Posted by
Art Kendall on
Apr 12, 2011; 3:39pm
URL: http://spssx-discussion.165.s1.nabble.com/p-value-type-I-error-tp4296382p4298550.html
Type I error is a possible� result of the decision after the test (trial).
Think of a two by two table to evaluate the decision (verdict) to
switch to HA (found guilty) or stay with HO (found not guilty)
the row labels are test results (verdict)
A1 stayed with H0� rejected HA, found insufficient evidence (not
guilty)
A2 switched to HA , accepted HA, found sufficient evidence�
(guilty).
The columns labels are "truth"
B1 false (did not do it)
B2 true (did it).
a1b1 � staying� � was the right decision, true negative,� no
error.
a1b1 � staying� � was the wrong decision, false negative, type II
error.
a2b1� � switching was the wrong decision, false positive, type I
error.
a2b2� � switching was the right decision, true positive,� no error.
The decision of a test (trial) is whether there is sufficient
evidence to switch, i.e., go with HA.�
HTH
Art Kendall
Social Research Consultants
On 4/12/2011 3:37 AM, drfg2008 wrote:
Thank you Bruce,
(what I mean by “the difference” is the problem how to combine p and type I
error concepts.)
The p-value is the probability of obtaining a test statistic at least as
extreme as the one that was actually observed, assuming that the null
hypothesis is true. [1]
This definition does not imply a decision (!). It’s a ‘result’ (I don’t have
a better word for it). However, in scientific research I have to make
decisions. And that’s my problem now, since this implies type I and II
errors.
If I for example compute a t-Test and get as a result (let’s say) p=0,0123
I would reject the H0 since p < 0,05. The result is considered
‘statistically significant’. So far so good. However, what about the type I
error. Is the type I error 0,0123 ?
Thanks
[1] http://en.wikipedia.org/wiki/P-value
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Art Kendall
Social Research Consultants