Re: st: one-sample t test query

[Phil Schumm <pschumm@uchicago.edu>]

On Jan 13, 2014, at 3:21 AM, Gwinyai Masukume <parturitions@gmail.com> wrote:
> I have a dataset with 32 observations (20 females and 12 males). Males thus constitute 37.5% of the observations. Normally males should constitute 51.5% of the observations. I want to test if the observed 37.5% males are different from 51.5%. I have issued the following Stata command:
> 
> . ttest sex_baby = 0.515
> 
> One-sample t test
> ------------------------------------------------------------------------------
> Variable |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
> ---------+--------------------------------------------------------------------
> sex_baby |      32        .375     .086951    .4918694    .1976622    .5523378
> ------------------------------------------------------------------------------
>    mean = mean(sex_baby)                                         t =  -1.6101
> Ho: mean = 0.515                                 degrees of freedom =       31
> 
>  Ha: mean < 0.515             Ha: mean != 0.515             Ha: mean > 0.515
> Pr(T < t) = 0.0588         Pr(|T| > |t|) = 0.1175          Pr(T > t) = 0.9412
> 
> Looking at the two-tailed p-value, I conclude that 37.5% is not significantly different from 51.5% if p < 0.05 is considered significant.
> Have I used the correct Stata command and is my interpretation correct?


Since your variable sex_baby is binary (taking values 0 or 1) you want to use -bitest- instead, which will give you an exact p-value based on the binomial distribution.  Specifically, you would use

    bitest var1 = 0.515

which in this case yields a two-sided p-value of 0.156.  Thus, you cannot reject the null hypothesis (H0: p = 0.515) at the 0.05 level.

Alternatively, with a large enough sample size, you can approximate the distribution of the sample proportion with the Normal distribution, but with a variance of p(1-p)/n (this differs from the variance you obtained above by a factor of (n-1)/n).  In Stata, you can perform this calculation using the command -prtest-.  Note that this approximation is improved by use of the continuity correction.


-- Phil


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