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Topic: Trying to find out truth from random phenomena . . .
Replies: 2   Last Post: Jul 23, 2013 1:34 PM

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Luis A. Afonso

Posts: 4,526
From: LIsbon (Portugal)
Registered: 2/16/05
Re: Trying to find out truth from random phenomena . . .
Posted: Jul 19, 2013 6:51 PM
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2) p-value < alpha DOES induces that H0 is not true.

The Critical Value, C, by definition, is such that prob(W>C)= alpha, i.e., the more extreme value W must show if the Null Hypothesis is true, for a right tail significance test.
We are testing the parameter p: Suppose that you fail to reject H0: p=2 at alpha=5% significance level. This means that W the test statistics value say, w0, is such that the probability to get from random data, same sample sizes, prob(W>w0) > alpha when p=2.
In consequence the condition p-value < alpha induces the idea that H0 must be rejected.
Compare with: If H0 is true the associated test statistics W must not be grater than Critical Value, C, corresponding to alpha = 5%. or the sample is not random:
_____From the test I got w0<C, therefore or H0 is possibly untrue or data is not random.
But, be careful, is merely an inductive reasoning: it is miles apart to be a deductive then exact result as:___all human are mortals,___Socrates is human,___(therefore) Socrates is mortal.
The first two premises being stated compel the conclusion without any doubt.

Note that some researchers do not agree that the condition p-value<alpha is indicative that H0 should be rejected. They argue that are two entirely different entities then unable to be compared: alpha is an arbitrary set-before-test value, on contrary p is a random variable happening as a result of the test. Of course irrefutable in what concern the genesis but I do not see (and mostly people) how they are unable to be used at inductive terms.

Once p-value < alpha we are not allowed to state that H0 is true, no way. Ronald Fisher said it clearly at the time he rediscovered significance test: Any Hypothesis is liable to be proved true.



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