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. TRIALMASS(g)TRIALMASS(g) Average100.00Average Range±0.01Range±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 TRIALMASS(g)TRIALMASS(g) Average100.00Average Range±0.01Range±0.11

Let’s play darts!

Accurate? Precise?

Precise, but poor accuracy

Play again?

Accuracy? Precision?

Both accurate and precise

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 ± 0.5mm43.4 mm ± 0.5mm Add the uncertainties, therefore 43.4 mm ± 1mm

The Balance The balance measures to three decimal places: e.g g. The uncertainty is  g, 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  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: g, g, g 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

39 STARTER: Dartboard analogy How could you describe the following: Not accurate Not precise Accurate Not precise Not accurate Precise Accurate Precise

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 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. your eye

Human error 2 is best. 1 and 3 give the wrong readings. This is called a parallax error. your eye 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 x x x x

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 error All 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 90 o, 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