ERRORS IN MEASUREMENTS

What is an error?

An error is a mistake of some kind...

…causing an error in your results…

…so the result is not accurate.

ERRORS

Errors can be divided into 2 main classes

Random errors Systematic errors

MISTAKES

Mistakes on the part of an individual such as: misreading scales poor arithmetic and computational skills wrongly transferring raw data to the final

report using the wrong theory and equations

These are a source of error but are not considered as an experimental error

https://myportal.bsd405.org/personal/dossettl/advphys/Shared%20Documents/Types%20of%20Error.pdf

RANDOM ERRORS

Are due to variations in performance of the instrument and the operator

These errors cannot be rectified but can be minimized.

https://myportal.bsd405.org/personal/dossettl/advphys/Shared%20Documents/Types%20of%20Error.pdf

ERRORS RESULT FROM

vibrations and air convection currents in mass readings & temperature variations.

misreadings variations in the thickness of a surface

being measured (thickness of wire) not collecting enough data using a less sensitive instrument when a

more sensitive instrument is available human parallax error

https://myportal.bsd405.org/personal/dossettl/advphys/Shared%20Documents/Types%20of%20Error.pdf

http://www.physics4u.co.uk/

Random errors

These may be due to human error, or a faulty technique.

To reduce the error,take a lot of readings, and then calculate the average (mean).

http://www.physics4u.co.uk/

Random Error- Faulty technique

Example 1

Professor Messer is trying to measure the length of a piece of wood:

Discuss what he is doing wrong.

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Random Error- Faulty technique

1. Measuring from 100 end

2. 95.4 is the wrong number

3. ‘mm’ is wrong unit (cm)

4. Hand-held object, wobbling

5. Gap between object & the rule

6. End of object not at the end of the rule

7. Eye is not at the end of the object (parallax)

8. He is on wrong side of the rule to see scale.

Answers:

http://www.physics4u.co.uk/

Human error

Example 2

Reading a scale:

Discuss the best position to put your eye.

youreye

http://www.physics4u.co.uk/

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?

SYSTEMATIC ERRORS

causes random set of measurements to be spread about a value rather than spread about an accepted value

Systematic errors result from: Badly made instruments Poorly calibrated instruments An instrument having a zero error, a form of calibration Poorly timed actions Instrument parallax error Note that systematic errors are not reduced by

multiple readings

https://myportal.bsd405.org/personal/dossettl/advphys/Shared%20Documents/Types%20of%20Error.pdf

http://www.physics4u.co.uk

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 . . .

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Example 1Suppose 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):

http://www.physics4u.co.uk

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.

http://www.physics4u.co.uk

A particular type of systematic error

is called a zero error.

Systematic errors

Here are some examples . . .

http://www.physics4u.co.uk

Example 3

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?

http://www.physics4u.co.uk

Example 4

Look at this top-pan 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.

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Example 5

Look at this ammeter:

Zero errors

If you used it like this, what effect would it have on your results?

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Example 6

Look at this voltmeter:

Zero errors

What is the first thing to do?

Use a screwdriver here to adjust the pointer.

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Example 7

Look at this ammeter:

Zero errors

What can you say?

Is it a zero error?

ACCURACY VERSUS PRECISION

Accuracy is an indication of how close a measurement is to the accepted value

An accurate experiment has a low systematic error

Precision is an indication of the agreement among a number of measurements.

A precise experiment has a low random errorhttp://physicsstudents.edublogs.org/wiki/dp-physics-student-wikis-2014/sung-ei/sung-ei-topic-1/sung-ei-topic-1-2-69/

HIGH PRECISION - HIGH ACCURACY

HIGH PRECISION - LOW ACCURACY

LOW PRECISION - HIGH ACCURACY

LOW PRECISION - LOW ACCURACY

SCATTER GRAPH

http://www.mrcorfe.com/KS4/AQA/Glossary.php#Errors

Used to data display with two sets of variables (dependent and independent).

Points are plotted and a smooth 'Line of Best Fit' is drawn. This shows the general trend and averages out any errors in the data.

The 'Line of best Fit' on a scatter graph is the representation of our best guess at the true values.

The line could be straight ie. linear, or equally correct is a curved line. It is a judgment to be made when looking at the data points. Because of this, there should be at least 5 data points to enable the trend to be correctly identified.

RANDOM ERROR Random errors are represented

on a scatter graph by the distance from the 'Line of Best Fit'.

In the adjacent diagram the green lines show the error.

It is assumed that the error in measuring the independent variable is low compared to that of the dependant variable - hence the green lines are vertical.

If the points are all close to the 'Line of Best Fit' then we can say that our results are good as the error is minimal

http://www.mrcorfe.com/KS4/AQA/Glossary.php#Errors

SYSTEMATIC ERROR

These cause readings to be spread about some value other than the true value

in other words, all the readings are shifted one way or the other way from the true value.

http://www.mrcorfe.com/KS4/AQA/Glossary.php#Errors

ANOMALY

An anomaly is a point significantly out of place compared to the other results.

This is normally due to a misreading or a mistake in the recording / plotting of results.

These should be ignored both when calculating a mean drawing a 'Line of Best Fit' as they are clearly wrong - beyond the realms of random error.

http://www.mrcorfe.com/KS4/AQA/Glossary.php#Errors

RESOURCES

http://www.physics4u.co.uk http://www.mrcorfe.com/KS4/AQA/Gloss

ary.php#Errors

http://physicsstudents.edublogs.org/wiki/dp-physics-student-wikis-2014/sung-ei/sung-ei-topic-1/sung-ei-topic-1-2-69