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# st: R: Re: conditional probability

 From "Carlo Lazzaro" To Subject st: R: Re: conditional probability Date Fri, 22 Jul 2011 08:59:39 +0200

```Dear Nico,
I would go logistic in that instance (however, take a look at what others do
in your research field for managing the same issues).

Kindest Regards,
Carlo

-----Messaggio originale-----
Da: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di
nicostat@gmail.com
Inviato: giovedì 21 luglio 2011 23.20
A: Carlo Lazzaro; statalist@hsphsun2.harvard.edu
Oggetto: st: Re: conditional probability

> Thanks Carlo, but if I want to consider also some personal
> characteristics (age, gender, ect). How I can estimate these probability?
> is it enough a simple probit or logit?
>  thanks again
> Nico
>
> 2011/7/19 Carlo Lazzaro <carlo.lazzaro@tin.it>:
>> Nico wrote:
>> "and prob(B|H) is the jointly probability to hiring a black worker
>> conditional on being a H worker"
>>
>>
>>                High skilled  Low skilled       Total
>> ----------------------------------------------
>> Black                   20         40           60
>>
>> Others          30         50           80
>> ----------------------------------------------
>> Total                   50              90              140
>>
>> P(B|H)=probability of hiring a black worker conditional on being high
>> skilled [by the way, this is a conditional probability, not a joint one].
>>
>> P(B|H)=P(B,H)/P(H)
>>
>> Using data from the table above:
>>
>> P(B|H)=[(20/140)/(50/140)]=0.4
>>
>> Where:
>>
>> 20= high skilled black workers;
>> 140= total observations;
>> 50=total skilled workers.
>>
>> Put in other words, 0.4 can be read as the probability of sampling a
black
>> skilled worker from a sample of skilled workers (i.e.: 20/50=0.4).
>>
>> Beware of not reversing the condition: P(B|H) is conceptually different
from
>> P(H|B), even though the resulting probabilities may look not so
different.
>>
>> In Stata, you can type something like this:
>>
>> gen P(B|H)=[(20/140)/(50/140)].
>>
>> Obviously, you may want to replace the number between brackets with var
>> names.
>>
>> HTH and Kind Regards,
>> Carlo
>> -----Messaggio originale-----
>> Da: owner-statalist@hsphsun2.harvard.edu
>> [mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di
>> nicostat@gmail.com
>> Inviato: martedì 19 luglio 2011 0.41
>> A: statalist@hsphsun2.harvard.edu
>> Oggetto: st: conditional probability
>>
>> Dear Statalist,
>> I don't know in stata how can estimate this kind of probabilities
>>
>> probHB=prob(B|H)prob(H)/prob(B|H) prob(H) + prob(W|L) prob(L)
>>
>> where probHB is the probability to hire a High skill worker in the
>> market for black worker
>> and prob(B|H) is the jointly probability to hiring a black worker
>> conditional on being a H worker.
>>
>> Nico
>> *
>> *   For searches and help try:
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>> *   http://www.ats.ucla.edu/stat/stata/
>>
>>
>>
>

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```