Tag Archives: statistics

Diagnostics for first year students

The SEB113 teaching team last semester (me, Ruth Luscombe, Iwona Czaplinski, Brett Fyfield) wrote a paper for the HERDSA conference about the relationship between student engagement and success. We collected data on the timing of students’ use of the adaptive release tool we developed, where students confirm that they’ve seen some preparatory material before being given access to the lecture, computer lab and workshop material. We built a regression model that looked at the relationship between the number of weeks of material students gave themselves access to and their end of semester marks (out of 100%), and it showed that students who engaged more obtained better marks, where engagement also included active use of the Facebook group and attendance at workshop classes. I had assumed that we’d be able to get data on students’ maths backgrounds coming in, but with so many ways to enter university, we don’t have the background info on every student. QUT has set Queensland Senior Maths B as the assumed knowledge for SEB113 (and indeed the broader ST01 Bachelor of Science degree) and I’m interested in knowing whether or not the level of maths of students coming in has a bearing on how well they do over the course of the unit.

This semester, we decided that it’d be good to not just get a sense of the students’ educational backgrounds but to assess what their level of mathematical and statistical skills are. We designed a diagnostic to run in the first lecture that would canvas students on their educational background, their attitudes towards mathematics and statistics, and how well they could answer a set of questions that a student passing Senior Maths B would be able to complete. The questions were taken from the PhD thesis of Dr Therese Wilson and research published by Dr Helen MacGillivray (both at QUT), so I’m fairly confident we’re asking the right questions. One thing I really liked about Dr MacGillivray’s diagnostic tool, a multiple choice test designed for engineering students, is that each incorrect choice is wrong for a very specific reason, such as not getting the order of operations right, not recognising something as a difference of squares, etc.

I’m about to get the scanned and processed results back from the library and it turns out that a number of students didn’t put their name or student number on the answer sheet. Some put their names down but didn’t fill in the circles, so the machine that scans the answer sheet won’t be able to determine who the student is and it’ll take some manual data entry probably on my part to ensure that we can get as many students as possible the results of their diagnostic. So while I’ll have a good sense of the class overall, and how we need to support them, it’ll be harder than it should be to ensure that the people who need the help are able to be targetted for such help.

Next semester I’ll try to run the same sort of thing, perhaps with a few modifications. We’ll need to be very clear about entering student numbers and names so that we can get everyone their own results. It’d be good to write a paper that follows on from our HERDSA paper and includes more information about educational background. It might also be interesting to check the relationship between students’ strength in particular topics (e.g. calculus, probability) and their marks on the corresponding items of assessment. Getting it right next semester and running it again in Semester 1 2017 would be a very useful way of gauging whether students who are weak in particular topics struggle to do well on certain pieces of assessment.

 

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Workshops

I had a very full week last week, with the annual Bayes on the Beach (BOB) at the Gold Coast (Mon-Wed) and Bayesian Optimal Design of Experiments  (BODE) on Friday.

BOB is an annual workshop/retreat, run by Kerrie Mengersen and the BRAG group at QUT, that brings together a bunch of Australian and international statisticians for a few days of workshops, tutorials, presentations and fun in the sun. This year was, I think, my fourth year at BOB.

One of the recurring features is the workshop sessions, where around three researchers each pose a problem to the group and everyone decides which one they’re going to work on. This year I was asked to present a problem based on the air quality research I do and so my little group worked on the issue of how to build a predictive model of indoor PM10 based on meteorology, outdoor PM10 and temporal information. We were fortunate to have Di Cook in our group, who did a lot of interesting visual analysis of the data (she later presented a tutorial on how to use ggplot and R Markdown). We ended up discussing why tree models may not be such a great idea, the difference in autocorrelation and the usefulness of distributed lag models. It gave me a lot to think about and I hope that everyone found it as valuable as I did.

The two other workshop groups worked on ranking the papers of Professor Richard Boys (one of the keynote speakers) and building a Bayesian Network model of PhD completion time. Both groups were better attended than mine, which I put down to the idea that those two were “fun” workshops and mine sounded a lot like work. Still, a diverse range of workshops means something for everyone.

