Question about difference in medians test.

Hi I am working on my dissertation and have run up upon a problem that
I am having a hard time finding an answer to. All my econometrics
training has failed me when it comes to a simple question about
sample statistics. The goal of the project is to see how different a
median of a vector and the output of a algorithm (based on the median
of medians) that runs on that vector will be.What I need is a way to
test if the two values are statistically different from one another.

Here is what I am doing and how I am approaching the problem.

1.) I define a vector X that has a skewed (but single peaked)
distribution, and I find it's median m_X.

2.) I then divide that vector up into 15 vectors y_1 ... y_15 in a non
random way.

3) Now take the median of each of these vectors: m_1... m_15 and place
them in their own vector M.

4) Now I take the median of M: m_M

5). Steps 2-4 are repeated 1000 times and I get a vector of m_Ms lets
call it E

6) I take the average of this Ebar.

What I want to be able to say is whether Ebar and m_X are
statistically different from one another.

What I am doing now is calculating a confidence interval around the
difference between Ebar and m_X thusly:

CI_high=(Ebar-m_X) + (std(E)*1.645)

CI_low=(Ebar-m_X) - (std3*1.645)

And seeing if zero is in the CI. My committee is unsure if this is
proper since I am using the sample median rather than the sample mean.
I think that the only thing I am relying on is that E (the sample
medians) be distributed normally (thus I can use 1.645 from the t-
table).

Is there a better way?

Thanks so much, any help would be greatly appreciated. There is a
dearth of information online about the properties of sample medians,
so I thought this would be a good place to ask.

Economics Guy

.

Relevant Pages

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  • Re: Whale steak
    ... aimed at pure mathematics, engineering mathematics and psychology. ... Mode and median are different from the mean, ... professional writing, either the type of average being used is ... I do not pretend to great familiarity with statistics. ...
    (sci.archaeology)
  • Re: Whale steak
    ... aimed at pure mathematics, engineering mathematics and psychology. ... Mode and median are different from the mean, ... professional writing, either the type of average being used is ... I do not pretend to great familiarity with statistics. ...
    (sci.archaeology)