
 March 2, 2007 


Receiver Operating Curve
We will summarize our results for each test statistic by the relationship of type 1 and type 2 errors.
The type 1 error is the probability of false alarm. It is in fact the sigificance level
of the test, the probability that the test will reject the Null hypothesis when in fact the
Null hypothesis is true. The type 2 error is the probability of misdetection. It is the probability
that the test rejects the Alternative hypotehsis when in fact the Alternative hypothesis is true.
A type 2 error for us is when a point data set is generated according to the model,
i.e. according to the Alternative hypothesis, and the test
does not reject the Null hypothesis. Hence it is the probability that a point data set generated according to model
is misdetected. One minus the probability of misdetection is the power of the test. The curve
of the power of the test against the significance level of the test is the receiver operating curve
associated with the test statistic, the model and the values of its parameters.
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