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# st: R: conditional probability

 From "Carlo Lazzaro" To Subject st: R: conditional probability Date Tue, 19 Jul 2011 12:18:59 +0200

```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
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```