Module 6: Uncertainty Don’t just calculate—first think about sources of error, and don’t double-count errors Presentation of Uncertainty: 1. Components of overall uncertainty (field and lab measurement errors, representativeness) 2. Confidence intervals 3. Graphical presentation and interpretation module 6

Two Sources of Error Sampling Population How/where/when/who makes the measurements Population Actual variability in what you are measuring module 6

Measurement error specific to… Operator Instrument Lab Procedure Standard Time (day of week, year, season) Measurement level (harder to measure at low concentrations) module 6

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 6

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 6

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 Discuss diff parts of a QC system, with checks for lab, checks rotating around diff operators and sites, etc. module 6

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 6

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 6

See P&B DASC with PM Data This is brandy’s data that we will use for the calcs in the DASC.xls file module 6

PM2.5 Precision Estimate (40 CFR 58 App. A eq’n 11) This is the equation from CFR (eqn 11 in appendix A) that is the calculation of the upper confidence limit for the precision with a 90% level of confidence. This means that for this time period we can be sure that 90% of the time, if these results really represented the imprecision in the whole system, that 90% of the collocated results would be less than about 7.7% module 6

90% 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 Use this in tracking QC results: are results in next qrtr better or worse? module 6

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 module 6

UCL and LCL (upper and lower confidence level) module 6

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 6

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 6

Precision for qrtr 1 of 2003 Collocated pairs, so PRECISION estimate (if A is not consistently higher/lower than B) Results of collocated pairs, the stdev of the d’s (RPD between pairs) This is going to be less than the 90% CL for precision. module 6

Bias for 2003, based on independent checks module 6

Square Root of Sum of Squares HOORAY THIS MAKES SENSE! An estimate of total error of about 11% makes sense: the mean, plus or minus 11%, will contain the true mean more than half the time….(cant get too specific here, it is a rough estimate). module 6

Presenting Uncertainty Use error bars or upper, lower lines in graph In exercise we’ll do more sophisticated graphs module 6

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 6

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 module 6