I am testing the association of some antibodies with different symptoms. This is the same group of patients (with and without symptom). The n within each group is different and the variance ratio is high. In that case, what test should I consider the best one?


Code:
. swilk lmark4

                   Shapiro-Wilk W test for normal data

    Variable |    Obs       W           V         z       Prob>z
-------------+--------------------------------------------------
      lmark4 |     23    0.95818      1.094     0.182    0.42766

. ttest lmark4, by( petequia)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      21    8.803805    .0744901    .3413564    8.648421    8.959188
       1 |       2    9.171853    .0337019    .0476617     8.74363    9.600076
---------+--------------------------------------------------------------------
combined |      23    8.835809    .0714076    .3424588    8.687719    8.983899
---------+--------------------------------------------------------------------
    diff |           -.3680485    .2466404               -.8809652    .1448683
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -1.4922
Ho: diff = 0                                     degrees of freedom =       21

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0753         Pr(|T| > |t|) = 0.1505          Pr(T > t) = 0.9247

. ttest lmark4, by( petequia) unequal

Two-sample t test with unequal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      21    8.803805    .0744901    .3413564    8.648421    8.959188
       1 |       2    9.171853    .0337019    .0476617     8.74363    9.600076
---------+--------------------------------------------------------------------
combined |      23    8.835809    .0714076    .3424588    8.687719    8.983899
---------+--------------------------------------------------------------------
    diff |           -.3680485    .0817593               -.5415563   -.1945407
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -4.5016
Ho: diff = 0                     Satterthwaite's degrees of freedom =   15.792

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0002         Pr(|T| > |t|) = 0.0004          Pr(T > t) = 0.9998
Thank you!

Gabriel Ferreira
(Stata 10.1 SE)