Why statistics is not “just maths”

Stats are comingEarlier today, a colleague and I were talking about a paper that we’re working on regarding fish acoustics.  He was asking if I would have time to do some statistical modelling of presence in regard to several environmental variables, and I hinted that I am a bit time-poor at the moment.  While we were discussing who else in the department could help with the statistics, I rattled off a fellow PhD student’s name.

What, them?  But they doesn’t know how to do programming!” said my physics-, engineering-, maths-background colleague in dismay.

But it’s not programming as you think of it,” I replied.  “It’s statistics.

*sarcastic look*

What’s the difference?” he asked.

Well, the answer is that there is a pretty big difference…

Theory vs. Applied

When I was at secondary school, in our final year we had the choice of choosing Advanced Mathematics or Applied Mathematics (aka statistics).

The Advanced Mathematics course taught you how to “select and apply complex mathematical techniques in a variety of mathematical situations”.  This included units such as algebra, calculus, geometry, and equations.

The Applied Mathematics (Statistics) course taught how to “make sense of inherent natural variation in a wide variety of contexts through the collection, analysis and interpretation of data”.  This included units such as hypothesis testing, data analysis, data modelling, and statistical inference.

So basically, one course gave you a year of studying complex, in-depth equations and formulas whilst the other course gave you a year of mathematical problem-solving.  By that time I had already been accepted into studying Zoology, so was strongly encouraged to take this opportunity to get familiar with statistics.  The justification was that it would give me a head-start before I started using statistics in my research later on.

one-does-not-simply-pass-statisticsOf course, the fact that I spectacularly failed the course has nothing to do with anything.  Although in fairness, we started with a class of 30 and were swiftly whittled down to a class of 3 when the other students realised what a true form of hell statistics really are.  Many of them transferred to the Advanced Maths class instead, because they thought it was easier.  And despite my overall grade, it did in fact give me a head-start when I started studying statistics at a university level since most students had never touched the subject before.

As an added bonus, it means I can now also honestly say that you don’t need to pass Maths in high school to succeed in science.  However, this does make me rather unpopular with parents at University Open Days, and as a result I’m generally discouraged from attending…

Fear of statistics – or fear of maths?

Most biologists recoil in horror at the mere thought of statistics. Some less-kind scientists suggest that this is why biologists are studying biology and not a ‘hard’ science like physics.  However, the truth is that most physicists would recoil in horror from the idea of statistics too – if only they had to use them.  But their work is often better captured by the mathematical formulae and equations that fall into the ‘Advanced Mathematics’ camp, rather than modelling natural variation, so the opportunity to dabble in stats never arises.  Instead, mathematical knowledge feeds into computer programming to run loops, calculus, algebraic equations, and a whole number of other mysterious things.

When you create statistical models, yes there is still an element of programming to it.  But the underlying logic is quite different.  Statistics may fall under the umbrella of mathematics, but they have quite different applications.  For example, if I was to write a program that would could calculate different acoustic measurements from a bunch of recordings, this would be quite different to writing some code to compare those resulting measurements.  A fine line, but a line nonetheless.

Each year, I help teach a course on Quantitative Biology – which is basically statistics in disguise.  I help guide undergraduate biology students through their first steps in statistics and introduce them to a simple software program which will do most of the basic stuff for them in a couple of clicks.  Each year there are a few students who complain that they’re no good at maths, that they’ll never understand this, that they don’t see the point.  Yet by the end of term they’re analysing and clicking away without hesitation, and (in the words of one student) “finally understanding the results sections of papers”.  The key is removing the fear of statistics instigated originally by a fear of maths.

“Put your money where your mouth is”

Over the past few months, I have been working towards completing my first PhD paper.  This has focused on describing the soundscape of a section of the Swan River, and among other things involved modelling the occurrence of different sound sources across different temporal scales.  As a result, after a long sabbatical whilst in pursuit of fieldwork skills / scholarships / rent money, I was thrown in the deep-end of statistics.

p-valueAt first I avoided it; there were plenty of other things to do, and to be honest the thought terrified me.  After all, I failed this at school!  My Undergraduate and Masters classes were okay, but not particularly pleasant!  Can’t I just pay someone to do this?!  But, after completing every other possible task, I took a deep breath, opened our collection of Alain Zuur books, and plunged back in.

And whilst I wouldn’t say that I loved it, there was some enjoyment.  I liked investigating my data, confirming relationships, and finding significant results.  There were a few temper tantrums, but hell did I learn a lot.  So for now, I’d say that statistics and I have a cautiously optimistic relationship.

Conclusion

Hey girlSo in summary, mathematics is classroom theory whilst statistics is real-world applied data.  To be good at statistics, you don’t actually have to be particularly good at maths.  What you do need to be good at is problem-solving, applying logic, manipulating information, and pulling biological meaning from numbers.

In fact, I would even go so far as to say there is a significant difference between mathematics and statistics!

[Note – In statistics circles, this joke is hilarious.  Admittedly in normal circles, it may fall somewhat flat.  Hopefully my undergrads get it…]

And if nothing else, at least studying statistics has opened up a whole new world of internet memes!

Heteroscedacity

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