Basic Measurement Concepts ISAT 253 Spring 2005

2Dr. Ken Lewis Mod. 2 Measurement Concepts So far… In the Design of Experiments In the Design of Experiments Identify the problem/question Identify the problem/question Specify the variables and how they will be measured Specify the variables and how they will be measured Specify the Methodology Specify the Methodology Collect and Analyze Data (including uncertainty analysis) Collect and Analyze Data (including uncertainty analysis) Draw Conclusions Draw Conclusions

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts So far… 2 To maximize the correlation coefficient R 2 To maximize the correlation coefficient R 2 To minimize the variability To minimize the variability We use extreme care in We use extreme care in Defining the variables Defining the variables Defining the sampling or observations Defining the sampling or observations Analyzing the resultant data Analyzing the resultant data

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Have care in… 3 Variables Variables Specifying the independent and dependent variables Specifying the independent and dependent variables Figuring out the confounding factors Figuring out the confounding factors Knowing if our work is: Knowing if our work is: Experimental Experimental Observational Observational Modeling or simulation Modeling or simulation

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Have care in… 4 Sampling Sampling Identifying the population Identifying the population Choosing the sampling plan Choosing the sampling plan Random Random Systematic Samples Systematic Samples Stratified Samples Stratified Samples

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Have care in… 5 Analyzing the data Analyzing the data Identifying the distribution Identifying the distribution Calculating the sample statistics Calculating the sample statistics Studying the correlations Studying the correlations Deciding on possible cause and effects Deciding on possible cause and effects Calculating the coefficient of determination Calculating the coefficient of determination R2R2

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Caution A tenet of good experimentation 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 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

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts What we are about... What is a measurement? What is a measurement? What is a measuring instrument? What is a measuring instrument? What is resolution? What is resolution? Why is it important? Why is it important? How does resolution limit the display of the number of digits to display? How does resolution limit the display of the number of digits to display?

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts What we are about... 2 Visualize and differentiate between: Visualize and differentiate between: Accuracy Accuracy Precision Precision Resolution Resolution Understand the Sources of Uncertainty Understand the Sources of Uncertainty Understand the types of data error. Understand the types of data error.

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts What is a MEASUREMENT? From the WEB From the WEB “Determination of the magnitude of a quantity“ “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 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.” “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 Dr. Ken Lewis Mod. 2 Measurement Concepts What is a measurement system? A means for making the desired measurement. A means for making the desired measurement. What we are measuring The measurement method Usually an instrument Passive – a sensing element Active – a ruler Measured or quantified output

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts What is a measurand? In an experiment In an experiment Seek numerical values for physical variables Seek numerical values for physical variables These are known as “ measurands ” These are known as “ measurands ” Examples: Examples: Temperature Temperature Voltage Voltage Pressure Pressure Height Height

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Measurement Systems

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Measurement Systems Sensing element Signal Conditioning Measurand Human Interface

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Measurement Validity Extremely important that the output of a measurement system truly states the actual value of the measurand. Extremely important that the output of a measurement system truly states the actual value of the measurand. Nothing is perfect Nothing is perfect Always some deviation between actual value and measured value 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. Key is that the deviation is small enough that the measurement can be used for its intended purpose.

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Measurement Validity LIFE IS A BOX! The Smaller the allowed deviation The more expensive in time, equipment & money Will be the measurement system

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Measurement Error Error = measured value - true value

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Resolution Resolution is the smallest increment of a unit of measure that an instrument can detect or measure. Resolution is the smallest increment of a unit of measure that an instrument can detect or measure. Usually (not always) indicated by the scale or readout of an instrument Usually (not always) indicated by the scale or readout of an instrument Helps dictate the number of significant figures used in reporting the output. Helps dictate the number of significant figures used in reporting the output. It is important to understand the minimum resolution needed (avoid overkill) It is important to understand the minimum resolution needed (avoid overkill)

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts For Example… I am weighing food portions on my magical electronic scale. I am weighing food portions on my magical electronic scale. It exhibits weights to the ½ oz. It exhibits weights to the ½ oz. If I need weights to the nearest ¼ oz. I am out of luck If I need weights to the nearest ¼ oz. I am out of luck The resolution of the magical electronic scale is ± ½ oz. The resolution of the magical electronic scale is ± ½ oz. It cannot INHERENTLY see the difference between 1.2 oz. and 1.3 oz. It cannot INHERENTLY see the difference between 1.2 oz. and 1.3 oz.

