gathered in laboratory experiments.

However, there are some reasons to minimize the number of laboratory experiments. In some cases, the repeated laboratory experiments mean the consumption of a great deal of substances and reactants. In other cases, there is a range of ethically motivated reasons to reduce the number of animals (frogs, guinea pigs, etc) used in experimentation. As the previous conditions are quite contradictory, we have to search for a solution that balances them. We perform an actual laboratory experiment only once for each group of students, then we repeat the same laboratory experiment by simulations as many times as necessary,each student being able to take part in analyzing data, making exercises and inferences.

We implemented bootstrapping methods into software tools, as applications in our simulation system (Figure 3.2), with the purpose to simulate laboratory experiments in both didactic and research activities (Prodan & Câmpean, 2005). Usually, the result of a laboratory experiment is a set of output values v1, v2, ..., vn, named original, or actual sample. The experimenter (student, teacher, or researcher) uses this sample to perform data analysis and statistical inferences, then to draw conclusions. Bootstrapping methods involves repeating the original data analysis procedure with many replicate sets of pseudo-data. We implemented a general discrete distribution (Figure 3.10) to generate sets of pseudo-data, based on original set of data v1, v2, ..., vn. By resampling the original data, we generate artificial samples on which we make inference of interest as for the original sample. Using a bootstrapping e-tool and the computer power, the experimenter can repeat the original experiment without any consumption of substances and reactants, and without use of animals, obtaining pseudo-data as plausible as those obtained from the original experiment. Our bootstrapping tools use the computer power to obtain reliable standard errors, confidence intervals and other measures of uncertainty for a wide range of problems. Moreover, the bootstrap can produce a more accurate confidence interval than would produce based on normal approximation.