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Module 61 Module 6: Uncertainty Don’t just calculate—first think about sources of error, and don’t double-count errors.

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Presentation on theme: "Module 61 Module 6: Uncertainty Don’t just calculate—first think about sources of error, and don’t double-count errors."— Presentation transcript:

1 module 61 Module 6: Uncertainty Don’t just calculate—first think about sources of error, and don’t double-count errors

2 module 62 Two Sources of Error  Sampling –How/where/when/who makes the measurements  Population –Actual variability in what you are measuring

3 module 63 Measurement error specific to… –Operator –Instrument –Lab –Procedure –Standard –Time (day of week, year, season) –Measurement level (harder to measure at low concentrations)

4 module 64 Population 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

5 module 65 Minimizing the effect of population 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

6 module 66 QC measurements 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

7 module 67 PM 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?

8 module 68 How 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

9 module 69 See P&B DASC with PM Data

10 module 610 PM2.5 Precision Estimate (40 CFR 58 App. A eq’n 11)

11 module % confidence limit for 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

12 module 612 To estimate bias…  Use PEP audit results, if available  Use any comparisons that are independent as possible  Use DASC PM 2.5 Bias (Current PEP) tab  Calculates upper and lower 90% confidence intervals

13 module 613 UCL and LCL (upper and lower confidence level)

14 module 614 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%

15 module 615 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!

16 module 616 Precision for qrtr 1 of 2003 Collocated pairs, so PRECISION estimate (if A is not consistently higher/lower than B)

17 module 617 Bias for 2003, based on independent checks

18 module 618 Square Root of Sum of Squares

19 module 619 Presenting Uncertainty  Use error bars or upper, lower lines in graph

20 module 620 Uncertainty for Gaseous Methods  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

21 module 621 Summarizing Uncertainty: 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


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