WEBVTT
00:00:00.200 --> 00:00:03.640
In this video, we’re talking about measurement accuracy and precision.
00:00:03.880 --> 00:00:09.010
As we’ll see, these are two terms that come up often when we make measurements of physical quantities.
00:00:09.160 --> 00:00:17.370
And even though sometimes these two terms are treated as though they mean the same thing, in fact, they have very particular and very distinct definitions.
00:00:17.700 --> 00:00:25.140
Since accuracy and precision both come up in the context of making measurements, let’s think for a moment about just what a measurement is.
00:00:25.270 --> 00:00:30.700
We can define a measurement as a collection of numerical data that describes a physical quantity.
00:00:30.800 --> 00:00:42.430
Examples of this would include things like using a ruler to find the length of a pencil or using a scale to find the mass of some object or using a stopwatch to count how long it takes a runner to run around a track.
00:00:42.640 --> 00:00:48.400
In each one of these examples, we would collect some numerical data that describes a physical quantity.
00:00:48.580 --> 00:00:56.090
Now we know that the intention of a measurement is to come up with a value which matches the true value of the quantity we’re trying to measure.
00:00:56.270 --> 00:01:00.850
For example, let’s say that the actual true length of our pencil is 12 centimeters.
00:01:00.940 --> 00:01:06.620
When we go to measure the pencil’s length, we would hope to come up with a value that very closely matches that true length.
00:01:07.010 --> 00:01:10.260
But for a number of possible reasons, this doesn’t always happen.
00:01:10.560 --> 00:01:15.570
For example, maybe we don’t have the bottom of the pencil and the bottom of our ruler perfectly aligned.
00:01:15.750 --> 00:01:19.320
Or maybe the pencil and the ruler aren’t perfectly parallel with one another.
00:01:19.550 --> 00:01:23.340
Or it’s even possible to have everything about our measurements set up correctly.
00:01:23.550 --> 00:01:26.750
But we simply read off the incorrect value from our ruler.
00:01:27.000 --> 00:01:33.820
These are all possible error resources that would lead to a measurement that doesn’t match the true value of our pencil’s length.
00:01:34.280 --> 00:01:39.780
Let’s say that when we measure the length of this pencil, the value we read off of the ruler is 11 centimeters.
00:01:39.880 --> 00:01:47.270
And let’s further imagine that using this particular ruler, the best we can do in reading off values is to find a measurement to the nearest centimeter.
00:01:47.460 --> 00:01:50.820
So we make one measurement, which comes out to 11 centimeters.
00:01:51.050 --> 00:01:57.660
Now, if we don’t know the true value of the length of our pencil, we may very well think that this is it, that it’s 11 centimeters long.
00:01:57.940 --> 00:02:04.020
But aware that it’s possible to make a mistake in a measurement process, we decide to redo the experiment.
00:02:04.020 --> 00:02:05.530
We’re going to take a second measurement.
00:02:05.850 --> 00:02:10.000
Say that when we do, we find a result not of 11 but of 12 centimeters.
00:02:10.230 --> 00:02:15.340
And then say we repeat this measurement process one more time and we find a result of 13 centimeters.
00:02:15.490 --> 00:02:25.230
Based on these results, if we were to give one value for what we thought the length of the pencil was, a common and useful strategy is to average all of the measurements we’ve collected.
00:02:25.440 --> 00:02:29.380
The average of 11 and 12 and 13 is 12.
00:02:29.670 --> 00:02:32.760
So our average measurement of these three is 12 centimeters.
00:02:33.090 --> 00:02:41.170
Now, given the inside information that the true length of this pencil is indeed 12 centimeters, we would know that our answer is an accurate answer.
00:02:41.350 --> 00:02:46.720
And when we say that an answer is accurate, we mean that it closely matches the true value we wanted to measure.
00:02:46.990 --> 00:02:48.400
We can write that out this way.
00:02:48.630 --> 00:02:55.120
We can say that accuracy is an indication of how close measurements are to the true value of what is being measured.
00:02:55.400 --> 00:03:02.770
Our average value for the pencil length of 12 centimeters exactly matches its true value and therefore is a completely accurate result.
