What are typical sources of error in rotational rheometry ...
Two Sources of Error
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Module 6: Uncertainty
Don’t just calculate—first think about sources of error, and don’t
double-count errors
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Two Sources of ErrorTwo Sources of Error
Sampling – How/where/when/who makes the
measurementsPopulation
– Actual variability in what you are measuring
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Measurement Measurement error specific to…error specific to…
– Operator– Instrument– Lab– Procedure– Standard– Time (day of week, year, season)– Measurement level (harder to measure
at low concentrations)
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Population ErrorPopulation Error
Ideally, estimate some aspect of homogenous “clump” of air, water, people
If population is totally homogenous, only one measurement is necessary
The more variability in the population, the more measurements you need
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Minimizing the effect of Minimizing the effect of population uncertaintypopulation uncertainty
Careful sampling plan, designed to include measurements from all “over” the distribution
Sampling plan to measure smallest “homogenous” parts of environment as possible
Careful adherence to identical procedures
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QC measurements QC measurements designed to…designed to…
Identify where errors occur Quantify errors (difference from “reality”) Save $ by improving program Produce estimates of how certain your
conclusions can be… …therefore allowing decisions based on
what you really “can” know
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PM QC ResultsPM QC Results
Collocated Flow rate checks done with routine
standard Flow rate checks done with an external
standard PEP intercomparisons of external
instrument and lab What to do with each?
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How EPA Summarizes QCHow EPA Summarizes QC
First, estimate uncertainty for each site Use collocated results to calculate
confidence interval for precision (CV) Start with RPD (diff/mean) Always use same pair and order
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See P&B DASC with PM DataSee P&B DASC with PM Data
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PM2.5 Precision Estimate (40 PM2.5 Precision Estimate (40 CFR 58 App. A eq’n 11)CFR 58 App. A eq’n 11)
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90% confidence limit for 90% confidence limit for precision = 7.7%precision = 7.7%
Average over quarter = x microg/m3 +- 8% (with 90% confidence, from precision error alone)
Can use this as part of overall uncertainty estimate
Combine with bias estimates from flow rate and PEP audits
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To estimate bias…To estimate bias…
Use PEP audit results, if available Use any comparisons that are independent
as possible Use DASC PM2.5 Bias (Current PEP) tab Calculates upper and lower 90%
confidence intervals
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UCL and LCLUCL and LCL(upper and lower confidence (upper and lower confidence
level)level)
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What does this mean?What does this mean?
UCL is ~ 10% LCL is ~ -10% Uncertainty of bias
about 10% Average bias of 7%
could really be 7.7, or about 8%
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Combining precision and bias?Combining precision and bias?
For rough estimate: square root of sum of squares
Start with d=diff/mean for all QC checks
Calc STDEV of each set of d’s Square each STDEV Add squares Take square root, see if it makes sense!
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Precision for qrtr 1 of 2003Precision for qrtr 1 of 2003
Collocated pairs, so
PRECISION estimate (if A
is not consistently higher/lower
than B)
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BiasBias for 2003, based on for 2003, based on independent checksindependent checks
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Square Root of Square Root of Sum of SquaresSum of Squares
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Presenting UncertaintyPresenting Uncertainty
Use error bars or upper, lower lines in graph
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Uncertainty for Gaseous Uncertainty for Gaseous MethodsMethods
Simpler than PM RPD between known and measured for
automated and manual checks Estimates validated with results of
independent audits QC checks produce estimates that include
both precision and bias error
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Summarizing Uncertainty:Summarizing Uncertainty:COMMON SENSE first!COMMON SENSE first!
“Highest” estimate or worst-case calculation from results of independent audits (that encompass both precision and bias)
Uncertainty estimate should encompass (already include the error from) your internal assessments, so do not double-count results