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts For Example 2 I am measuring the surface area of a desk using a meter stick with a resolution of 1 cm. I am measuring the surface area of a desk using a meter stick with a resolution of 1 cm. I determine; I determine; The Width = 125 cm = 1.25 m The Width = 125 cm = 1.25 m The Length = 63 cm = 0.63 m The Length = 63 cm = 0.63 m I know that the Area = Width x Length I know that the Area = Width x Length What is the surface area of the desk? What is the surface area of the desk? Area = 1.25 m x 0.63 m = 0.79 m 2 Area = 1.25 m x 0.63 m = 0.79 m 2

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Precision & Accuracy Precision Precision This is the consistent repeatability of a measurement. This is the consistent repeatability of a measurement. Accuracy Accuracy This is how close the measurement is to the “true value”. This is how close the measurement is to the “true value”.

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts High Precision High Accuracy Low Precision High Accuracy High Precision Low Accuracy Measured Magnitude of the Quantity True Value Measurement

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Measurement Errors The truth is The truth is In general you can never really know the error in your experiment 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. 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. What we are after is the UNCERTAINTY in our measurements.

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Sources of Error or Uncertainty… Machine error or reliability Machine error or reliability Human reliability or error Human reliability or error Measurement error Measurement error Systematic pleasing error Systematic pleasing error Experimental design error Experimental design error Acts of God… Acts of God… Earthquakes Earthquakes Tsunamis Tsunamis Too much sun Too much sun

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Types of Error Bias error ( average of the measurements – true) Bias error ( average of the measurements – true) Non random Non random Systematic Systematic Destroys accuracy Destroys accuracy Precision error (measurement readings – average) Precision error (measurement readings – average) Random Random Hard to control without changing the measurement system Hard to control without changing the measurement system

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Bias or Systematic Errors Consistent, repeatable Consistent, repeatable Calibration errors Calibration errors Nonlinearity – the input and output may not have a simple linear relationship Nonlinearity – the input and output may not have a simple linear relationship Input Weight (kg) Output Signal (millivolts)

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Bias or Systematic Errors Loading errors Loading errors The insertion of the measuring system alters the measurand. The insertion of the measuring system alters the measurand. Example: Example: Place a mercury and glass thermometer into a beaker of water. Place a mercury and glass thermometer into a beaker of water. If they are initially at different temperatures energy will be exchanged If they are initially at different temperatures energy will be exchanged Measured temperature will be NEITHER the initial water temperature or the initial thermometer. Measured temperature will be NEITHER the initial water temperature or the initial thermometer.

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Bias or Systematic Errors Loading errors Loading errors The insertion of the measuring system alters the measurand. The insertion of the measuring system alters the measurand. Example 2: Example 2: Interview a person off the street on national TV. Interview a person off the street on national TV. The newness and excitement of the attention may taint the responses. The newness and excitement of the attention may taint the responses.

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Bias or Systematic Errors Extraneous errors Extraneous errors Variables not being measured affect the measurement Variables not being measured affect the measurement Example: Example: The walls of a room are at a lower temperature than the air 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. A thermometer measuring the room air temperature will read low because of radiation energy exchange.

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Bias or Systematic Errors Spatial errors Spatial errors Variables change in the environment Variables change in the environment Example: Example: A single measurement of room air temperature A single measurement of room air temperature Different parts of the room may be at different temperatures. 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. Temperature measured directly over the floor heat vent will always be higher than the rest of the room.

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Random errors Lack of repeatability in the output Lack of repeatability in the output Can originate from the measuring system itself. Can originate from the measuring system itself. Amplifier may be temperature dependent Amplifier may be temperature dependent Electrical noise Electrical noise Instruments operate in a sea of electrical and magnetic noise Instruments operate in a sea of electrical and magnetic noise Building wiring Building wiring Radio stations Radio stations Cell phones Cell phones

Spring Dr. Ken Lewis Mod. 2 Measurement Concepts Error summary True Value Average Measure Precision Error Random Error Bias Error Systematic Error