Date:         Sun, 2 May 2010 08:44:47 -0400
Reply-To:     mike wessel <wesselouki@GMAIL.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         mike wessel <wesselouki@GMAIL.COM>
Subject:      Re: stats testing particular points of an empirical CDF's
Comments: To: Mark Miller <mdhmiller@gmail.com>
In-Reply-To:  <g2hfea0842b1005012106zc334d03cz84ad6d54961bf6d4@mail.gmail.com>
Content-Type: text/plain; charset=ISO-8859-1

I agree, they are both empirical; however, i would like to use the reference
distribution as the "expectation" or "gold standard". Im not looking to
assign or test against a particular probability distribution but rather to
assess if there are significantly more exceedances of a particular value
compared to the reference distribution. I am currently  using the binomial
to test the hypothesis that the probability of exceedance of a particular
value (e.g., the 30th percentile baseline value) is not different from the
baseline distribution. Im interested in the increased or decreased frequency
of exceedance rather than the values themselves. The purpose will be to use
this as a scoring tool each year or two and i want to incorporate
uncertianty: Statistically more is bad; statistically less is good;
otherwise Ok. I have plotted the distributions such as a Q-Q plot but would
prefer the objectivity of a statistical outcome.



On Sun, May 2, 2010 at 12:06 AM, Mark Miller <mdhmiller@gmail.com> wrote:

> Wes,
>
> They are both emiprical CDFs.
> K-S looks for the maximum absolute difference but is agnostic
> about the distribution.
> Anderson-Darling requires specifying parameters for the
> reference distribution.
> Other tests have other limitations.
>
> Why not just use a Q-Q plot?
>
> ... Mark Miller
>
>
>
>
>
> On Sat, May 1, 2010 at 10:28 PM, Wes <wesselouki@gmail.com> wrote:
>
>> Hello- I am trying to compare an empirical CDF to a CDF from a baseline
>> distribution(e.g. a CDF of 10 years of river flow data to a CDF of 100
>> years of a baseline period). Instead of using a K-S test to test the
>> difference between the curves at any point along the distribution, i would
>> like to test at a particular point (e.g., the 30th percentile). That is, i
>> want to compare whether the 10 year data has more than thirty percent of
>> the values below the 30th percentile value of the baseline
>> distribution...with statistical significance. Are the binomial test or the
>> Chi square test my best options? if so, which is better. If not, what is a
>> better test?
>> thanks in advance.
>>
>
>