Basic Measurement Concepts
ISAT 253
Spring 2005
So far…
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In the Design of Experiments
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Identify the problem/question
Specify the variables and how they will be
measured
Specify the Methodology
Collect and Analyze Data (including
uncertainty analysis)
Draw Conclusions
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So far…2
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To maximize the correlation coefficient R2
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To minimize the variability
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We use extreme care in
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Defining the variables
Defining the sampling or observations
Analyzing the resultant data
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Have care in…3
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Variables
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Specifying the independent and dependent
variables
Figuring out the confounding factors
Knowing if our work is:
Experimental
 Observational
 Modeling or simulation
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Have care in…4
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Sampling
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Identifying the population
Choosing the sampling plan
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Random
Systematic Samples
Stratified Samples
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Have care in…5
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Analyzing the data
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Identifying the distribution
Calculating the sample statistics
Studying the correlations
Deciding on possible cause and effects
Calculating the coefficient of determination
R2
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Caution
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A tenet of good experimentation
Data is data
There is no good or bad data
Thus,
One must have very strong and clear reasons
To justify
Not using ALL the data
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What we are about...
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What is a measurement?
What is a measuring instrument?
What is resolution?
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Why is it important?
How does resolution limit the display of the
number of digits to display?
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What we are about...2
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Visualize and differentiate between:
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Accuracy
Precision
Resolution
Understand the Sources of Uncertainty
Understand the types of data error.
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What is a MEASUREMENT?
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From the WEB
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“Determination of the magnitude of a quantity“
“The process of using dimensions, quantity, or
capacity by comparison with a standard in
order to mark off, apportion, lay out, or
establish dimensions”
“The process or result of observing an event or
object in order to determine its extent or
quantity by comparison with a known unit and
then assigning it a numerical value.”
Spring 2005
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What is a measurement system?
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A means for making the desired measurement.
What we are
measuring
Measured
or
quantified
output
The measurement method
Usually an instrument
Passive – a sensing element
Active – a ruler
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What is a measurand?
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In an experiment
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Seek numerical values for physical variables
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These are known as “
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Examples:
measurands”
Temperature
 Voltage
 Pressure
 Height
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Measurement Systems
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Measurement Systems
Measurand
Sensing
element
Human
Interface
Signal Conditioning
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Measurement Validity
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Extremely important that the output of a
measurement system truly states the actual
value of the measurand.
Nothing is perfect
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Always some deviation between actual value
and measured value
Key is that the deviation is small enough that
the measurement can be used for its intended
purpose.
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Measurement Validity
LIFE IS A BOX!
The Smaller the allowed deviation
The more expensive in time, equipment
& money
Will be the measurement system
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Measurement Error
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Resolution
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Resolution is the smallest increment of a unit
of measure that an instrument can detect or
measure.
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Usually (not always) indicated by the scale or
readout of an instrument
Helps dictate the number of significant figures
used in reporting the output.
It is important to understand the minimum
resolution needed (avoid overkill)
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For Example…
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I am weighing food portions on my magical
electronic scale.
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It exhibits weights to the ½ oz.
If I need weights to the nearest ¼ oz. I am
out of luck
The resolution of the magical electronic scale
is ± ½ oz.
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It cannot INHERENTLY see the difference
between 1.2 oz. and 1.3 oz.
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For Example2
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I am measuring the surface area of a desk
using a meter stick with a resolution of 1 cm.
I determine;
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The Width = 125 cm = 1.25 m
The Length = 63 cm = 0.63 m
I know that the Area = Width x Length
What is the surface area of the desk?
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Area = 1.25 m x 0.63 m = 0.79 m2
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Precision & Accuracy
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Precision
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This is the consistent repeatability of a
measurement.
Accuracy
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This is how close the measurement is to the
“true value”.
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True
Value
High Precision
High Accuracy
High Precision
Low Accuracy
Low Precision
High Accuracy
36 37 38 39 40 41 42 43 44
Measured Magnitude of the Quantity
Measurement
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Measurement Errors
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The truth is
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In general you can never really know the error
in your experiment
If you knew the true value of the measurand
there would be no point in making the
measurement.
What we are after is the UNCERTAINTY in
our measurements.
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Sources of Error or Uncertainty…
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Machine error or reliability
Human reliability or error
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Measurement error
Systematic pleasing error
Experimental design error
Acts of God…
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Earthquakes
Tsunamis
Too much sun
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Types of Error
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Bias error ( average of the measurements – true)
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Non random
Systematic
Destroys accuracy
Precision error (measurement readings – average)
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Random
Hard to control without changing the measurement
system
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Bias or Systematic Errors
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Consistent, repeatable
Calibration errors
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Nonlinearity – the
input and output may
not have a simple
linear relationship
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Input
Weight (kg)
2
Output
Signal
(millivolts)
20
4
42
6
65
8
90
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Bias or Systematic Errors
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Loading errors
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The insertion of the measuring system alters
the measurand.
Example:
Place a mercury and glass thermometer into a
beaker of water.
 If they are initially at different temperatures
energy will be exchanged
 Measured temperature will be NEITHER the
initial water temperature or the initial
thermometer.
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Bias or Systematic Errors
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Loading errors
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The insertion of the measuring system alters
the measurand.
Example 2:
Interview a person off the street on national
TV.
 The newness and excitement of the attention
may taint the responses.
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Bias or Systematic Errors
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Extraneous errors
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Variables not being measured affect the
measurement
Example:
The walls of a room are at a lower temperature
than the air
 A thermometer measuring the room air
temperature will read low because of radiation
energy exchange.
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Bias or Systematic Errors
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Spatial errors
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Variables change in the environment
Example:
A single measurement of room air temperature
 Different parts of the room may be at
different temperatures.
 Temperature measured directly over the floor
heat vent will always be higher than the rest of
the room.
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Random errors
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Lack of repeatability in the output
Can originate from the measuring system
itself.
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Amplifier may be temperature dependent
Electrical noise
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Instruments operate in a sea of electrical and
magnetic noise
Building wiring
 Radio stations
 Cell phones
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Error summary
Precision Error
Random Error
Bias Error
Systematic Error
True
Value
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Average
Measure
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