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Re: st: sign test output


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: sign test output
Date   Wed, 16 Jan 2013 09:33:16 +0000

In addition, it could be as or more useful to think in terms of
confidence intervals. With this sample size and average, 0.5 lies well
outside 95% intervals for the probability of being positive, and that
is robust to method of calculation:

. cii 346 221

                                                         -- Binomial Exact --
    Variable |        Obs        Mean    Std. Err.       [95% Conf. Interval]
-------------+---------------------------------------------------------------
             |        346    .6387283    .0258248        .5856497    .6894096

. cii 346 221, jeffreys

                                                         ----- Jeffreys -----
    Variable |        Obs        Mean    Std. Err.       [95% Conf. Interval]
-------------+---------------------------------------------------------------
             |        346    .6387283    .0258248        .5871262    .6880204

. cii 346 221, wilson

                                                         ------ Wilson ------
    Variable |        Obs        Mean    Std. Err.       [95% Conf. Interval]
-------------+---------------------------------------------------------------
             |        346    .6387283    .0258248        .5868449    .6875651

Nick

On Wed, Jan 16, 2013 at 9:13 AM, Maarten Buis <maartenlbuis@gmail.com> wrote:
> On Wed, Jan 16, 2013 at 9:38 AM, Nahla Betelmal wrote:
>> I have generated this output using  non-parametric test "one sample
>> sign test" with null: U=0 , & Ua > 0
>>
>> However, I do not understand the output. where is the p-value? is it
>> 0.5 in all cases or the 0.000 ( as in the first and third cases) and
>> 1.000 as in the second case?
>>
>>. signtest DA_T_1= 0
>>
>> Sign test
>>
>>         sign |    observed    expected
>> -------------+------------------------
>>     positive |         221         173
>>     negative |         125         173
>>         zero |           0           0
>> -------------+------------------------
>>          all |         346         346
>>
>> One-sided tests:
>>   Ho: median of DA_T_1 = 0 vs.
>>   Ha: median of DA_T_1 > 0
>>       Pr(#positive >= 221) =
>>          Binomial(n = 346, x >= 221, p = 0.5) =  0.0000
>
> The p-value is the last number, so in your case 0.0000. The stuff
> before the p-value tells you how it is computed: it is based on the
> binomial distribution, and in particular it is the chance of observing
> 221 successes or more in 346 trials when the chance of success at each
> trial is .5. For this tests this chance is the p-value, and it is very
> small, less than 0.00005. If you type in Stata -di binomialtail(346,
> 221, 0.5)- you will see that this chance is 1.381e-07, i.e.
> 0.00000001381.
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