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<p>[QUOTE=&quot;Burton Strauss III, post: 2452987, member: 59677&quot;]How high is up?</p><p><br /></p><p>Seriously, in order to measure an error rate you actually need to know the value of what you are measuring. And the accuracy of your measurement procedure.</p><p><br /></p><p>Since you rarely know the exact value, you typically make multiple measurements (each of which has an error interval), take the average and compute the statistical confidence interval around the average of those measurements. This allows you to report that the value is X +/- Y with a 95%CI.</p><p><br /></p><p>That is frequently (erroneously) interpreted as saying the actual value is between X-Y and X+Y 95% of the time (and the other 5% the true value is actually outside the X +/- Y interval. That’s actually bunk.</p><p><br /></p><p>/1/ This assumes a bell curve (normal distribution), which is not always true.</p><p>/2/ The error interval, Y is actually related to the measurement PROCEDURE and is established a priori (before the measurements are taken).</p><p><br /></p><p>To figure out the error interval, you need to understand your tools - for example, let&#039;s measure a meter stick in inches. I know the actual value, its 39.37&quot;.</p><p>If I make my measurements using an yard stick (36&quot;) with typical 1/16th marks, the correct answer is 39 5.92/16ths. But I have to admit that my measurement procedure sucks (I have to move the yard stick and that introduces uncertainty of at least a 1/16nd). And then there is the 1/16th accuracy of both the 36&quot; and 3.37&quot; measurement. So my error interval is 3/16ths (these add as that&#039;s the worst case).</p><p><br /></p><p>If I take 10 measurements I would <i>EXPECT </i>that they should average to just under 39 6/16ths (but +/- 3/16 as averaging doesn’t reduce the error).</p><p><br /></p><p>This looks horrible (so a meter is somewhere between 39 3/16 and 39 9/16? That&#039;s useless - which is why most people use statistics to define a &#039;better&#039; looking result).</p><p><br /></p><p><br /></p><p>Now if I make my measurements using a 4 foot stick, I don&#039;t have the reposition error and I only have a single error related to the marked intervals on the stick.</p><p>With that 1/16&quot; stick some measurements will be 39 5/16 and some 39 6/16. My error interval is +/- 1/16nd, so my result of 39 6/16 +/- 1/16&quot; looks a lot better, like I did a better job. Don&#039;t fool yourself, it&#039;s just better, more appropriate tools.</p><p><br /></p><p>With good tools, e.g. an electronic multimeter, the error interval is actually part of the specifications, either +/- 0.0005 or +/- one count in the last digit, etc.</p><p><br /></p><p><br /></p><p>In situations where you don&#039;t know the actual value, sometimes you fall back on repeatability and the math also works the other way: if I know the exact value and have a number of measurements, I can calculate the error interval (but this is typically where people throw it into a stats program and calculate the statistical confidence interval and present THAT as the measurement accuracy).</p><p><br /></p><p><br /></p><p>So to bring this back to the coin grading realm, you would need to establish the actual grade of a particular coin and then conduct multiple measurements (submissions to a TPG). You would need to do this with enough different coins (series, date, strike, etc.) to be a truly representative sample and against several TPGs.</p><p><br /></p><p>This doesn’t happen because /a/ nobody agrees on the actual grade and /b/ not enough money to perform the tests and /c/ the more time that elapses in conducting the tests, the more likely something changes (e.g. new grader) that makes the results invalid anyway…</p><p><br /></p><p>At best for time &amp; money reasons, people submit a coin to a couple TPGs and say “X” sucks because they were different from “Y” who’s answer I like.[/QUOTE]</p><p><br /></p>

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