James McGree (QUT) asked me if I could come to the BODE workshop to discuss some open challenges in air quality research with regards to experimental design. I gave a brief overview of regulatory monitoring, the UPTECH project’s random spatial selection and then brought in the idea that the introduction of low cost sensors gives us the opportunity to measure in so many places at once but we still need to sort out where we want to measure if we want to characterise human exposure to air pollution. While it was a small group I did get to have a good chat with the attendees about some possible ways forward. It was also good to see Julian Caley (AIMS) talk about monitoring on the Great Barrier Reef, Professor Tony Pettitt (QUT) talk about sampling for intractable likelihoods and Tristan Perez (QUT) discuss the interplay between experimental design and the use of robots.

It’s been a great end to the year to spend it in the company of statisticians working on all sorts of interesting problems. While I do enjoy my air quality work and R usage is increasing at ILAQH it’s an entirely different culture to being around people who spend their time working out whether they’re better off with data.table and reshape2 or dplyr and tidyr.

Marrying differential equations and regression

Professor Fabrizio Ruggeri (Milan) visited the Institute for Future Environments for a little while in late 2013. He has been appointed as Adjunct Professor to the Institute and gave a public talk with a brief overview of a few of his research interests. Stochastic modelling of physical systems is something I was exposed to in undergrad when a good friend of mine, Matt Begun (who it turns out is doing a PhD under Professor Guy Marks, with whom ILAQH collaborates), suggested we do a joint Honours project where we each tackled the same problem but from different points of view, me as a mathematical modeller, him as a Bayesian statistician. It didn’t eventuate but it had stuck in my mind as an interesting topic.

In SEB113 we go through some non-linear regression models and the mathematical models that give rise to them. Regression typically features a fixed equation and variable parameters and the mathematical modelling I’ve been exposed to features fixed parameters (elicited from lab experiments, previous studies, etc.) and numerical simulation of a differential equation to solve the system (as analytic methods aren’t always easy to employ). I found myself thinking “I wonder if there’s a way of doing both at once” and then shelved the thought because there was no way I would have the time to go and thoroughly research it.

Having spent a bit of time thinking about it, I’ve had a crack at solving an ODE within a Bayesian regression model (Euler’s method in JAGS) for logistic growth and the Lotka-Volterra equations. I’ve started having some discussions with other mathematicians about how we marry these two ideas and it looks like I’ll be able to start redeveloping my mathematical modelling knowledge.

This is somewhere I think applied statistics has a huge role to play in applied mathematical modelling. Mathematicians shouldn’t be constraining themselves to iterating over a grid of point estimates of parameters, then choosing the one which minimises some Lp-norm (at least not without something like Approximate Bayesian Computation).

I mean, why explore regions of the parameter space that are unlikely to yield simulations that match up with the data? If you’re going to simulate a bunch of simulations, it should be done with the aim of not just finding the most probable values but characterising uncertainty in the parameters. A grid of values representing a very structured form of non-random prior won’t give you that. Finding the maximum with some sort of gradient-based method will give you the most probable values but, again, doesn’t characterise uncertainty. Sometimes we don’t care about that uncertainty, but when we do we’re far better off using statistics and using it properly.

Two pieces of good news this week

The full paper from the EMAC2013 conference last year is now available online. If you’re interested in the statistical methodology we used for estimating the inhaled dose of particles by students in the UPTECH project, you should check out our paper at the ANZIAM Journal (click the link that says “PDF” down the bottom under Full Text).

More importantly, though, we were successful in applying for an ARC Discovery Project! This project will run for three years and combines spatio-temporal statistical modelling, sensor miniaturisation and mobile phone technologies to allow people to minimise their exposure to air pollution. Our summary of the project, from the list of successful projects:

This interdisciplinary project aims to develop a personalised air pollution exposure monitoring system, leveraging the ubiquitousness and advancements in mobile phone technology and state of the art miniaturisation of monitoring sensors, data transmission and analysis. Airborne pollution is one of the top contemporary risks faced by humans; however, at present individuals have no way to recognise that they are at risk or need to protect themselves. It is expected that the outcome will empower individuals to control and minimise their own exposures. This is expected to lead to significant national socioeconomic benefits and bring global advancement in acquiring and utilising environmental information.

