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    Re: Lunars and accuracy generally
    From: Frank Reed
    Date: 2013 Jan 2, 16:33 -0800

    Greg, your first set:
    "Off Arc
    32.9'
    32.7'
    32.7'
    32.4'
    32.5'"

    The standard deviation of that set is 0.17'.

    Your second set:
    "On Arc
    32.4'
    32.4'
    32.6'
    32.7'
    32.7'"

    The standard deviation of that set is 0.14'. These are small data sets, of course, with all the caveats that go with that, but still these are SMALL numbers indicating very good, accurate observations.

    Both these sets average to 32.6' just as one would expect. So you have succeeded in measuring the angular diameter of the Sun with a standard deviation of about one-sixth to one-seventh of a minute of arc (consistent with 7x magnification of the eye's normal one minute of arc resolution), and by averaging a set of 5 you have have reduced the net error down to the limit of the precision of the observations. Excellent.

    You observations, as above, demonstrate very nicely exactly what I have said again and again. But your comments and analysis are quite strange.
    You wrote:
    "So what do I think my absolute precision is based on today's observations ? As a personal rule of thumb I double the range so with a range of 0.5' I can expect to be able to observe to ± 0.5'. "

    As I am sure you would agree, there is no such thing as "absolute precision" (or accuracy). Setting that aside, your "rule of thumb" makes no sense at all. If you double the range of a long series of observations, you're not estimating its accuracy. You're doing something opposite. With MORE observations, you will inevitably end up with outliers (the max and min value for your range) that would be more extreme, and by your rule this would give you lower trust in a larger number of observations. That range does not tell you much about the accuracy of your observations. You don't need this homebrew "rule of thumb". You have all the tools of basic statistics available to you. And this is not rocket science. Just calculate the standard deviation using whatever convenient tool you have (spreadsheet, calculator, table of logarithms, if you want!). And then understand what that number means. Much better than trusting your observations (of this specific type of angle) to +/-0.5', you should be trusting each observation, about two-thirds of the time, to +/-0.15', and you can trust sets of four, averaged, to +/-0.08'.

    By the way, from your analysis of your camera observations, which you seem to trust more than your sextant observations (?), you gave the apparent diameter of the Sun today as "32.66'". In fact, it was probably about 0.1' smaller than that. But your sextant observations appear to be spot on.

    -FER


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