My Path Through Research

The Trials and Triumphs of Doing a PhD

I <3 Straight Lines

I have one love which surpasses my love of graphs, and that is my love of straight lines in graphs!

But why am I bringing this up now?

I am currently in the process of analysing some of the data I have been collecting over the past few weeks. I was looking to monitor the change occurring during degradation of my photographs by calculating the rate of change.

Now, if you look back to your maths classes, you might remember that rate of change can be determined by the gradient (i.e. slope)  of a time-graph (i.e. graph of how a value is changing against time). This is quite easy to analyse if you have a straight line, as the gradient is just a single value. However, if you don’t, you start running into more complicated problems!

So I plotted my data.

To my satisfaction I did get a regularly changing line (i.e. there is some significant effect in what I was measuring), but to my dismay, it was a polynomial (i.e. curve), not a straight line!

You can get a straight line from a polynomial curve by taking a derivative of the equation. However, as my brother wisely pointed out to me, you do lose quite a bit of information in doing that, which is not ideal.

My other option was to find a value which DID change linearly with time. So I converted my data into other monitoring systems, and…tada!!!..I got straight lines!

I am happy that I managed to get my straight lines without a lot of data handling. Of course, the more you work on your data, the more information you lose. However, in this case, the two ways I used where just two different ways of measuring the same thing only using a different standard.

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February 2018
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