Abstract:

Statistics is a compulsory course in Science and Engineering degrees, as well as in many Social Science degrees. Thus, it is a crossing field of knowledge that is applied to a number of problems of diverse nature, but that can be approached with the same statistical technique.

Experience tells us that the statistical courses are not interesting enough among students. Regardless of the reasons for that lack of interest, we would like to highlight in this work the difficulty students have in understanding abstract concepts. And the fact that this difficulty extends beyond undergraduate studies. Unfortunately, it is common to see graduates in industry who are not able to cope with statistical analysis that they are supposed to have learned at college. In this work we propose the use of innovative interactive applications that help, on the one hand, to the understanding of statistical concepts, and on the other hand, to the greater involvement and motivation of students in the subjects.

For the development of the interactive applications, we used the statistical software and programming language R (https://www.r-project.org). R has been the “de facto” standard for data analysis for years. Moreover, as it is also a programming language, its possibilities are unlimited, as demonstrated by the more than 18,000 packages developed by the community for a wide variety of application domains. Some packages are true “frameworks” for application development, such as the “shiny” package (https://shiny.rstudio.com). Shiny allows us to develop interactive applications that run in the browser, without the need to know how to program web pages. Everything is generated by R functions in an analogous way to how a data analysis would be done.

We showcase our work with an application that illustrates the definition of probability as relative frequency in the limit. A classic example would be to flip a coin repeatedly and count the number of heads that come up in a succession of n “experiments”. The probability of getting heads would be, asymptotically, the number of heads divided by the total number of flips. A “manual” activity could be to have students flip coins, record the heads in a sheet of paper, and do the calculations. But it would take too much time for a basic concept.

Data Science methods and tools, such as simulation and R statistical software, allow us to simulate any random experiment, a large number of times, and customized for each application domain. We have developed an interactive application to explain this important concept, which is published at https://elcano.shinyapps.io/probability_as_relative_frequency/. The advantage over the coin example is that we can use “events” closer to the students’ interests. For example, in the Degree in “Video Game Design and Development“ we can talk about the probability that an attacker or a defender will appear; in the Degree in Biology, we can talk about the probability that a treatment will be effective or not; and so on.

It is important to remark that the proposed methodology is not exclusive to the teaching of Statistics, but can be applied to any subject in which data, mathematical functions, graphs, or simulation can be used, and in which student interaction produces different results that help them to grasp the concepts.

Keywords:

Interactive applications, Statistics teaching, Simulation, R Software.