st: R: re. information

["Seed, Paul" <paul.seed@kcl.ac.uk>]

Dear Panos, 
Carlo's account of how to read the Stata output and to think about Null and Alternative hypotheses is correct.

However, it is simpler to look at the Confidence Interval: 346.6682 to 387.3318.
423 is clearly ruled out.

End of story.


Paul T Seed, Senior Lecturer in Medical Statistics, 
Division of Women's Health, King's College London
Women's Health Academic Centre, King's Health Partners 
(+44) (0) 20 7188 3642.



> Date: Thu, 21 Nov 2013 11:44:45 +0100
> From: "Carlo Lazzaro" <carlo.lazzaro@tiscalinet.it>
> Subject: st: R: re. information
> 
> Dear Panos:
> 
> - - the first one-way p-value Pr(T < t) = 0.0000 says that, provided that the
> null hypothesis is true (the null hypothesis you test is that population
> mean is = 423), repeating a virtually endless number of times the same
> experiment using new data each time, with a sample of the same size, the
> probability of obtaining a value for the mean < 423 is negligible (0.0000).
> Hence the null hypothesis is rejected at 0.05;
> - - the second one-way p-value Pr(T > t) = 1.0000 is simply the difference
> between 1 and the first one-way p-value (i.e., 1-0.0000=1). Hence the null
> hypothesis is not rejected at 0.05;
> - - the two-way p-value Pr(|T| > |t|)= 0.0001 says that, provided that the
> null hypothesis was true (the null hypothesis you tested is that population
> mean is = 423), repeating a virtually endless number of times the same
> experiment using new data each time, with a sample of the same size, the
> probability of obtaining a value for the mean = 423 is negligible (0.0001).
> Hence the null hypothesis is rejected at 0.05.
> 
> Hence, the big deal is what you are making hypothesis test for.
> 
> Kind regards,
> Carlo
> - -----Messaggio originale-----
> Da: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di PAPANIKOLAOU P.
> Inviato: mercoledì 20 novembre 2013 15:49
> A: statalist@hsphsun2.harvard.edu
> Oggetto: st: re. information
> 
> Dear all,
> Running this ttesti, I have got the results below. Does this mean that I
> accept the hypothesis that he mean would be 423?
> What exactly means each of the three Pr(T?t) seen below, please?
> 
> ttesti 12 367 32 423
> 
> One-sample t test
> - ------------------------------------------------------------------------
> - ------
>          |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf.
> Interval]
> - ---------+--------------------------------------------------------------
> - ------
>        x |      12         367    9.237604          32    346.6682
> 387.3318
> - ------------------------------------------------------------------------
> - ------
>     mean = mean(x)                                                t =
> - -6.0622
> Ho: mean = 423                                   degrees of freedom =
> 11
> 
>    Ha: mean < 423               Ha: mean != 423               Ha: mean >
> 423
>  Pr(T < t) = 0.0000         Pr(|T| > |t|) = 0.0001          Pr(T > t) =
> 1.0000
> 
> Thanks, Panos
> 
> *



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