Bias, Precision, Total Error Pat Ellsworth ITEP

Bias Error How far off, generally in one direction, your measurement is from the truth AKA: Systematic error A systematic distortion of a measurement process, which causes errors in one direction (i.e., the expected sample measurement is different from the sample’s true value). Some problem that affects the measurements in the same way Minimized by calibrating equipment against a standard Compare standard to field and/or lab equipment This measures any bias in your equipment

Quantifying Bias Error Expressed as percentage (multiply by 100) If bias error = 0.02, express as 2% Bias error can be positive or negative WHAT DOES NEGATIVE BIAS MEAN?

Quantifying Bias Error (cont.) Find bias error True ozone concentration is 80 ppb Your measurement is 75 ppb What is the bias error? Express as %

What might cause bias error?

Precision Error How well your measurements of the same thing agree with each other AKA: Random error How well different measurements of the same thing under prescribed similar conditions agree with each other. “Random” component of error—sometimes high, sometimes low. Estimated by measuring the same thing several times Minimized by carefully following procedures

Quantifying Precision Error Expressed as percentage If precision error = 0.02, express as 2% Precision error of 2 measurements in percent form can be called Relative Percent Difference, or RPD CAN WE USE MORE THAN 2 VALUES FOR RPD? High precision has low precision error An estimate of the “wiggle” in your measurements Discuss spread between 2 different measurements, using a histogram WHAT DO AIR QUALITY PROFESSIONALS USE RPD FOR?

Quantifying Precision Error (cont.) Find precision error First ozone measurement is 95 ppb Second ozone measurement is 89 ppb What is the precision error? What is the relative percent difference (RPD)? RPD is a descriptive stat that CAN be used for bias or total error (remember some parts of EPA still use accuracy to represent total error) but RPD is usually used for precision.

What might cause precision error?

Bias Error & Precision Error: Examples Small precision error Large bias error Large precision error Small bias error (average of hits) Upper right example…if take the average bias, it equals 0 IDEAL is lower right Moderate precision error Large bias error Small precision error Small bias error

Accuracy How much an observed value agrees with a reference or standard value Combination of precision error (random error) and bias error (systematic error) NEED AN EXAMPLE OF ACCURACY The difference between your answer and the “truth” Reality is that we don’t know what our precision error is Meaning we don’t know truly how precise our measurements or instruments are

Total Error

What does all of this have to do with me? EPA standards for monitoring Precision error <10% Bias error <10% Total Error ≤10% using measurement against a standard COLLOCATED MONITORS One of the monitors will be the “true” measurement The bias is how well one agrees with the “true” value as compared to the true value The precision is how well the 2 agree with each other as compared to the average of the two