CAUSES AND TYPES OF EXPERIMENTAL ERRORS

Presented By:Milind A. Pelagade

The error in measurement is the difference between the measured value and the true value of the measured dimension.

What is an error?

TYPE OF ERRORS

Type of errors1) Gross error/human Errors2) Random Errors3) Systematic Errors4) Constant Errors5) Absolute Errors6) Relative Errors7) Percentage Errors

Static Errors

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

Human error

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?

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.

3 types of systematic error :-(i) Instrumental error(ii) Environmental error(iii) Observational error

TYPES OF STATIC ERROR

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

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.

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

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.

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 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):

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 3A 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 4Look 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.

Example 5Look at this ammeter:

Zero errors

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

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 90o, with no parallax.

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.

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.   

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).

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.

Another types of ErrorThree other ways of defining the error are:

Absolute errorRelative errorPercentage error

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

Calculation the Absolute ErrorAbsolute error. ea = |True value – Approximate value|

Error=XX=e 'a

Calculating the ErrorAbsolute error: ea = |True value – Approximate value|

Relative error is defined as: Error=XX=e '

a

XXX=

ValueTrueErrorAbsolute=e

'

r

Absolute ErrorThe 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%

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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%

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Calculating the Error

Percentage error is defined as:

XXX=e=e'

rp 100100

Examples

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

2

valueeApproximat– valueTrue=ea

1.414213562 =

1.414-1.41421356∴ =ea= 0 . 00021356

error)(absolute

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

2

1.414213562 =

20.00021356

∴ =er3100.151 =

error)(relative

ValueTrue

Error=er

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.

THANK YOU