Errors and Error Measurements

Thorough study of Experimental Errors occurred during experimentation using different experimental techniques.
A clear picture about techniques for error measurement is given in the presentation.

1. CAUSES AND TYPES OF
EXPERIMENTAL ERRORS
Presented By:
Milind A. Pelagade

2. The error in measurement is the difference
between the measured value and the true
value of the measured dimension.
What is an error?

3. TYPE OF ERRORS
Type of errors
1)Gross error/human Errors
2)Random Errors
3)Systematic Errors
4)Constant Errors
5)Absolute Errors
6)Relative Errors
7)Percentage Errors
Static Errors

4. 1) Gross Error
cause by human mistakes in reading/using instruments
may also occur due to incorrect adjustment of the instrument and
the computational mistakes
cannot be treated mathematically
cannot eliminate but can minimize
Eg: Improper use of an instrument.
This error can be minimized by taking proper care in reading and
recording measurement parameter.
In general, indicating instruments change ambient conditions to
some extent when connected into a complete circuit.
Therefore, several readings (at three readings) must be taken to
minimize the effect of ambient condition changes.
TYPES OF STATIC ERROR

5. Human error
Reading a scale:
Discuss the best position to put
your eye.
your
eye

6. 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?

7. TYPES OF STATIC ERROR
2) Systematic Error
-due to shortcomings of the instrument (such as
defective or worn parts, effects of the environment on the
instrument)
In general, systematic errors can be subdivided into static and dynamic
errors.
Static – caused by limitations of the measuring device or the
physical laws governing its behavior.
Dynamic – caused by the instrument not responding very fast
enough to follow the changes in a measured variable.

8. 3 types of systematic error :-
(i) Instrumental error
(ii)Environmental error
(iii)Observational error
TYPES OF STATIC ERROR

9. TYPES OF STATIC ERROR
(i) Instrumental error
- inherent while measuring instrument because of
their mechanical structure (eg: friction in the bearings of various
moving component, irregular spring tension, stretching of spring, etc)
- error can be avoid by:
(a) selecting a suitable instrument for the particular
measurement application
(b) apply correction factor by determining
instrumental error
(c) calibrate the instrument against standard

10. TYPES OF STATIC ERROR
(ii)Environmental error
- due to external condition effecting the
measurement including surrounding area condition
such as change in temperature, humidity,
barometer pressure, etc
- to avoid the error :-
(a) use air conditioner
(b) sealing certain component in the instruments
(c) use magnetic shields
(iii) Observational error
- introduce by the observer
- most common : parallax error and estimation error (while reading the scale)
- Eg: an observer who tend to hold his head too far to the left, while reading
the position of the needle on the scale.

11. TYPES OF STATIC ERROR
3) Random error
- due to unknown causes, occur when all systematic
error has accounted
- accumulation of small effect, require at high degree of
accuracy
- can be avoid by
(a) increasing number of reading
(b) use statistical means to obtain best approximation
of true value

12. What is systematic error?
Systematic error is caused by any factors that systematically affect
measurement of the variable across the sample.
For instance, if there is loud traffic going by just outside of a
classroom where students are taking a test, this noise is liable to
affect all of the children's scores in this case, systematically
lowering them.
Unlike random error, systematic errors tend to be consistently
either positive or negative because of this, systematic error is
sometimes considered to be bias in measurement.

13. 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 . . .

14. 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):

15. 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.

16. A particular type of systematic error
is called a zero error.
Systematic errors
Here are some examples . . .

17. 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?

18. 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.

19. Example 5
Look at this
ammeter:
Zero errors
If you used it like this,
what effect would it have
on your results?

20. Example 8
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.

21. What is random error?
Caused by any factors that randomly affect measurement of the
variable across the sample.
Each person’s mood can inflate or deflate their performance on
any occasion. In a particular testing, some children may be in a
good mood and others may be depressed. Mood may artificially
inflate the scores for some children and artificially deflate the
scores for others.
Random error does not have consistent effects across the entire
sample. If we could see all the random errors in a distribution,
the sum would be zero.
The important property of random error is that it adds
variability to the data but does not affect average performance
for the group.

22. Random Errors
Random errors are “not inherent to the measuring process”. 
Frequently they are introduced by external factors that cause a
scattering of the measured data.
When the scattering is distributed equally about the true value, the
error can be mitigated somewhat by making multiple measurements
and averaging the data. 
• Vibration in mechanical devices produces random errors.
•  In electronic devices, noise produces random errors.   

23. 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 average (mean).

24. Constant Error
•When the results of observation are in error by the same
amount, the error is said to be a constant error. e.g. if a scale
of 15 cm actually measures 14.8 cm. Then it is measuring 0.2
cm more in every observation. This type of error will be same
in all measurements done by the scale.

25. Another types of Error
Three other ways of defining the error are:
Absolute error
Relative error
Percentage error

26. Calculating the Error
A simple way of looking at the error is as the difference between the
true value and the approximate value.
i.e:
Error (e) = True value – Approximate value

27. Calculation the Absolute Error
Absolute error.
e
a = |True value – Approximate value|
| || |Error=XX=e
'
a
-

28. Calculating the Error
Absolute error:
e
a = |True value – Approximate value|
Relative error is defined as:
| || |Error=XX=e
'
a
-
½
½
½
½
½
½-
½
½
½
½
½
½
X
XX
=
ValueTrue
ErrorAbsolute
=e
'
r

29. Absolute Error
The difference between the measured value and the true value is
referred to as the absolute error. Assume that analysis of an iron ore
by some method gave 11.1% while the true value was 12.1%, the
absolute error is:
11.1% - 12.1% = -1.0%
29

30. Relative Error
The relative error is the percentage of the absolute error to the true
value. For the argument above we can calculate the relative error
as:
Relative error = (absolute error/true value)x100%
= (-1.0/12.1)x100% = -8.3%
30

31. Calculating the Error
Percentage error is defined as:
½
½
½
½
½
½-
X
XX
=e=e
'
rp 100100

32. Examples
Suppose 1.414 is used as an approx to . Find the absolute, relative
and percentage errors.

2
| | valueeApproximat– valueTrue=e
a
1.414213562=
| |1.414-1.41421356∴=e
a
=0.00021356
error)(absolute

33. Examples
Suppose 1.414 is used as an approx to . Find the absolute, relative
and percentage errors.

2
1.414213562=
½
½
½
½
½
½
2
0.00021356
∴=e
r
3
100.151
-
´=
error)(relative
½
½
½
½
½
½
ValueTrue
Error
=e
r

34. 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 average
(mean).
•Parallax errors can be avoided.
•Anomalous results can be seen on a graph.

35. THANK YOU