hypothesis_notes - Notes on hypothesis testing 1 Null and...

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Unformatted text preview: Notes on hypothesis testing November 21, 2010 1 Null and alternate hypotheses In scientific research one most often plays off some hypotheses against certain others, and then one performs an experiment to decide whether to reject or not reject certain of these hypotheses. Notice that I said “reject” or “not reject”; that is, I didn’t say, “reject” or “accept”. By saying that I “reject” or “not reject”, I am actually saying less than if I said “reject” or “accept”; and in saying less, the conclusion has a greater chance of actually being true , though often more daring individuals will actually say “accept” instead of “not reject”. Scientific expierments could potentially involve testing many hypothe- ses at once, but typically one only works with two of them, called the null hypothesis , denoted H , and the alternate hypothesis , denoted H a . The null hypothesis is so named because it represents the “default po- sition” or “prior belief”. An example would be the hypothesis “the drug has no effect” in testing a drug for efficacy against some disease, and an- other example would be that “all electrons have almost exactly the same rest mass”. It is actually slightly inaccurate to call the null hypothesis a “default position”, because prior to setting up the experiment it may be that the hypothesis hasn’t even been considered before. It is only “default” in the sense that if the hypothesis were true it would have little obvious significance to our expanding body of scientific knowledge (though maybe on deeper reflection it could have significance). This is perhaps why sometimes one hears the phrase “hypothesis of no consequence” when defining H . The alternate hypothesis H a basically represents what we would like to be true, since it would have some obvious significance if it were true. For this 1 reason we hope that the outcome of a scientific experiment indicates that we should reject H (or even that we should accept H a ). By negating the above two examples of null hypotheses, we arrive at two good examples of alternate hypotheses: H a might be the claim that “the drug does have an effect” against some disease; or, it might be the claim that “not all electrons have the same rest mass”. Often, null hypotheses are written in terms of parameters related to the experiment; for example, it might be H : μ = μ . This may seem a little strange since, of course, in many cases we wouldn’t expect to be able to measure some parameter μ accurately enough to say that it has value exactly equal to μ ; however, within the limits of the test we may not be able to exclude this possibility, so we would continue to accept (or not reject) that μ = μ ....
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This note was uploaded on 10/23/2011 for the course MATH 3225 taught by Professor Staff during the Spring '08 term at Georgia Tech.

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hypothesis_notes - Notes on hypothesis testing 1 Null and...

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