Other people at ILAQH were also successful in getting a Discovery Project grant looking at new particle formation and cloud formation in the Great Barrier Reef. I won’t be involved in that project but it sounds fascinating.

posterior samples

I probably should have put this post up earlier because it’s now a huge collection of stuff from the last month. Here we go!

It appears that Hilary Parker and I have similar (but by no means identical) work setups for doing stats (or at least we did two years ago). It’s never too late to come up with a sensible way of organising your work and collection of references/downloaded papers.

Applied statisticians should probably teach scientists what it is we do, rather than just the mathematics behind statistics. This is a difference I’ve noticed between SEB113 and more traditional statistics classes; we spend a lot less time discussion F distributions and a lot more time on model development and visualisation.

Speaking of visualisation, here’s a really great article on visualisation and how we can use small multiples and colour, shape, etc. to highlight the interesting differences so that it’s very clear what our message is.

Jeff Leek has compiled a list of some of the most awesome data people on Twitter who happen to be female.

In the ongoing crusade against abuse of p-values, we may want to instead focus on reproducibility to show that our results say what we say they do. Andrew Gelman and Eric Loken have an article in The American Statistician reminding us that p-values have a context and we need to be aware of issues like sample size, p-hacking, multiple comparisons, etc.

 

 

 

 

Posterior samples

SEB113 students really seemed to enjoy looking at mathematical modelling last week. The Lotka-Volterra equations continue to be a good teaching tool. A student pointed out that when reviewing the limit idea for derivatives it’d be useful to show it with approximating the circumference of a circle using a polygon. So I knocked this up:

approximations

Are you interested in big data and/or air quality? Consider doing a PhD with me.

This week I showed in the workshop how Markov chains are a neat application of linear algebra for dealing with probability. We used this interactive visualisation to investigate what happens as the transition probabilities change.

Zoubin Ghahramani has written a really nice review paper of Bayesian non-parametrics that I really recommend checking out if you’re interested in the new modelling techniques that have been coming out in the last few years for complex data sets.

Exercism.io is a new service for learning how to master programming by getting feedback on exercises.

The problem with p values

A coworker sent me this article about alternatives to the default 0.05 p value in hypothesis testing as a way to improve the corpus of published articles so that we can actually expect reproducability and have a bit more faith that these results are meaningful. The article is based on a paper published in the Proceedings of the National Academy of Sciences which talks about mapping Bayes Factors to p values for hypothesis tests so that there’s a way to think about the strength of the evidence.

The more I do and teach statistics the more I detest frequentist hypothesis testing (including whether a regression coefficient is zero) as a means of describing whether or not something plays a “significant” role in explaining some physical phenomenon. In fact, the entire idea of statistical significance sits ill with me because the way we tend to view it is that 0.051 is not significant and 0.049 is significant, even though there’s only a very small difference between the two. I guess if you’re dealing with cutoffs you’ve got to put the cutoff somewhere, but turning something which by its very nature deals with uncertainty into a set of rigid rules about what’s significant and what’s not seems pretty stupid.

My distaste for frequentist methods means that even for simple linear regressions I’ll fire up JAGS in R and fit a Bayesian model because I fundamentally disagree with the idea of an unknown but fixed true parameter. Further to this, the nuances of p values being distributed uniformly under the Null hypothesis means that we can very quickly make incorrect statements.

I agree with the author of the article that shifting hypothesis testing p value goal posts won’t achieve what we want and I’ll have a bit closer a read of the paper. For the time being, I’ll continue to just mull this over and grumble when people say “statistically significant” without any reference to a significance level.

NB: this post has been in an unfinished state since last November, when the paper started getting media coverage.