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Re: st: Interpretation of Two-sample t test with equal variances?


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Interpretation of Two-sample t test with equal variances?
Date   Wed, 20 Mar 2013 16:28:29 +0000

Student's t test is famous for working pretty well even if the
underlying assumptions are not well satisfied. One really good
discussion is

Miller, Rupert G. 1986, reissued 1997. Beyond ANOVA: Basics of applied
statistics. New York: John Wiley; reissued London: Chapman and Hall.
[now under CRC Press imprint]

NB: Always capital S for Student, the pseudonym of William S. Gosset.
See vignette in [R] ttest or indeed the StataCorp bookmark

http://www.stata.com/giftshop/bookmarks/series1/

On Wed, Mar 20, 2013 at 4:16 PM, Gwinyai Masukume
<parturitions@gmail.com> wrote:
> Thank you so much everyone. Appreciated.
>
> David - it was indeed a very helpful discussion.
> Nick - indeed those are means of maternal age. you are significant.
> yes, the mother's ages are skewed. what do you mean by student's t
> test works well even if you lie to it?
> Carlo - it seems all the relevant independent variables have not been
> included, the very low pseudo r2 is bizarre to me.
>
> Thanks again.
> Gwinyai
>
> On 3/20/13, Carlo Lazzaro <carlo.lazzaro@tiscalinet.it> wrote:
>> Gwinyai,
>> your Pseudo R2       =     0.0015 seems very low.
>> Are you sure that all the relevant independent variables have been included
>> in your model?
>>
>> You may also consider searching for interactions between mode_delivery &
>> age.
>>
>> Best regards,
>> Carlo
>>
>> -----Messaggio originale-----
>> Da: owner-statalist@hsphsun2.harvard.edu
>> [mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di Gwinyai Masukume
>> Inviato: mercoledì 20 marzo 2013 06:05
>> A: statalist@hsphsun2.harvard.edu
>> Oggetto: Re: st: Interpretation of Two-sample t test with equal variances?
>>
>> Thank you Richard. Yes, I guess the t-test suggests the counter intuitive
>> though it probably won’t change things much.
>> How can I reverse the situation?
>>
>> I ran a logistic regression for binary outcomes as you suggested:
>> Essentially no significance is shown?
>>
>> . logit mode_delivery age
>>
>> Iteration 0:   log likelihood = -159.58665
>> Iteration 1:   log likelihood = -159.34203
>> Iteration 2:   log likelihood = -159.34197
>> Iteration 3:   log likelihood = -159.34197
>>
>> Logistic regression                               Number of obs   =
>> 250
>>                                                   LR chi2(1)      =
>> 0.49
>>                                                   Prob > chi2     =
>> 0.4842
>> Log likelihood = -159.34197                       Pseudo R2       =
>> 0.0015
>>
>> ----------------------------------------------------------------------------
>> ---
>> mode_delivery |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
>> Interval]
>> --------------+---------------------------------------------------------
>> --------------+-------
>>           age |   .0155454   .0222368     0.70   0.485     -.028038
>> .0591288
>>         _cons |  -1.133737   .6630978    -1.71   0.087    -2.433385
>> .1659111
>> ----------------------------------------------------------------------------
>> ---
>>
>> With thanks,
>> Gwinyai
>>
>> On 3/20/13, Richard Williams <richardwilliams.ndu@gmail.com> wrote:
>>> Your t-test seems to suggest that age is affected by mode of delivery,
>>> rather than mode of delivery is affected by age. It probably won't
>>> change things much but this makes more sense to me given your
>>> hypotheses:
>>>
>>> logit mode_delivery age
>>>
>>> At 11:08 PM 3/19/2013, Gwinyai Masukume wrote:
>>>>Dear Stata list,
>>>>
>>>>I would like to double check the interpretation and appropriateness of
>>>>the following statistical test I performed.
>>>>My alternate hypothesis is that, “There is a difference in the baby’s
>>>>mode of delivery depending on maternal age” And the null hypothesis is
>>>>that, “There is no difference in the baby’s mode of delivery depending
>>>>on maternal age”
>>>>Looking at the output ­ “Ha: diff != 0, Pr(|T| > |t|) = 0.4861”, I
>>>>fail to reject the null hypothesis and conclude that, “There is no
>>>>difference in the baby’s mode of delivery depending on maternal age”
>>>>
>>>>Is this a sound and appropriate interpretation?
>>>>
>>>>. *** Doing a T-test
>>>>. ttest age, by(mode_delivery)
>>>>
>>>>Two-sample t test with equal variances
>>>>--------------------------------------------------------------------------
>> ----
>>>>    Group |     Obs        Mean    Std.
>>>> Err.   Std. Dev.   [95% Conf. Interval]
>>>>---------+------------------------------------------------------------
>>>>---------+--------
>>>>  Vaginal
>>>> |     166    28.83072    .4696729    6.051313    27.90338    29.75807
>>>>C/sectio |      84    29.39524    .6579862    6.030543    28.08653
>>>> 30.70395
>>>>---------+------------------------------------------------------------
>>>>---------+--------
>>>>combined |     250     29.0204    .3818851    6.038134    28.26826
>>>> 29.77254
>>>>---------+------------------------------------------------------------
>>>>---------+--------
>>>>     diff
>>>> |           -.5645152    .8093331               -2.158558    1.029528
>>>>--------------------------------------------------------------------------
>> ----
>>>>     diff = mean(Vaginal) -
>>>> mean(C/sectio)                         t =  -0.6975
>>>>Ho: diff = 0                                     degrees of freedom =
>>>> 248
>>>>
>>>>     Ha: diff < 0                 Ha: diff != 0                 Ha: diff
>>>> >
>>>> 0
>>>>  Pr(T < t) = 0.2431         Pr(|T| > |t|) =
>>>> 0.4861          Pr(T > t) = 0.7569
>>>>

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