Bo: Hey guys.
Billy: Hey Bo!
Bobby: Hi Bo.
♫ (lyrics) Flipping Physics ♫
Mr. P: Ladies and gentlepeople, the bell has rung therefore, class has begun.
Therefore, you should be seated in your seat,
ready, excited about Accuracy and Precision.
Billy: Yes!
Mr. P: First off, understand that in your common vernacular,
you would probably consider both words to mean the same thing.
For example, if you were to say to your friends,
"Hey Man, that's so accurate!" or if you would have said,
"Hey! Man, that's so precise!"
your friends wouldn't be able to tell that
you may actually mean two different things.
However, now that you have taken this class,
you will be able to explain to them the differences.
SAH-WEET!
Now let's define them.
Accuracy ...
Accuracy is how close your observed,
or measured values are to the accepted value.
Please notice that I do not use the terms
"real value" or "actual value" because there isn't
really any such thing.
There are numbers that are the "accepted values",
meaning that the scientific community all "accepts"
that they will get a certain number when they measure it.
For example, the accepted value for the acceleration
due to gravity here on planet earth is 9.81 m/s^2.
This isn't an "actual value" or a "correct value"
because it isn't "actually" the same at every location on the planet.
However, the scientific community all agrees that too
3 sig figs, the acceleration due to gravity on earth, is 9.81 m/s^2.
Great! Again, accuracy is how close your observed
or measured value is to the accepted value.
And precision ...
Precision is how close your observed
or measured values are to one another.
Another way to look at precision is how
repeatable your experiment is.
If you get a similar result each time,
then you experiment is precise.
Bobby: I thought precision was how many numbers
after the decimal your number had, isn't that right?
Mr. P: Yes, Bobby, that is another definition of precision,
however, that's not the one we're going to be using right here.
When we are talking about accuracy versus precision.
Now let's go through some examples and discuss accuracy and precision.
All of these examples will have the same question
and that question is ...
Which of the following is true about
the Accuracy and Precision represented by this target?
I'll draw the target in just a minute.
1) High Accuracy and High Precision,
2) Low Accuracy and High Precision,
3) Low Accuracy and Low Precision,
4) High Accuracy and Low Precision,
5) Can't determine Accuracy or Precision,
6) Can't determine Precision,
and 7) Can't determine Accuracy.
So let me draw the target.
Now I'm going to shoot arrows at this target.
Please realize I was in my middle school's
archery club in 8th grade, that's how cool I am.
Oh, and one more thing, before I shoot my first arrow,
Billy, where am I attempting to shoot my arrow?
Billy: At the bull's-eye.
Mr. P.: And where is the bull's-eye?
Billy: In the very middle of the target.
Mr. P.: Relax! Some people have never shot an arrow before
and don't know, so how was I to know that y'all already knew?
And Bo, what does the bull's-eye represent in our
Accuracy and Precision analogy?
Bo: Uhh, I would guess the actual value.
Bobby: There is no such thing as an actual value.
Billy: Yeah, it's called the accepted value.
Bo: Oh, thanks guys. That's right.
The bull's-eye represents the accepted value.
Mr. P: Great! Here we go!
I've got my daughter's safe bow and arrow!
[Geneve], do you mind if I borrow your bow and arrow?
Geneve: No, Dad, that's fine. Just don't hurt yourself.
Mr. P: Thanks, Geneve.
Ryan: Dad, would you like to borrow one of my dolls?
Mr. P: Not yet, Ryan, I will when we get to
vector sums of forces, but not quite yet ...
thanks for offering! All right, let's shoot!
(thud)
YES!
One, bink-bink ...
(thud)
YES!
(thud)
YES!
So Bo, what do you think the answer is the question is?
Bo: All the arrows are near the bull's-eye,
so that means that all the measurements would be
near the accepted value, so that's high accuracy.
Also, it looks like all the measurements are
near one another, so your measurements are
highly repeatable, so high precision as well.
So the answer's number 1, they're both High Accuracy and High Precision.
Mr. P: Exactly, Bo! Let's do another one!
(thud)
WOO!
(thud)
YES!
(thud)
YES!
WOO!
Bobby? Thoughts?
Bobby: Just like in the previous example,
all the arrows are close to one another,
so it's highly repeatable or highly precise,
however, now all the arrows or measurements are not
near the accepted value or the bull's-eye,
so it's gonna be Low Accuracy ...
so the answer is number 2, Low Accuracy, but High Precision.
Mr. P.: Also correct! Bobby, let's do another one!
(thud)
Ok! I'll take that one!
Come on, baby, come on! Give it to me! Give it to me!
(thud)
YEAH!
(thud)
YEAH!
One more, baby! One more!
It's all I need!
Okay, go-go-go-go-go!
(thud)
YEAH!
Billy, how about this one?
Billy: Well, all the arrows are far from one another,
so it's not repeatable, so then that would be
Low Precision ...
um, I'm not sure about accuracy.
They are all far from the accepted value,
so is it Low Accuracy?
Bobby: I think, if I may, Billy ...
that if you take the average of all the arrows
or the measurements, that you actually get
an average measure that's pretty close to the accepted value,
or relatively close to the accepted value,
so I would actually call this High Accuracy.
