Posted by
Art Kendall on
Apr 12, 2011; 2:31pm
URL: http://spssx-discussion.165.s1.nabble.com/p-value-type-I-error-tp4296382p4298361.html
In my experience, many people have trouble grasping
"fail to to reject H0". I find that it helps them to elaborate
that H0 is the default i.e., a priori, PREsumed, or existing
theoretical position, practice, policy, understanding.
An additional elaboration emphasizes the subjunctive in the
statement of "if Ho were true". These tests can be thought of as
looking at the comparison of obtained results with what would happen
_if_ there _were_ zero difference or relation. The HA is asserted
only if there is sufficient evidence.
People who are used to common law like that in the US, are familiar
with the concept of a presumed position. The assertion of guilt is
proven or not proven at a given standard of evidence. "Not guilty"
means "guilt not proven". A person is presumed not guilty unless it
is found that there is sufficient evidence to assert guilt.
If a posteriori there is sufficient evidence, then the a priori H0
is replaced by HA, otherwise H0 stands.
When p does not reach alpha, there is insufficient evidence to adopt
HA. p is the amount of evidence, alpha is the standard.
HTH
Art Kendall
Social Research Consultants
On 4/11/2011 2:03 PM, Bruce Weaver wrote:
Do you by chance mean what is the difference between the p-value and alpha?
If so, bear in mind that the alpha value can (and should) be set before you
look at the data. The p-value, on the other hand, can only be computed
after you have the data.
Alpha is the maximum probability of Type I error you are willing to accept.
Where you set it is arbitrary; but as I'm sure you know, the overwhelming
convention in many fields is to set alpha = .05.
As Paul said, p = the probability of getting a result at least as extreme
(i.e., at least as favorable to the alternative hypothesis) as the observed
result IF the null hypothesis is true. In other words, it is a conditional
probability.
Finally, the usual decision rule is: If p LE alpha, reject H0; if p >
alpha, fail to reject H0.
HTH.
drfg2008 wrote:
Considering the concepts of Fisher and Neyman Pearson:
What is the difference of the p-value and the type I error ?
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Bruce Weaver
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Art Kendall
Social Research Consultants