1. Bias, Precision, Total Error
Pat Ellsworth
ITEP

2. 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

3. 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?

4. 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 %

5. What might cause bias error?

6. 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

7. 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?

8. 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.

9. What might cause precision error?

10. 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

11. 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

12. Total Error

13. 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