In this case, we will hypothesize that the probability of a bit error, p, for the system is less than some target BER, P 0 . This hypothesis is stated formally in equation 25.D-3. We now construct a test for this hypothesis. In this case, we will take the obvious approach of sending n bits and counting the number errors, k. We will interpret the test results as shown in table 25.D-1. We now acknowledge the possibility that our conclusion is in error.
Statisticians define two different categories of error.
A type I error is made when the hypothesis is rejected even though it is true. A type II error is made when the hypothesis is accepted even though it is false. The probability of type I and a type II error are denoted as and respectively. Table 25.D-2 defines type I and type II errors in the context of this test. The probability of a type II error is given in equation 25.D-4.