Measurement Error & Uncertainty- Max 9

Measurement Uncertainty

(MINIMISE ERROR EFFECTS) -Already introduced subject of uncertainty when defining accuracy of a measuring system -Existence of measurement uncertainty mean it's entirely wrong to assume that the output of a system is the exact value of the measured quantity -Measurement errors are impossible to avoid BUT we can MINIMISE magnitude when measuring sport equipment by good measurement system choice, design, testing & appropriate analysis/processing

Error/Uncertainty SUMMARY

-Any measurement will include an error -Uncertainty is the concept used to describe & consider the influence of error -Sources of error: systematic or random -Systematic errors reduced through calibration, consideration of sensor type & environment -Random errors can be reduced through repeat measures -Best way to minimise error is to make careful measurements & avoid mistakes -A measurement is only truly complete when expressed with an uncertainty & a confidence -Confidence is often taken to be 95% (2SDs)

Other good practice for minimising errors

-Pilot testing before actual measurement -Familiarising with measurement system -Choosing most appropriate measurement system based on characteristics -Audit of all sources of error -Clear & concise instructions for operator -Maintaining same operator (if possible) -Identifying correct resolution (ADC bits) & sampling rate -Account & plan for environmental factors (e.g. avoid using doppler radar in the wind when measuring golf ball in flight)

Standard Error of the mean

-Some error exists between mean values of finite measurements & the true value (ie. if we could take infinite measurements) -The SD of mean values of a finite set of measurements relative to some true mean can be defined by standard error (∞) ∞=SD/SQRT(n) <n=no. of measurements

Confidence & SD

-Statistical maths tells us that for an anomally distributed measurement, the % of measurement values contained within a given multiple number of SD's is given by: % of data points in boundary & probability data point outside boundary -When stating an uncertainty it is important to include a confidence level=stating what limits are being used in the measurement -An appropriate way to express this is as follows 22.0+-1cm at 95% (2SD), which goes in order of: measured value, uncertainty, confidence level -A measurement is only complete when expressed with an uncertainty & confidence

E.G. Systematic Errors (& fixing)

-Uncalibrated force load cell sensor>up to date calibration certificates -Drift in load cell sensor>load cell types less susceptible to drift (e.g. strain gauge) -Operating environment temp> monitor temperature, air conditioning -Alignment of test specimen> alignment aids/rigs -Can be corrected if a bias is known

Statistical analysis for random errors

-random errors largely eliminated through averaging HOWEVER not entirely eliminated as only finite number of measurements are usually taken -practical situation magnitude of random error reduced to a small (but non-zero) value -degree of confidence that calculated value is close to correct value indicated by SD or variable

Sources of error in the Measurement

Calubration; drift/noise; thermal effects; data acquistion; specimen measurement; resolution

Systematic/Fixed Errors

DEF= a function of the measurement system, which contribute a consistent erroe to the measurement -measurement consistently on one side of the correct reading all errors are positive of negative -major sources: uncalibrated system; drift in system characteristics; system disturbances due to measurement (e.g. cold thermometer in hot liquid); environmental changes (e.g. changes in ambient/temp conditions) -systematic errors can be easily solved i.e. calibration -inherent in all systems & accuracy characteristics capture these errors

Sources of error in the Machine

Damsge & wear; mass & stiffnes; Alignment; backlash; machine control; interface with accessories

Reproducibility

Describes agreement between set of measurements where different people, methods or conditions are involved

Repeatability

Describes the agreement within sets of measurements ie. same person uses the same equipment in the same way under the same conditions (obtaining the same results)

Error

Difference between the measured value and the true value

Uncertainty

Doubt that exists about the result of any measurement

Sources of error in the material

Handling; properties; geometry; interface with system; preparation

Confidence in measurement E.G. ITF

ITF requires accuracy of 5mm or better from impact location Hawkeye accuracy/mean error stated between 2.6-3.6mm: -compared to high speed video at 2000Hz -unknown what shots mean error is calculated Binary decision 'in' or 'out' Statistical chance that technology will give the call in their favour or against Should uncertainty be incorporated into Hawkeye decisions?

Sources of Error

Initial stage is to identify sources of error & opportunities to eliminate or reduce magnituse of errors Two types of errors: systematic (all close together) and random errors

Tolerance

Maximum error expected in some value

Accuracy

Measurements agree closely with the actual value

Sources of error in the Method

Method set up; software version; calculations used; algorithm; test procedure; inadequate specifications

Where errors can occur?

Method; Measurement; Operator; Material; Machine; Environment all=Total system error

Testing Tip

Perform an audit of your lab, equipment & operating procedures to see which of these variables could be causing variability in your results

Random Errors

Pertubations of the measurement either side of the true value caused by random, unpredictable effects such that positive & negative errors are approximately equal in numbers (mainly small pertubations) Main sources: -human observation of analogue meter (bias) -electrical noise -random environmental changes (e.g. sudden gust of wind when using a launch monitor); hard to alter effects unless go in a lab which is then not realistic environment

Sources of error in the Operator

Procedural error; Technique; system set up; specimen handling

How random errors can be shown?

SD bar on line graph (with higher or lower percentiles) Histograms (with bell shaped curve)

Standard Deviation

SD= gives us the measure of observed error for our finite number of measurements (n) i.e. 100 measurements of football diameter

Precision

Several measurements that agree closely with eachother

Sources of error in the Environment

Temp/humidity; power; vibration; air quality; installation

Measurement Uncertainty Importance

Uncertainty is of significant importance throughout measurement -does a measurement pass or fail a test? -does a measurement lie within a given tolerance? -how can you report your measurement to another person? Standard measures are requires to establish consistencies throughout trade, industry competitive sporting arenas, sporting equipment etc. (everything must respect standards) Achieve consistent standards measurement methods & procedures have been established to assist in the recording of consistent measures

Parallax Error

When the measurement of an object's length is more or less than the true length because your eye's positioned at an angle to the measurement markings

Bias

system consistently gives readings which are too high or too low