Re: st: Two questions on interpreting -signtest- output

[n j cox <n.j.cox@durham.ac.uk>]

As you say, whether a one-tailed or two-tailed test is more appropriate
is for you to decide, given whatever science underlies
this problem.

You have an
enormous sample size, which makes P ~ 0 almost inevitable in
one tail and 1 - P ~ 1 ditto in the other.

That said, your test raises several distinct issues. Here are two:

1. Your calculation is still dependent on various independence 
assumptions, both within the economy at one time and between
two states of the economy.

2. You would probably learn more from a graph, a direct examination
of summary statistics and/or an attempt to estimate pr(x > y), even
if only as a descriptive statistic, say by using Roger Newson's
-somersd-.

Reza C Daniels

I am having difficulty interpreting output from two -signtest- commands.


* (1) Testing distribution of variable in 1995 and 2000 are equal
. signtest rtotshare95=rtotshare00

Sign test
         sign |    observed    expected
-------------+------------------------
     positive |        9646       13135
     negative |       16624       13135
         zero |           0           0
-------------+------------------------
          all |       26270       26270

One-sided tests:
   Ho: median of rtotsha~95 - rtotshare00 = 0 vs.
   Ha: median of rtotsha~95 - rtotshare00 > 0
       Pr(#positive >= 9646) =
          Binomial(n = 26270, x >= 9646, p = 0.5) =  1.0000

   Ho: median of rtotsha~95 - rtotshare00 = 0 vs.
   Ha: median of rtotsha~95 - rtotshare00 < 0
       Pr(#negative >= 16624) =
          Binomial(n = 26270, x >= 16624, p = 0.5) =  0.0000

Two-sided test:
   Ho: median of rtotsha~95 - rtotshare00 = 0 vs.
   Ha: median of rtotsha~95 - rtotshare00 != 0
       Pr(#positive >= 16624 or #negative >= 16624) =
          min(1, 2*Binomial(n = 26270, x >= 16624, p = 0.5)) =  0.0000
-----

* (2) Testing distribution of variable in 2000 and 2004 are equal
. signtest rtotshare00=rtotshare04

Sign test
         sign |    observed    expected
-------------+------------------------
     positive |       15276       13135
     negative |       10994       13135
         zero |           0           0
-------------+------------------------
          all |       26270       26270

One-sided tests:
   Ho: median of rtotsha~00 - rtotshare04 = 0 vs.
   Ha: median of rtotsha~00 - rtotshare04 > 0
       Pr(#positive >= 15276) =
          Binomial(n = 26270, x >= 15276, p = 0.5) =  0.0000

   Ho: median of rtotsha~00 - rtotshare04 = 0 vs.
   Ha: median of rtotsha~00 - rtotshare04 < 0
       Pr(#negative >= 10994) =
          Binomial(n = 26270, x >= 10994, p = 0.5) =  1.0000

Two-sided test:
   Ho: median of rtotsha~00 - rtotshare04 = 0 vs.
   Ha: median of rtotsha~00 - rtotshare04 != 0
       Pr(#positive >= 15276 or #negative >= 15276) =
          min(1, 2*Binomial(n = 26270, x >= 15276, p = 0.5)) =  0.0000
-----

My first question is: am I supposed to use a one sided test or the
two-sided test? My inclination is to use the one sided test given my
priors concerning the relationships between the variables.

My second question is: is it usual to see values of either 0.0000 or
1.0000 in this test, or is this more a function of my particular
variables in this dataset?

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