Um ….. here’s a new tool for exploring probability distributions!
I developed the probability distribution explorer as part of my Masters research into teaching probability distribution modelling. The proposed teaching framework and the tool were developed in response to use of data for distribution modelling for AS91586, in particular the need for students to demonstrate use of methods related to the distribution of true probabilities versus distribution of model estimates of probabilities versus distribution of experimental estimates of probabilities.
The tool was developed primarily to support comparisons of the “distribution of experimental estimates of probabilities” and “distribution of model estimates of probabilities”. When reviewing research literature, I found limited examples of how to teach this comparison using an informal approach i.e. not using a Chi-square goodness-of-fit test. Consequently, I also found a lack of statistically sound criteria to enable drawing of conclusions in such resources as textbooks, workbooks and assessment exemplars.
This led to my research, which involved a small group of New Zealand high school statistics teachers. Focusing on the Poisson distribution, the criteria used by ten Grade 12 teachers for informally testing the fit of a probability distribution model was investigated. I found that criteria currently used by the teachers were unreliable as they could not correctly assess model fit, in particular, sample size was not taken into account.
After exploring the goodness-of-fit using my visual inference tool, teachers reported a deeper understanding of model fit. In particular, that the tool had allowed them to take into account sample size when testing the fit of the probability distribution model through the visualisation of expected distributional shape variation. I’ve re-developed the tool this year to support NZQA as they explore opportunities for assessment within a digital environment. A team of teachers are developing prototype assessment activities for AS91586 and these will be trialled with students in schools later in the year.
The video below gives a general introduction to the tool, using data on how many times I say “um” when I’m teaching. The video itself provides another source of data because, um … well, you’ll see if you watch!
More videos, teaching notes and related resources can be found here: stat.auckland.ac.nz/~fergusson/prob_dist_explorer/teachers/