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    Re: Real accuracy of the method of lunar distances
    From: Fred Hebard
    Date: 2004 Jan 1, 16:40 -0500

    Jan,
    
    I hope we're not bothering the list too much!
    
    I alluded to this key point of inferring the basic standard deviation
    from the mean values in my last post, sent just before your current
    post to which I am responding.
    
    In a one-way analysis of variance, the Mean Square for Error (within
    groups) would equal the error variance, in a components of variance
    model.  The Mean Square for the model (among groups) would equal the
    error variance plus (the variance between groups multiplied by the mean
    sample size).  I am assuming that there is no variance between groups,
    so that the two mean squares are equal, the F statistic is
    insignificant, and that either serves as a measure of error mean
    square.  This is why I was previously alluding to increases or
    decreases in observer proficiency or drifts in sextant accuracy over
    the course of the voyage; these are the only factors of which I can
    conceive that would violate this assumption.  I  believe, though, that
    they would increase the "standard deviation" rather than decrease it,
    which would be OK for our purposes, as we are trying to put an upper
    bound on accuracy, not a lower bound.
    
    I've been looking at some of my own data, which include a few data sets
    others have sent in, to estimate this.  I also suggested previously
    some tests you might try with Bolte's data set.  Unfortunately, we have
    a social engagement to celebrate New Years, so I'm afraid I must desist
    from this interesting diversion for the time being.
    
    The one thing that throws me off in all this is knowing what the
    correct answer is! So I hope I haven't fouled things up here due to
    that.
    
    At any rate, Happy New Year!
    
    Fred
    
    On Jan 1, 2004, at 2:08 PM, Jan Kalivoda wrote:
    
    > Fred,
    >
    > Maybe we bother the list with the too detailed discussion already. But
    > it is easy to erase our postings, if needed, I hope.
    >
    > Nevertheless, to verify your point of view, one would need to know the
    > standard deviation of the basic sets of six measurements. We can
    > suppose that it was stable throughout all the period of observations,
    > as you say, but we don't have the data for each measurement to
    > ascertain it, we have the data only for the means from each set of six
    > measurements. But you state that it is possible to deduce the standard
    > deviation you need from the variance of the whole series of the means
    > - without giving any details.
    
    
    

       
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