00:03:02.960 --> 00:03:11.510
On the other hand, if we had measured the average length of the pencil to be, say, four centimeters, then that would be less accurate than this result we found here.
00:03:11.850 --> 00:03:16.180
Now, when we’re talking about measurement accuracy, there are a couple of different ways to think of it.
00:03:16.400 --> 00:03:20.050
One way is to think of the accuracy of individual measurements we make.
00:03:20.260 --> 00:03:28.290
So, for example, the measurement accuracy of this 11-centimeter reading or this 12-centimeter reading or this 13-centimeter reading individually.
00:03:28.340 --> 00:03:36.920
But another approach, the way that we went about doing it, was to find the average value of a set of measurements and then compare that average to the true value.
00:03:37.290 --> 00:03:45.840
Either way, whether we’re working with an individual measurement or an average measured value, we’re still able to talk about the accuracy of those measurements.
00:03:45.910 --> 00:03:51.140
That’s because accuracy involves comparing those measurements against the true value of what we’re trying to measure.
00:03:51.440 --> 00:03:55.810
The more closely these two values agree, the more accurate the measurement was.
00:03:56.100 --> 00:03:58.100
So that’s the meaning of accuracy.
00:03:58.360 --> 00:04:03.140
Now let’s consider a second set of measurements which would help us understand the term precision.
00:04:03.460 --> 00:04:07.860
Say that once more we make three independent measurements of the length of our pencil.
00:04:08.070 --> 00:04:10.520
The first measurement comes out to be four centimeters.
00:04:10.630 --> 00:04:13.420
The second comes out to be 28 centimeters.
00:04:13.480 --> 00:04:15.740
And the third measurement is four centimeters.
00:04:15.980 --> 00:04:21.540
Now, if we were to once more consider these three values as a set of data and find the average of them.
00:04:21.800 --> 00:04:25.880
The average of four and 28 and four is 12.
00:04:26.230 --> 00:04:29.560
So once again, we report a pencil length of 12 centimeters.
00:04:29.850 --> 00:04:35.060
Now, even though these two final results are the same, we can see that there’s something different about the way we got them.
00:04:35.270 --> 00:04:43.130
The first set of measured values were all tightly clustered around 12 centimeters, while the second set was very spread out compared to that.
00:04:43.320 --> 00:04:48.900
It’s precisely that spread within a set of measured values that the term precision refers to.
00:04:49.130 --> 00:04:54.490
The term precision means how close two or more measurements are to each other.
00:04:54.840 --> 00:04:58.760
Side by side then, we can see how precision and accuracy are different.
00:04:59.060 --> 00:05:05.810
When we talk about precision, we’re talking about two or more measurements of some value and comparing them to one another.
00:05:06.050 --> 00:05:09.240
If the values are close together, we say that they are precise.
00:05:09.400 --> 00:05:14.560
But then, if the values are very different from one another, we would say that that data set is not precise.
00:05:14.790 --> 00:05:21.310
So comparing the first set of measurements we made with the second set, we can say that the first set is more precise.
00:05:21.530 --> 00:05:28.450
Because the difference between these three measured values is smaller than the difference between these three measured values.
00:05:28.710 --> 00:05:35.700
Interestingly, the precision of a measured value has nothing to do with the actual, true, value that we want to measure.
00:05:36.090 --> 00:05:45.820
As far as the precision of our measurements made in trying to find the true length of our pencil, we don’t even need to know that true length to know whether our results are precise or not.
00:05:46.310 --> 00:05:54.030
This is very different from what we found for accuracy, where accuracy necessarily compares the true value with the measured value.
00:05:54.460 --> 00:05:59.040
Along with this difference between accuracy and precision, there’s one other that we should mention.
00:05:59.340 --> 00:06:03.990
It’s completely reasonable to talk about the accuracy of a single measurement we would make.
00:06:04.290 --> 00:06:09.090
That’s because we’re comparing that measured value with the true value of the quantity of interest.
00:06:09.280 --> 00:06:14.640
But when it comes to precision, it doesn’t make sense to talk about the precision of a single measurement.
00:06:15.070 --> 00:06:15.810
Why is that?
00:06:16.130 --> 00:06:22.710
It’s because precision necessarily involves a comparison between multiple measured values, at least two of them.
