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John, you wrote:
"But remember, that's only one of many different probability estimates.  The max error is still L*N/2."

You're right that there are many different ways of describing probability 
limits and estimating the odds of extreme outcomes. But the key is that you 
should always compare apples with apples. If we're looking at ONE standard 
deviation error in one variable, then we should never be comparing that to a 
TWO standard deviation measure of error, or yet some other measure of error 
(like max error), in another variable. 

So what about that maximum potential error in round-off? If we're dropping 
tenths, each round-off could be as large as 0.5 minutes of arc, and if there 
are a dozen round-offs, then that might lead to an error as large as +6.0 or 
-6.0, equal to the L*N/2 you gave. But this just isn't relevant in practice 
because we have no means of distinguishing round-off error from observational 
error (except, of course, by the obvious approach of running the calculation 
again without rounding off). To put it differently, we already should 
consider the possibility, rather low in probability, that our observations 
are off by +/-6.0 minutes of arc, and unlike round-off error, this is not an 
upper limit. Then we should ask whether the probability of being that far off 
is significantly increased by the possibility of round-off error. And that 
all depends on how the standard deviation of observational error compares 
with the standard deviation of round-off error. As noted in my post a little 
earlier today, if the standard deviation of the observational error is just a 
little above 1 minute of arc, the increase in the net standard deviation from 
rounding off (dropping the tenths) is not that great, less than 33%. It is 
nearly identical to assuming that your observational error is moderately 
higher and the round-off error is zero. 

-FER



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