Billy: Oh. Yeah. I can see that, so the answer is number 4.
It's got High Accuracy, but Low Precision.
Mr. P.: Absolutely! This helps you to understand
the importance of both Accuracy and Precision.
While this experiment was highly accurate, well, I did my best,
it's pretty close to accurate, it was not very precise
or repeatable and notice they're very spread out.
Let's do one more.
Come on, baby! Give it to me! Give it to me!
(thud)
YEAH! Did you see that? WOO-HOO-HOO!
Bo? What do you think?
Bo: Um, there's high accuracy because the arrow or the measurement
is in the bull's-eye, or the accepted value.
Mr. P.: Bo, that is true, however, simply high accuracy
is not one of our choices, so I do need to
hear you talk about precision, please.
Bo: Oh. Oh, wait, I get it.
If there's only one measurement, then we can't compare it
to any of the other measurements,
so we can't determine precision ...
so the correct answer is number 6.
Mr. P.: YES! BO! In the absence of any other measurements
to compare to is impossible to figure out precision.
Now it's time for our first equation of the class.
Here it is ...
First I'm gonna read it with just the letters,
so E sub R is equal to O minus A, divided by A, times 100.
Now I'm actually gonna walk my way through what all of this means.
E sub R is called the Relative Error.
O is the Observed Value and A stands for the Accepted Value.
In other words, we can read this equation as
the Relative Error is equal to the Observed Value,
minus the Accepted Value, that quantity divided by
the Accepted Value, the whole thing multiplied by 100.
Bobby, is this a measurement of Accuracy or Precision?
Bobby: How would I know? Oh, wait-wait-wait ...
I think I see. Because the equation has Accepted Value in it,
and Precision has nothing to do with the Accepted Value,
it must be a measurement of Accuracy.
Mr. P.: Very nice, Bobby.
Relative Error is a measurement of Accuracy.
Billy, what are the dimensions for Relative Error?
Billy: If we don't know the dimensions for the Observed Value
or the Accepted Value, how would we be able to
figure out the dimensions for Relative Error?
Mr. P.: That is a good question!
It turns out that no matter what dimensions you use
for the Observed and Accepted Values,
you will always get the same dimensions for Relative Error because ...
Bo: Because the dimensions for the Observed Value
and the Accepted Value will be the same
and therefore, the dimensions will cancel out ...
and you multiply by 100, you get a percentage.
Mr. P.: Exactly, Bo! The equal dimensions on top and bottom
cancel out and Relative Error ends up being a percentage.
Lastly, just so you know there are equations for Precision,
however, I'm not going to cover them at this time.
The basic idea is that you need to figure out the
mean and the standard deviation and that
if the values are within one standard deviation of the mean,
the data would be considered to be precise.
Well, that ends our discussion of Accuracy and Precision.
I enjoyed learning with you and I hope
you enjoyed learning with me.
Voiceover: Lecture Notes are available at FlippingPhysics.com.
Please enjoy Lecture Notes responsibly.
All right.
Wish me luck, everybody.
(laughs) I hope they stick!
(thud)
Ugh!
That one didn't count.
(thud)
NO!
This was such a good idea.
(thud)
And none of them are sticking!
(thud)
YES! I got one! It stuck!
Not what I was going ...
(laughs)
(thud)
YES!
(thud)
YES!
(thud)
NOPE!
(thud)
Come on. Stick. Stick!
(thud)
Stuck to the floor ...
(thud)
Nope, not up there ...
(thud)
Aw! Man, my arm is getting tired!
(thud)
Oh! Okay!
At least it's stuck then ...
(thud)
Great idea.
(thud)
Ugh!
(thud)
YES!
(thud)
YOO!
(thud)
(laughs) Was SUCH a good idea!
(thud)
Except they don't stick!
Why don't they stick? Why don't they stick?
(thud)
Nope. Not close enough.
(thud)
COME ON!
(thud)
Nope.
Still not close enough.
(thud)
(sigh) Such a good idea! (laughs)
(thud)
Why doesn't it just stick to the wall!
(thud)
Now stick to the floor, will ya ...
(thud)
That's not on the target.
(thud)
At least I'm finding a way to get it to stick.
(thud)
Okay, as soon as I say that, of course it doesn't work.
(thud)
(sigh)
(thud)
YES!
One more ...
One more Team! Come on, let's do it!
(thud)
Aw, it was right there. It was there!
(thud)
GAH!
(thud)
Come on ...
(thud)
It was right there, it's just not sticking.
How many times do we do this?
(thud)
Ugh!
(thud)
YES!
Okay, just stick. Just stick anywhere.
(thud)
Oh no ...
(thud)
Okay, I'll take that one.
Come on, baby, come on! Give it to me! Give it to me!
(thud)
YEAH!
(thud)
YEAH!
One more, baby, one more!
It's all I need.
Okay, go-go-go-go-go!
(thud)
YEAH!
Where's this one gonna go?
Tell me! Tell me! Seven minutes left?
Where's it gonna go?
One arrow close to the bull's-eye.
(thud)
OH! OH! It was there! It was there!
Come on, baby! Give it to me! Give it to me!
(thud)
YEAH! Did you see that?
WOO-HOO-HOO!