00:06:23.060 --> 00:06:32.950
Considering once more this second set of data, if we were asked, what is the precision of this measurement here of four centimeters, there’s no way we could give a sensible answer.
00:06:33.230 --> 00:06:38.090
That value has no precision except in comparison to the other measured values.
00:06:38.310 --> 00:06:43.950
It’s only when we consider two or more measurements together that we’re able to talk about the precision of data.
00:06:44.360 --> 00:06:55.860
So summing all this up, to know the precision of a measured value, say our final value of 12 centimeters for the length of the pencil, we need to have two or more measured values we can compare with one another.
00:06:56.050 --> 00:06:59.720
And we don’t need to know the true value of the quantity we’re trying to measure.
00:07:00.020 --> 00:07:04.370
To find the accuracy of a result though, only one measured value is needed.
00:07:04.610 --> 00:07:08.940
But we do need to know the actual true value of the quantity we’re trying to measure.
00:07:09.300 --> 00:07:14.690
Along with our understanding of these two terms, we can now notice something else about our measurement results.
00:07:14.880 --> 00:07:20.590
We saw that our first set of measurements taken together were more precise than our second set of measurements.
00:07:20.850 --> 00:07:26.590
Yet despite that difference, the accuracy of our final result in both cases was the same.
00:07:26.900 --> 00:07:33.470
This means it’s possible for us to arrive at an accurate final answer using an imprecise set of measurements.
00:07:33.780 --> 00:07:36.960
And what’s more, the reverse is also a possibility.
00:07:37.270 --> 00:07:40.690
We could have a very precise set of measured values.
00:07:40.870 --> 00:07:45.530
Say we made three measurements of the pencil’s length and we found the same values each time.
00:07:45.700 --> 00:07:49.440
So when we average them together, we get a result of 17 centimeters.
00:07:49.610 --> 00:07:56.270
We could say that this measurement set is very precise, as precise as it possibly could be, since the values are the same.
00:07:56.450 --> 00:07:58.590
And yet our answer is not accurate.
00:07:58.880 --> 00:08:00.150
Here’s what we’re finding then.
00:08:00.390 --> 00:08:03.250
It’s possible to be precise but not accurate.
00:08:03.560 --> 00:08:06.350
And it’s possible to be imprecise and accurate.
00:08:06.600 --> 00:08:11.090
It comes down to the differences between these two terms, accuracy and precision.
00:08:11.450 --> 00:08:15.230
Let’s test our understanding of these terms through a couple of examples.
00:08:15.610 --> 00:08:20.970
Which of the following statements most correctly describes the meaning of the precision of measurements?
00:08:21.250 --> 00:08:25.030
A) A precise measurement is more accurate than an accurate measurement.
00:08:25.500 --> 00:08:32.550
B) The more precise the measurement of a quantity is, the closer the measured value is to the actual value of the measured quantity.
00:08:33.010 --> 00:08:37.000
C) A precise measurement is made using a correct measurement method.
00:08:37.470 --> 00:08:47.760
D) The more precise the measurement of a quantity is, the smaller the predictable change that can be made between the measured value and other measured values of the same quantity.
00:08:48.320 --> 00:08:55.820
Okay, we can see that the answer to this question is all about the specific meaning of the word precision when it comes to making measurements.
00:08:56.040 --> 00:09:01.200
We have these four different candidates for the most correct description of the precision of measurements.
00:09:01.430 --> 00:09:04.460
So let’s go through them one by one and evaluate each in turn.
00:09:04.730 --> 00:09:08.940
Option A says that a precise measurement is more accurate than an accurate measurement.
00:09:09.260 --> 00:09:16.110
Now, one thing this option gets right is that it acknowledges that there’s a difference between a precise measurement and an accurate measurement.
00:09:16.110 --> 00:09:17.310
They don’t mean the same thing.
00:09:17.590 --> 00:09:22.850
But what it doesn’t get right is in claiming that a precise measurement is more accurate than an accurate one.
00:09:23.050 --> 00:09:31.070
Because precision and accuracy are two different terms with two different meanings, a precise measurement will not be more accurate than an accurate one.
00:09:31.290 --> 00:09:33.370
We can cross off option A then.
