June 13, 2012
Summer at last… I think? Yes, the May weather in Belfast is indeed changeable at this time of the year, with clothing stores presenting their “summer collection” while the rain beats down on people scrambling for shelter on the streets and pavements. I however, brave such elements in order to acquire my morning ‘eye-opener’ of a tall filter coffee, knowing full well what I have to face on my computer screen on my return, which requires something a lot stronger than coffee! “Once more unto the breach, dear friends, once more” the famous words uttered by Shakespeare’s King Henry V. Words which I must admit hit me every time I have to analyse my data, something of a battle that is a little less bloody than the Battle of Agincourt but still a battle.
As most approaches I have adopted to examining the Sundarbans sediment are adapted from those developed in Geology, it is important to recognise that Geology has often been regarded as one of the qualitative sciences. In which, discussions and ‘analysis’ are often centred on questions regarding ‘what happened?’ and ‘in what order did it happen?’. However, such questions regarding processes and in particular the inter-relationships between processes can be examined quantitatively, through statistical and mathematical procedures. Why do we do this? Mainly for the simple reason; science progresses by the testing of hypotheses through objective approaches. It is of no benefit to the investigator to simply look at the data acquired from x-ray diffraction, or from particle size analysis or any laboratory technique for that matter and then not question it. How do we know what we are seeing is really what we are seeing? How can we explain what is happening and more importantly, why is it happening? To quote the American theoretical Physicist Richard Feynman: “The first principle is that you must not fool yourself, and you are the easiest person to fool.” Thus, question the data, putting the data through its paces is of the most importance during any stage of a project. With coffee in hand, data prepared for questioning, I proceed gingerly to starting up the SPSS statistical package.
Inputting my quarter-phi particle size data from the Lothian Island core, I check that all the variables are in the correct order and that nothing is missing from the dataset that would cause any erroneous calculations. The analysis I am particularly interested in carrying out is called principle components analysis (PCA). Principle components analysis or ‘PCA’ for short is a data reduction technique which takes a set of correlated variables and recombines them into uncorrelated components using a procedure called Eigendecomposition. Now, this might sound slightly complicated but in actuality it is quite simple.
Say you have two variables; age and height and when these are presented in a scatter plot, age on the x-axis (horizontal) and height on the y-axis (vertical) they appear related to one another (i.e. correlated). Now, all this graph can really show for example is that with age, height increases and nothing much more than that. However, what if we pass a line through long axis of the cloud of points and another line perpendicular to the first and passing through this long line at the centre of the cloud of points and then imagine removing the original x- and y-axes. So now, we then rotate the new lines and points such that the long line through the cloud of points is horizontal and the perpendicular line is vertical. We have the same data but new information regarding age and height… This is PCA. What makes PCA special is that it helps visualise complex datasets that not even the human mind can imagine, say when you have something like 24 variables which exist in Eigenspace… It can become complicated!
The power of this technique does not mean to say that things become any easier for the investigator and it’s not long before user intervention is required to interpret what is going on. However, to quote the Belfast born physicist William Thomson (Lord Kelvin); “I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.”
Bearing these words in mind while sipping my tepid coffee, I press on with the analysis in Heraclean fashion!
Till next time folks!
Rory Flood, PhD Student, Queen’s University Belfast, School of Geography, Archaeology and Palaeoecology (GAP), http://www.qub.ac.uk/schools/gap/
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