# PRECISION OF MEASUREMENT

When talking about measurements and accuracy and precision of those measurements it always helps to clearly define terms. So in the following I will use     "True BAC" to mean a person's true BAC if it could be measured with 100% accuracy and precision;and    "Measured BAC" to refer to a measurement of the True BAC determined by a breathalyzer test and recorded to all four decimal places. So "Measured BAC" doesn't include the post-measurement rounding-down step (I'll deal with that later). Assuming that the breathalyzer is accurate (it has been calibrated properly), it is still not 100% precise.  Thus if a person's True BAC is .09, then we would expect replicate values of Measured BAC to vary around this true value. Some measurements will be higher than .09 and some will be lower than .09.  And if the breathalyzer is calibrated properly then, the likelihood of higher-than-.09 measurements would be expected to be the same as the likelihood of lower-than-.09 measurements.  This means that the probability of a higher-than-.09 measurement and the probability of a lower-than-.09 measurement are both equal to 1/2 (the probability of hitting .0900 exactly to four decimal places is so small we can disregard it). Now if a person's True BAC was equal to .079999999 (I'm exaggerating with all the 9s, but by this I mean a value just under the limit of .08), then it is still true that very nearly half the time a Measured BAC value will exceed .08 (actually just a very very little less than half the time);  and nearly half the time a Measured BAC value will be less than .08 (actually just a very very little more than half the time).   So assuming that a person's True BAC = .079999999 (and thus they are technically not intoxicated as defined by the law), and also assuming that the errors in the breathalyzer measurements are on the order of the third or fourth decimal place, then two replicate Measured BAC that are rounded down have the following chances of occurring:    Both = .08 ---- approximately .25 (actually a very  very small amount less than .25)  Both = .07 ---- approximately .25 (actually a very  very small amount greater than .25)   One = .07, one = .08 ---- approximately .5 Another way of thinking about this is as follows.  If two breathalyzer measurements are made on a large number of people all of whom have a True BAC just under .08, then approximately one-fourth of the time, the two measurements will be .08 and .08 (after rounding). In other words, even though every person is not intoxicated by definition, the lack of precision in the breathalyzer measurements will make one out of four look guilty.  To help understand this, suppose that True BAC = .079999999 and that the error in a Measured BAC is +.0001, then the Measured BAC = .079999999 + .0001 = .08009999 which is rounded down to .08.  So even a very tiny error can cause a Measured BAC to exceed .08 when the True BAC is actually less than .08. My personal opinion is that I would not want to convict a person of DUI based solely on the evidence of two .08 BAC measurements. A 25% chance of getting the decision wrong (assuming the person is really innocent) is too high.