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

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

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)

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

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

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

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?

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

module 69 See P&B DASC with PM Data

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

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

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

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%

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!

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

module 617 Bias for 2003, based on independent checks

module 618 Square Root of Sum of Squares

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

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

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