Precision and Accuracy

Precision and Accuracy are the quantitative equivalent of Reliability and Validity.

A. Reliability is the quantitative form of Precision. For example, a psychiatric diagnosis is reliable if different psychiatrists tend to come up with that same diagnosis on the same patient. An experiment is reliable if different peoople using the same procedure gives the same result most of the time.
Precision means that all the measurements of a numerical value are close one anoother. Counting is very precise when done directly and exhaustively.

B. Validity and accuracy again mean the same thing but again the former is qualitative and the latter is quantitative. For a diagnosis to be valid it must mean the subject fits the critieria of the diagnosis closely and is not overwhelmingly changed by other criteria present which are applicable to another diagnosis. For example they all said she was schizophrenic, but she actually had tinnitus. Saying the board is 4.21 meters long is not accurate if on measuring it is 4.21 centimeters long. Or saying that the color green is wet is also invalid, as the criteria does not apply to each other.

Here is how the Goldsteins apply it (page 23]

The Speed of Light

"The subjective nature of an accuracy estimate can be illustrated by an example from that most exact of sciences, physics ... A. A. Michelson(1852-1931) on of the most eminent experimental physicists of his time and the first American Nobel Laureate, devoted the last few years of his life to an attempt to measure the speed of light more accurately ... he died before the measuring was complete but his work was continued by his collaborators, who published the results of about 3,000 separate measurements in 1935. The average of their determinations was 299,774 km/second.
Their accuracy was evaluated by another eminent physicists, P.T. Birge, an authority on measurements and errors, who studied their techniques and data and conccluded that their measurements was probably within 4 km/sec of the correct value.

A few decades later, the develpment of radar ... permitted more accurate determination of the speed of light. Michelson's value was found to be 16 km/sec low. [This accuracy] was thus much lower than Birge's estimate. No satisfactory explantion for the error in the measurement of Michelson and his associates has ber been found. Even with hindsight it is not easy to criticize Birge's optomistic estimate of Michelson's accuracy."BR>
It is interesting to speculate, which is necessary since I do not know the details of the separate experiments, if there is a difference because Michelson was measuirng the speed of light in a laboratory vacuum and the later ones in a different environment vacuum. Or if the other experiments were assuming radar and light move at the same speed, which theoretical (Clerke Maxwell's electromagnetic equations) say they should but in fact radar and light don't move at the same speed in a vacuum. Many hypothesis must be check out to test all the assumptions in the measurement of a phenomena. Einstein made an ad hoc assumption that the speed of light was constant and a limiting velocity everywhere.
Even if they are the same the medium of the two experiements may have accounted for the difference. For example if the radar was shot from place to place on the mon, how does the vacuum on the moon compare with an experimental vacuum on earth? If there is a difference is enough to account for the 12 km/sec difference between the radar mid poiint and the closest estimate of the speed of light?

Now with respect to precision and accuracy in measurement:

(pp 233, Goldsteins) "The range of values we have found from a series of measurements of one quantity related to the precision of the measurement, the smaller the range, the greater the precision ... Precision can be determined in a straightforward way by performing the measurement many times."

However accuracy:

(pp 233) " Accuracy is our estimate of how close the value we measure might be to the true value."

To know what the 'true' value is requires a subjective judgment, an appreciation of measuring errors we may be experiencing in our determination and usually a theoretical deduction that the expected value is a certain value. Knowing the value is required only to a certain precision and no further (for pratical reasons Pi calculated to 100,000 places suffices for all work including cosmological, and past a certain point it is not needed. For example pulse taking is good enough in twenty seconds of counting instead of a whole minute since whether the pulse is 72 or 72.5 is of no practical consequence.