Biology by Mr Bradford
To the student who emailed me this week: no, you can't just pick whichever one makes your data look tidier.
Every year, same question, different inbox. A student has a beautiful data table, a mean, maybe even error bars, and then asks me whether they should be reporting "the uncertainty" or "the percentage error." As if they're two brands of the same product. They're not. They're answering two completely different questions, and most IAs only need one of them.
Uncertainty is about your equipment. Error is about the truth.
Uncertainty asks: how precise is my measurement, given the tool I used to take it? If your ruler has 1 mm gradations, your reading uncertainty is ±0.5 mm. Full stop. It doesn't care what value you got. It doesn't care if you're right. It's a property of the instrument sitting on your bench, not a judgement on your biology. That's why it belongs in the column heading: "Length of shoot / mm (±0.5)", one uncertainty, stated once, because it applies to every value in that column.
The smallest division on the ruler is 1 mm, so the reading uncertainty is half of that either way: ±0.5 mm, regardless of where the tip actually falls.
Percentage error asks something much bigger and much rarer: how far is my result from a known, accepted value? That means you need an accepted value to compare against, a textbook rate of photosynthesis, a published Km, a certified concentration. If you don't have one of those sitting in a paper somewhere, you cannot calculate a percentage error. You can only pretend to.
This is where most students go wrong: not in the maths, in the assumption.
They calculate their own mean, then calculate "percentage error" against their own mean. That's not error. That's percentage difference, and it's measuring precision (how consistent your repeats were), not accuracy (how correct your answer was). Two different words for a reason. Confuse them in your IA and a moderator will notice, not because the arithmetic is wrong, but because it tells them you don't know what number you actually produced.
So what should actually go where.
- Instrument uncertainty (±) in every data table column heading: non-negotiable, comes from the equipment, stated once.
- Propagated uncertainty through your calculations, if you're combining measurements (add absolute uncertainties for addition/subtraction, add percentage uncertainties for multiplication/division). This is where most of the marks in "processing" actually live, and it's the bit students skip because it's fiddly.
- Percentage difference between your mean and a classmate's mean, or between two conditions: fine, useful, and honest about what it shows.
- Percentage error, only if you have a genuine accepted value from the literature. Most enzyme kinetics IAs don't. Most photosynthesis rate IAs don't. If you're not sure whether yours does, it probably doesn't.
Uncertainty tells you how sure you can be. Error tells you how right you were. An IA only needs the second one if it can actually answer that question. Most can't, and that's fine.
Got an IA question like this one? Send it my way on LinkedIn. Half these posts start life as an email exactly like the one above.