You didn’t think I was done collecting experimental data did you? This morning I was back at it, collecting lots of data – and hoping I was doing it with minimal ERROR! And then I ended up with a lot of data I actually had to analyze… Which had me thinking a lot about ACCURACY and PRECISION – yes there’s a difference between those 2! So, as wrangle with this data, here’s a review!
PRECISION is a measure of CONFIDENCE in a measurement, whereas ACCURACY is a measure of how close the measurement is to the TRUE value. So a certain politician… could tell the same lie over and over and stick true to their telling, thus being precise, but inaccurate. But I’m going to stick with a less inflammatory example today.
Imagine you’re playing pin the tail on the donkey
- situation 1: you’re confident that, even with a blindfold, you know where the donkey’s bottom is & you have perfect aim, so you pin the tail over & over in the same spot
- situation 2: you’re not sure where the donkey’s bottom is exactly, so you try out spots around where you think it is
Now take off your blindfold
In situation 1, if all the tails are close together AND in the correct location (donkey’s bottom) you were both PRECISE (because the tails are close together) ✅ & ACCURATE (because the tails are in the right spot) ✅
BUT if you take off the blindfold & find that the tails are close together but what you thought was the donkey’s *rear* was actually its *ear*, you were still PRECISE ✅ BUT you are NOT ACCURATE ❌ you had false confidence
In situation 2, if your tails were a bit separated, but they were all on the donkey’s bottom, you were NOT very precise ❌ BUT you WERE ACCURATE ✅
If the tails are separated & not on the donkey’s bottom then you were neither precise ❌ nor accurate ❌
So precision & accuracy measure 2 different things
Thankfully, in science, we don’t have to worry about molecules lying to us. But since they can’t directly “talk” to us, it’s up to us to interpret what they’re “saying” through making measurements – like how heavy something is (weight) or how much space it takes up (volume). The things we’re measuring can’t “lie” to us – but instead “lies” can be introduced accidentally when we “record” & “re-tell” their stories.
Imprecision is like if the story changes a lot. So this is easier to notice because you just have to ask a bunch of times (make multiple measurements). But accuracy’s harder to determine, because it requires you to know what the true story is! A good sign is if multiple different measuring tools give you the same answer.
So why might the story be “off”? When we can blame the equipment we call it INSTRUMENT ERROR but if we have no one to blame but ourself it’s OPERATOR ERROR. But don’t feel bad! Some error is inevitable, you might even say it’s standard! Both operator & instrument can cause RANDOM ERRORS & SYSTEMATIC ERRORS
RANDOM ERRORS are “unbiased.” This is like having a shaky arm that leads to poor aim – your tails rarely directly hit their target. BUT they’re not biased towards any one direction (e.g. you don’t have a tendency to pin left of target vs right) & they vary in how “off” they are. As a result these errors “cancel out” if you average enough of them, so RANDOM errors do NOT affect average, just the variability around the average.
SYSTEMATIC ERRORS, on the other hand, are BIASED (error’s always in a certain direction) & they don’t “fix themselves.” This is like always pinning to the left of the target (or the right, or above, or below (but not all of them))
Since these SYSTEMATIC errors are DIRECTIONAL, the average measurement *will* reflect this error – e.g. if you always err to the left, so will your average
If you know the amount & direction of systematic error, you might be able to correct for it after the fact. If I keep pinning the tail on the donkey’s ear, I can “cheat” after the fact & move the donkey so the tails are in the right spot. BUT I need to know how to move it…
Let’s look at an example -> in lab, we’re more often dealing w/meniscus bottoms, not donkey bottoms… When you measure liquids, edges of the liquid get pulled up walls of the container leading to a smile we call a meniscus http://bit.ly/2AeB1B6 & it’s important to measure from BOTTOM of meniscus ⚠️ BUT where bottom looks like it is depends on angle you’re looking from. To get a good eye-level, direct, glance, adopt a “titration stance” (that’s what my o-chem teacher called it)
Still, chances are, despite good form, each time you go to measure, you’re looking from a slightly different angle, so location will be slightly different – but different in different, random, ways (1 time your glance is more right-angled another time it’s more left-angled, etc.) This would be an example of RANDOM ERROR & I learned it has a cool name: PARALLAX ERROR
You can also get SYSTEMATIC ERRORS when measuring liquids. They can be “fixable” like if you measure volume & then realize you left stir bar in – you can subtract out volume of the stir-bar from the volume of the stir-bar + liquid
In that case you can see stir bar (or get an unwelcome surprise when you’re pouring the liquid & hear a thunk…). But the important thing is you found it! What’s even more dangerous is when you don’t know that a systematic error’s there. if you keep measuring & getting similar results, you might feel pretty confident – I mean, why doubt it? But what if marking lines on your graduated cylinder are off, so it’s like you always forgot the stir bar in there?
Some systematic errors are harder to correct for even if you know they exist – like if you only learn that you’re supposed to be reading from BOTTOM of meniscus *after* you’ve already made measurements. If you’d been reading from top or edge of meniscus, your recorded values will ALL be too high, but how much “too high” is hard to know.