00:09:33.660 --> 00:09:41.320
Option B says that the more precise the measurement of a quantity is, the closer the measured value is to the actual value of the measured quantity.
00:09:41.560 --> 00:09:47.480
So option B is saying that we have these two values: a measured one and the actual correct one for some quantity.
00:09:47.610 --> 00:09:51.570
And it says that the closer these two values are, the more precise the measurement is.
00:09:51.670 --> 00:09:55.690
But this statement is confusing the terms for precision and accuracy.
00:09:55.790 --> 00:10:01.230
If we replace this word “precise” with the word “accurate,” then this description would be correct.
00:10:01.430 --> 00:10:06.850
The closeness of a measured value to an actual true value is the meaning of an accurate measurement.
00:10:07.080 --> 00:10:14.030
But because precision and accuracy don’t mean the same thing, Option B is not a correct description of a precise measurement.
00:10:14.350 --> 00:10:19.150
Moving on to option C, this says that a precise measurement is made using a correct measurement method.
00:10:19.400 --> 00:10:24.180
Well, it’s certainly more likely that using a correct measurement method will lead to a precise measurement.
00:10:24.340 --> 00:10:25.930
But that’s not always the case.
00:10:26.060 --> 00:10:29.190
It’s possible, for example, to have a correct measurement method.
00:10:29.410 --> 00:10:32.110
But the way we carry out that method has errors in it.
00:10:32.400 --> 00:10:37.730
And those errors, which would influence the measurements we would make, might lead to imprecise measurements.
00:10:37.940 --> 00:10:41.100
Overall then, option C is not looking like a great choice.
00:10:41.230 --> 00:10:48.270
But because it’s not explicitly incorrect, let’s table it for now, keep it in mind, and then move on to our last choice, option D.
00:10:48.590 --> 00:10:58.610
This option says that the more precise the measurement of a quantity is, the smaller the predictable change that can be made between the measured value and other measured values of the same quantity.
00:10:58.810 --> 00:11:00.620
Now here’s what this description is saying.
00:11:00.880 --> 00:11:03.500
Let’s say that we have some true value for a quantity.
00:11:03.540 --> 00:11:04.900
And we’ll call that value 𝑉.
00:11:05.040 --> 00:11:07.360
This could be the length of an object or its mass.
00:11:07.360 --> 00:11:10.710
But the point is it’s the accurate representation of that quantity.
00:11:10.920 --> 00:11:15.480
In order to discover what that correct quantity is, we make a series of measurements.
00:11:15.610 --> 00:11:18.630
We can say that the result of our first measurement is 𝑀 one.
00:11:18.780 --> 00:11:22.800
And then we make another measurement 𝑀 two, another one 𝑀 three, and so on.
00:11:22.980 --> 00:11:28.300
We can make any number of these measurements attempting to figure out the true value of the quantity we’re interested in.
00:11:28.470 --> 00:11:32.230
Now, statement D is not talking about this true value 𝑉.
00:11:32.280 --> 00:11:37.100
What it’s comparing is the different measured values of this quantity one to another.
00:11:37.360 --> 00:11:43.480
And it’s saying that the smaller the difference between these measured values, the more precise our measurement is.
00:11:43.620 --> 00:11:46.530
And this is a good description of measurement precision.
00:11:46.610 --> 00:11:52.410
It compares measured values to one another and says the closer they are to one another, the more precise our measurements are.
00:11:52.650 --> 00:11:59.050
Since option D is an explicitly correct description of the precision of measurements, we choose this as our answer.
00:11:59.250 --> 00:12:04.740
Let’s look now at one more example, this one helping us understand what measurement accuracy means.
00:12:05.250 --> 00:12:10.350
Which of the following statements most correctly describes the meaning of accuracy of measurements?
00:12:10.780 --> 00:12:12.870
Okay, let’s go through these statements one by one.
00:12:13.190 --> 00:12:18.710
A) An accurate measurement has a value that is the same value when a quantity is repeatedly measured.
00:12:19.000 --> 00:12:24.600
Now to set this up a bit, let’s say that this quantity that we’re measuring has some true accurate value.
00:12:24.690 --> 00:12:26.050
We’ll call that value 𝑇.
