Re: Fallacy of Hypothesis Testing

From: Allen McIntosh (nospam_at_mouse-potato.com)
Date: 02/26/05 

Date: Fri, 25 Feb 2005 21:18:45 -0500

passerby wrote:

> The following similar argument is INVALID though almost all
> hypothesis testings are based on it:
>
> If H is true then the probability that E is true is (very) low.
You missed:
If H is false, then the probability that E is true is high(er).
Otherwise, the occurrence of E would not be evidence that H is
false.
>
> E is true.
>
> Hence, the probability that H is true is (very) low.
Not in classical hypothesis testing. The hypothesis is either true
or false. Period. There is no probability associated with it.
>
> Following is a counter example:
> Consider this argument:
> (P1) If A is working in US then the probability that A is working at New
> York is (very) low.
> (P2)A is working at New York.
> Hence,
> (C) the probability that A is working in US is (very) low.
Absolutely not. If A is not working in the US, then Pr{P2} is
zero. Therefore, the occurrence of P2 provides no evidence against
P1.

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