The Commission on Elections has announced that some 80,000 Counting Machines to be used in the 2010 national elections must be capable of 99.995% reading accuracy--which means that for any batch of 20,000 optical marks the Counting Machine attempts to interpret, it is not expected to make more than one error.
The Precinct Count Optical Scan (PCOS) machine to be used in the balloting will be tested this week, according to Comelec spokesperson James Jimenez.
The accuracy requirement of 99.995 percent means a threshold of “one error out of 20,000 markings,” Jimenez said. If it falsely reads two or more ballot markings, the machine will be rejected, he said.
Jimenez said the accuracy rate was based on the number of ballots that would be fed into the voting and counting machine. Each PCOS equipment is expected to process about 1,000 ballots with 35,000 markings, he said.
This Margin of Error depends mainly on the Sample Size, or in this case the number of test marks. Intuitively, the Margin of Error goes down as the number of test marks goes up. It is the exact same animal as the plus or minus 2.8 percent (or 3%) margin of error in the standard 1200-respondent SWS survey, where also, the margin of error intuitively goes down as the number of respondents goes up. Both come from the formula that gives the Margin of error to be plus or minus the reciprocal of the square root of the number of survey respondents or test marks.
The correct sample size depends on the precision desired and how strictly we want to run the test. Careful calculation should now be done by Comelec as to what that correct number of test marks is. I can tell you it is far many more that 20,000! [More in a subsequent post!]
An excellent standard statistical reference on accuracy and precision in statistical quality control testing, sample size and margin of error is: Intermediate Statistics for Dummies which explains things mostly in plain English.
Question: What is the required number of test marks to measure the reading accuracy rating of a given machine with a Margin of Error of, say, 0.0025 percent (half the last digit of precision in the spec of 99.995 percent)?