11/22   I posted this last week but no one responded (thinking it was
        a HW problem) so I'll ask again: given a group of several
        values, is there a way to evaluate or determine if the variability
        between those numbers are significant or not? And if so, what
        statistical test should be used? Thanks.
        \_ Where did the numbers come from?  Is there an underlying
           stochastic (or otherwise) process you can describe? -- ilyas
                \_ No it's not stochastic. Does it matter, though? Can't
                   you just take the numbers at face value?
                   \_ I don't know what 'variability' means.  If it's a
                      normal distribution from which the numbers come,
                      you can estimate the variance, and that's one
                      notion of 'variability.'  If the process is not
                      stochastic, and has no stochastic interpretation,
                      why are you interested in 'variability'? -- ilyas
                        \_ OK, so I have a series of about 10 numbers.
                           I want to know if they really are the "same"
                           or not. Let's say I had 3.0, 2.9, and 3.1,
                           I want to determine whether they are actually
                           centering around one central value (in this
                           contrived example, 3). Is it enough to calculate
                           the percent change from one number to the next
                           and note that it's low, or is there a more
                           objective statistical test I can use?
                           \_ If you want to quantify how much variation there
                              is in your numbers, there are lots of ways: some
                              common ones are range, sample standard deviation,
                              population standard deviation, and average
                              deviation.  You have to pick an appropriate
                              measure and an appropriate cutoff point for
                              "the same" based on what the numbers mean.
                              Just looking at your numbers above in isolation,
                              you can't say they're the same at all -- say you
                              were measuring the speed of light in different
                              media, in units of 10^8 m/s.  If you got 3.0 for
                              some and 2.9 for others it would conclusively
                              show that the media were different, and if you
                              got 3.1 it would be earth-shattering.  --mconst
                                \_ Well the series of values were taken
                                   from a biological source, where there
                                   actually is some baseline value (in
                                   theory).
                           \_ It's called an average...
                           \_ You can't make something from nothing.  You
                              need to make assumptions about the numbers
                              (if you don't know how you got them), or think
                              about how the numbers are created. -- ilyas
                           \_ I think the problem is that you're looking for
                              a one size fits all solution to a humongous class
                              of problems for which none exists. Why don't
                              you just put the data in /csua/tmp and let us
                              mess around with it?
                           \_ Any series of numbers can be the "same" for some
                              arbitrary distribution.
        \_ GIVE US THE GODDAMN DATA!  And tell us the context.  The whole
           context.  Saying "it's a bunch of numbers" does not constitute
           giving the context, and saying you want to "determine the
           variablility" doesn't really tell us what you want to know.
        \_ You need a statistics education.  The motd cannot help.