Transcript Errors and Uncertainties in Biology

Errors and Uncertainties in
Biology
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
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 is digital and 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.
 Always use .1 for digital devices

The stopwatch

An exception to the uncertainty being half the
smallest instrument value is when using a
stopwatch.
 According to the display you can measure time
to the nearest 100th of a second (0.01 s) with
our stopwatches.
 Because human reaction time must always be
factored in you need to use  1 second
Data Collection

Whenever you record raw data you must
include the uncertainty of the measuring
device.
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: 23.3mm, 23.5mm, 23.6mm

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

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



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


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


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

Now try the uncertainty practical
Dartboard analogy

How could you describe the following:
Not accurate
Not precise
Accurate
Not precise
Not accurate
Precise
Accurate
Precise
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Types of errors
Types of errors

There are two types of errors that we are
concerned with when looking at our
experimental data:
Types of errors

There are two types of errors that we are
concerned with when looking at our
experimental data:

Systematic errors
Types of errors

There are two types of errors that we are
concerned with when looking at our
experimental data:
Systematic errors
 Random errors

Systematic errors

Result from a defect in an instrument or
procedure. E.g. the balance is incorrectly
calibrated.
Systematic errors

Result from a defect in an instrument or
procedure. E.g. the balance is incorrectly
calibrated.
 The systematic error is always in one
direction. E.g. the incorrectly calibrated
balance always gives readings that are too
high by 0.1g.
Systematic errors

Result from a defect in an instrument or
procedure. E.g. the balance is incorrectly
calibrated.
 The systematic error is always in one
direction. E.g. the incorrectly calibrated
balance always gives readings that are too
high by 0.1g.
 Comparison to standard samples can help
overcome systematic errors. E.g. use a
standard of known mass on the balance.
Systematic errors
Systematic errors affect the accuracy of the readings.
Random errors

Result from random fluctuations in procedures
and measuring devices.
Random errors

Result from random fluctuations in procedures
and measuring devices.
 Because this error is random in nature it can
be too high or too low than the actual value.
Random errors

Result from random fluctuations in procedures
and measuring devices.
 Because this error is random in nature it can
be too high or too low than the actual value.
 Random errors can be reduced by taking the
average of several replicate measurements.
Random errors
An average of the measurements will be more accurate, closer
to the actual value.
Random errors
average
An average of the measurements will be more accurate, closer
to the actual value.