00:12:26.330 --> 00:12:32.850
And what we’re doing is we’re making measurements of this quantity with the hope that those measurements reveal to us 𝑇, that true value.
00:12:33.040 --> 00:12:34.960
So we make a series of measurements.
00:12:34.990 --> 00:12:39.400
And their results we can call 𝑀 one, 𝑀 two, 𝑀 three, and so forth.
00:12:39.750 --> 00:12:48.600
Now this option A is saying that if 𝑀 one, 𝑀 two, 𝑀 three, and the other measured values we have all have the same value, then that’s what an accurate measurement is.
00:12:48.640 --> 00:12:54.050
But notice that all these measurements could be the same thing and yet be very different from our true value 𝑇.
00:12:54.180 --> 00:13:00.300
So just because our measured values agree with one another, just because they have the same value doesn’t mean our measurement is accurate.
00:13:00.540 --> 00:13:02.530
So option A is off our list.
00:13:02.700 --> 00:13:12.810
Moving on to option B, the more accurate the measurement of a quantity is, the smaller the predictable change that can be made between the measured value and other measured values of the same quantity.
00:13:13.090 --> 00:13:20.990
Similar to option A, option B is comparing these measured values one to another, and it’s not comparing them to the true value 𝑇.
00:13:21.180 --> 00:13:27.510
Option B is saying that the closer 𝑀 one, 𝑀 two, 𝑀 three, and so on are together, the more accurate the measurement is.
00:13:27.560 --> 00:13:31.350
But again, this leaves out a comparison with the true value of this quantity.
00:13:31.510 --> 00:13:33.660
So option B can’t be our choice either.
00:13:33.890 --> 00:13:37.930
Option C says that an accurate measurement is made using a correct measurement method.
00:13:38.100 --> 00:13:44.650
It’s true that using a correct measurement method makes it more likely that our measurement will be accurate, but it doesn’t make it inevitable.
00:13:44.750 --> 00:13:47.480
It’s possible to have a perfectly correct measurement method.
00:13:47.670 --> 00:13:52.640
But to execute that method incorrectly, leading to measurement values which are not accurate.
00:13:53.030 --> 00:13:57.060
That is, do not match up closely with the true value of the quantity we’re measuring.
00:13:57.380 --> 00:14:00.150
So option C doesn’t seem like it will be our choice either.
00:14:00.370 --> 00:14:02.570
On then, to our last hope, option D.
00:14:02.910 --> 00:14:09.700
This says the more accurate the measurement of a quantity is, the closer the measured value is to the actual value of the measured quantity.
00:14:09.890 --> 00:14:17.640
In Option D, for the first time, we’re talking about making a comparison between the measured quantities and the true value of the quantity we’re measuring.
00:14:17.790 --> 00:14:25.800
Option D says that the smaller that gap is, the smaller the difference between the true value and a measured value, the more accurate that measured value is.
00:14:25.870 --> 00:14:26.720
And this is true.
00:14:26.930 --> 00:14:32.930
Accuracy refers to a comparison between the true value of some quantity and the measured value of that quantity.
00:14:33.160 --> 00:14:37.720
This then is the statement that most correctly describes the meaning of accuracy of measurements.
00:14:38.910 --> 00:14:43.660
Let’s take a moment now to summarize what we’ve learned in this lesson on measurement accuracy and precision.
00:14:44.080 --> 00:14:49.140
We’ve seen that accuracy and precision are two terms we use in describing measurements.
00:14:49.180 --> 00:14:51.740
And that each one of these terms has a distinct meaning.
00:14:52.250 --> 00:15:01.680
We learned that the closer a measured value or average measured value is to the true value of the quantity being measured, the more accurate that measured value is.
00:15:01.970 --> 00:15:08.660
And then the closer a set of two or more measured values are to one another, the more precise the measurement is.
00:15:08.920 --> 00:15:14.740
So accuracy then involves comparing measured values with the true or actual value of the quantity being measured.
00:15:14.930 --> 00:15:23.080
While precision involves a comparison among measured values, without any reference to the true or actual value of the quantity of interest.
00:15:23.420 --> 00:15:27.570
So accuracy in measurement and precision in measurement are both useful terms.
00:15:27.650 --> 00:15:30.080
And each one has its own distinct meaning.