Many thanks for the suggestions. I have printed out the Box paper and I'm
going to read it. Honestly.
Ada Ma
Department of Economics
University of Aberdeen, Scotland
[email protected]
----- Original Message -----
From: "Nick Cox" <[email protected]>
To: <[email protected]>
Sent: Monday, May 05, 2003 5:33 PM
Subject: st: RE: need mini tutorial in ttest result reading
> Ada Ma
> >
> > I've been staring at the results for days and read the
> > related part of the
> > Stata manual 10 times or more and I'm still confused. I
> > want to find out
> > whether the results tell me that I can reject these hypostheses:
> >
> > H0: mean(he) = mean(hexo) [HA: mean(he)~=mean(hexo)]
> > H0: sd(he) = sd(hexo) [HA: sd(he)~=sd(hexo)]
> >
> > Does the following results tell me that I can can reject
> > both HA and thus
> > accept H0? Is it that the larger is the P figure, the more
> > likely I'll have
> > to accept HA?
> >
> >
> > . ttest LFShe=LFShePOT if regwk==1, unpaired
> >
> > Two-sample t test with equal variances
> >
> > ------------------------------------------------------------
> > ------------------
> > Variable | Obs Mean Std. Err. Std. Dev.
> > [95% Conf.
> > Interval]
> > ---------+--------------------------------------------------
> > ------------------
> > LFShe | 560 9.520129 .2146156 5.078732
> > 9.098578
> > 9.941681
> > LFShePOT | 560 8.862436 .2016839 4.772713
> > 8.466285
> > 9.258587
> > ---------+--------------------------------------------------
> > ------------------
> > combined | 1120 9.191283 .1475172 4.93687
> > 8.901841
> > 9.480724
> > ---------+--------------------------------------------------
> > ------------------
> > diff | .6576928 .2945102
> > .0798378
> > 1.235548
> > ------------------------------------------------------------
> > ------------------
> > Degrees of freedom: 1118
> >
> > Ho: mean(LFShe) - mean(LFShePOT) = diff = 0
> >
> > Ha: diff < 0 Ha: diff ~= 0
> > Ha: diff > 0
> > t = 2.2332 t = 2.2332
> > t = 2.2332
> > P < t = 0.9871 P > |t| = 0.0257 P
> > > t = 0.0129
> > . sdtest LFShe=LFShePOT if regwk==1
> >
> > Variance ratio test
> >
> > ------------------------------------------------------------
> > ------------------
> > Variable | Obs Mean Std. Err. Std. Dev.
> > [95% Conf.
> > Interval]
> > ---------+--------------------------------------------------
> > ------------------
> > LFShe | 560 9.520129 .2146156 5.078732
> > 9.098578
> > 9.941681
> > LFShePOT | 560 8.862436 .2016839 4.772713
> > 8.466285
> > 9.258587
> > ---------+--------------------------------------------------
> > ------------------
> > combined | 1120 9.191283 .1475172 4.93687
> > 8.901841
> > 9.480724
> > ------------------------------------------------------------
> > ------------------
> >
> > Ho: sd(LFShe) = sd(LFShePOT)
> >
> > F(559,559) observed = F_obs = 1.132
> > F(559,559) lower tail = F_L = 1/F_obs = 0.883
> > F(559,559) upper tail = F_U = F_obs = 1.132
> >
> > Ha: sd(1) < sd(2) Ha: sd(1) ~= sd(2)
> > Ha: sd(1) > sd(2)
> > P < F_obs = 0.9290 P < F_L + P > F_U = 0.1420 P >
> > F_obs = 0.0710
>
> I am not clear whether you intend some kind of joint test or
> if one test is considered as prerequisite to another.
>
> Setting that aside, according to many statisticians,
> your question(s) cannot be answered because you
> don't tell us what your alternative hypothesis was
> (e.g.) before you carried out the t test, i.e.
> two-tailed or one-tailed, etc. And according to the
> same conservative view your test is dubious if not
> meaningless without that being sorted out in
> advance.
>
> However, informally, I imagine most users
> would feel encouraged, if not obliged, to reject the
> null hypothesis of no difference between means and accept
> instead the alternative hypothesis of a positive difference, on this
> evidence, and at a level of 0.05. Clearly, if you use a different
> threshold, the decision may vary (notably, one of 0.01).
>
> This year marks the 50th anniversary of George
> Edward Pelham Box's paper in Biometrika which pointed
> out that the t test for means is in
> practice much more robust than a test comparing variances.
> He used some more colourful language: if I recall
> correctly, he compared the common practice of F test
> before t test to putting out
> to sea in a dinghy to see if it was safe for an
> ocean liner to leave port.
>
> Having said that,
>
> 1. Looking at confidence intervals is often preferable.
>
> 2. I'd still look at a graph to compare the
> whole of the distributions, e.g. -qqplot-.
>
> Not what you asked, but possibly relevant
> to the scientific problem which presumably
> underlies this.
>
> Nick
> [email protected]
>
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