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# st: RE: median equality test for non normal variables

 From "Nick Cox" To Subject st: RE: median equality test for non normal variables Date Mon, 24 May 2010 15:18:59 +0100

```The sign test does not assume normality. Please tell me which text this
comes from so that I know to shun it.

In my view the best way to compare two distributions is to draw a graph,
say -qqplot-.

Otherwise if you insist on some kind of P-value, I'd head straight for
-somersd- by Roger Newson (-findit- for locations). In a strong sense it
subsumes and goes beyond the Wilcoxon-Mann-Whitney machinery of the
1940s.

Conversely, there's a lot of literature that shows that the t test is
more robust than many people think. Of course, that is a function of
what many people think.

But arm-waving aside, consider this:

sysuse auto, clear
(1978 Automobile Data)

ttest price, by(foreign)

Two-sample t test with equal variances
------------------------------------------------------------------------
------
Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf.
Interval]
---------+--------------------------------------------------------------
------
Domestic |      52    6072.423    429.4911    3097.104    5210.184
6934.662
Foreign |      22    6384.682    558.9942    2621.915     5222.19
7547.174
---------+--------------------------------------------------------------
------
combined |      74    6165.257    342.8719    2949.496    5481.914
6848.6
---------+--------------------------------------------------------------
------
diff |           -312.2587    754.4488               -1816.225
1191.708
------------------------------------------------------------------------
------
diff = mean(Domestic) - mean(Foreign)                         t =
-0.4139
Ho: diff = 0                                     degrees of freedom =
72

Ha: diff < 0                 Ha: diff != 0                 Ha: diff
> 0
Pr(T < t) = 0.3401         Pr(|T| > |t|) = 0.6802          Pr(T > t) =
0.6599

foreach l in "identity" "power 0.5" "log" "power -1" {
di "{col 20}" %8.3f  _b[foreign]/_se[foreign]
}

The t or z statistic is pretty insensitive to the exact form of the
distribution. (The sign on the last link's result is to be expected.)

Nick
n.j.cox@durham.ac.uk

amatoallah ouchen

I have  two related observations (i.e. two observations per subject)
and I want to see  if the median  on these two  non -normally
distributed variables differs from one another. so I used the sign
test, but I think  that this approach  is based on normality
assumptions. Is there any test that allow to test median equality for
non normal data?

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```