errors and uncertainties in science accuracy accuracy indicates how close a measurement is to the...
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Errors and Uncertainties in Science
Accuracy
Accuracy indicates how close a measurement is to the accepted value. For example, we'd expect a balance to read 100 grams if we placed a standard 100 g weight on the balance. If it does not, then the balance is inaccurate.
Precision
Precision indicates how close together or how repeatable the results are. A precise measuring instrument will give very nearly the same result each time it is used. The precision of an instrument reflects the number of significant digits in a reading.
TRIAL MASS(g) TRIAL MASS(g)
1 100.01 1 100.10
2 100.00 2 100.00
3 99.99 3 99.88
4 99.99 4 100.02
Average 100.00 Average 100.00
Range ±0.01 Range ±0.11
Precision
Precision indicates how close together or how repeatable the results are. A precise measuring instrument will give very nearly the same result each time it is used. The precision of an instrument reflects the number of significant digits in a reading.
More precise
Less precise
TRIAL MASS(g) TRIAL MASS(g)
1 100.01 1 100.10
2 100.00 2 100.00
3 99.99 3 99.88
4 99.99 4 100.02
Average 100.00 Average 100.00
Range ±0.01 Range ±0.11
Let’s play darts!
Let’s play darts!
Let’s play darts!
Let’s play darts!
Accurate? Precise?
Precise, but poor accuracy
Play again?
Play again?
Play again?
Play again?
Play again?
Accuracy? Precision?
Both accurate and precise
One more time!
One more time!
One more time!
One more time!
One more time!
Well?
Poor accuracy and precision
Uncertainty in measurement
An error in a measurement is defined as the difference between the true, or accepted, value of a quantity and its measured value.
Uncertainty in measurement
An error in a measurement is defined as the difference between the true, or accepted, value of a quantity and its measured value.
In reading any scale the value read is numbers from the scale and one estimated number from the scale and an error of ½ a division.
The Ruler
0.0mm ± 0.5mm 43.4 mm ± 0.5mm
Add the uncertainties, therefore 43.4 mm ± 1mm
The Balance
The balance measures to three decimal places: e.g. 24.375g.
The uncertainty is 0.0005g, but once again we have to determine two points, the zero (with no mass on the balance) and the mass of the object to be measured.
Therefore the uncertainty is 0.001 g
Data Collection
Whenever you record raw data you must include the uncertainty of the measuring device.
Now try the uncertainty practical
Plenary: Which is more precise?
The ruler or the balance?
Which is more precise?
The ruler or the balance?The balance has a greater precision than
the ruler, it measures to more decimal places and therefore the measurements are closer together.
Which is more precise?
The ruler or the balance?The balance has a greater precision than
the ruler, it measures to more decimal places and therefore the measurements are closer together.
E.g. Balance: 23.456g, 23.453g, 23.458g
Ruler: 23mm, 23mm, 24mm
Accuracy and Precision
Two students set out to measure the size of a cell that is known to be 100 m in length.
Each student takes a number of measurements and they arrive at the following answers:
Accuracy and Precision
Two students set out to measure the size of a cell that is known to be 100 m in length.
Each student takes a number of measurements and they arrive at the following answers:
Student A: 101 m 8 m Student B: 95 m 1 m
Accuracy and Precision
Two students set out to measure the size of a cell that is known to be 100 m in length.
Each student takes a number of measurements and they arrive at the following answers:
Student A: 101 m 8 m Student B: 95 m 1 m Which students measurements are more precise? Which students measurements are more accurate?
Accuracy and Precision
Two students set out to measure the size of a cell that is known to be 100 m in length.
Each student takes a number of measurements and they arrive at the following answers:
Student A: 101 m 8 m Student B: 95 m 1 m Which students measurements are more precise? B Which students measurements are more accurate?
Accuracy and Precision
Two students set out to measure the size of a cell that is known to be 100 m in length.
Each student takes a number of measurements and they arrive at the following answers:
Student A: 101 m 8 m Student B: 95 m 1 m Which students measurements are more precise? B Which students measurements are more accurate? A
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STARTER: Dartboard analogy How could you describe the following:
Not accurateNot precise
AccurateNot precise
Not accuratePrecise
AccuratePrecise
What is an error?
An error is a mistake of some kind...
…causing an error in your results…
…so the result is not reliable.
What is an error?
Some are due to human error…
For example,
by not using the equipment correctly
Let’s look at some examples.
Human error
Example 1
Professor Messer is trying to measure the length of a piece of wood:
Discuss what he is doing wrong.
How many mistakes can you find?
Human error
1. Measuring from 100 end
2. 95.4 is the wrong number
3. Hand-held object, wobbling
4. Gap between object & the ruler
5. End of object not at the end of the ruler
6. Eye is not at the end of the object (parallax)
7. He is on wrong side of the ruler to see scale.
Answers:
How many did you find?
Human error
Example 2
Reading a scale:
Discuss the best position to put your eye.
youreye
Human error
2 is best.
1 and 3 give the wrong readings.
This is called a parallax error.
youreye
It is due to the gap here, between the pointer and the scale.Should the gap be wide or narrow?
Anomalous results
When you are doing your practical work, you may get an odd or inconsistent or ‘anomalous’ reading.
This may be due to a simple mistake in reading a scale.
The best way to identify an anomalous result is to draw a graph.
For example . . .
Anomalous results
Look at this graph:Which result do you think may be anomalous?
A result like this should be taken again, to check it.
x
x
xx
xx
Types of errors
When reading scales,there are 2 main types of error:
Let’s look at some examples . . .
• Random errors
• Systematic errors.
Random errors
These may be due to human error,a faulty technique, or faulty equipment.
To reduce the error,take a lot of readings, and then calculate the mean.
These errors cause readings to be shifted one way (or the other) from the true reading.
Systematic errors
Your results will be systematically wrong.Let’s look at some examples . . .
Example 1
Suppose you are measuring with a ruler:
Systematic errors
If the ruler is wrongly calibrated, or if it expands,then all the readings will be too low (or all too high):
Example 2
If you have a parallax error:
Systematic errors
with your eye always too high
then you will get a systematic errorAll your readings will be too high.
A particular type of systematic error
is called a zero error.
Systematic errors
Here are some examples . . .
Example 1
A spring balance:
Zero errors
Over a period of time, the spring may weaken, and so the pointer does not point to zero:What effect does this have on all the readings?
Example 2
Look at this mass balance:
Zero errors
There is nothing on it, but it is not reading zero.What effect do you think this will have on all the readings?
It has a zero error.
Example 3
Look at this ammeter:
Zero errors
If you used it like this, what effect would it have on your results?
Example 4
Look at this voltmeter:
Zero errors
What is the first thing to do?
Use a screwdriver here to adjust the pointer.
Example 5
Look at this ammeter:
Zero errors
What can you say?
Is it a zero error?
Or is it parallax?
Example 6
Look at this ammeter:
Zero error, Parallax error
What is it for?
How can you use it to stop parallax error?
It has a mirror behind the pointer, near the scale.
When the image of the pointer in the mirror is hidden by the pointer itself, then you are looking at 90o, with no parallax.
In summary
• Human errors can be due to faulty technique.
• Systematic errors, including zero errors, will cause all your results to be wrong.
• Random errors can be reduced by taking many readings, and then calculating the mean
• Parallax errors can be avoided.
• Anomalous results can be seen on a graph.
Tasks for the rest of the lesson:
1. Finish your booklet
2. Try the Intro to Biology crossword