Biomedical Engineering Reference
In-Depth Information
Fig. 11.4
Probability density
P
n
(
r
n
) for measurement of net
count rate
r
n
when no activity is present. See example in text.
(Courtesy James S. Bogard.)
radioactivity of the sample. In practice, a critical count level is often established
for screening when large numbers of samples must be routinely processed un-
der identical conditions. If a given sample reads more than the critical number of
gross counts, it is assumed to have significant activity, and graded action can then
be taken. A type-I error is said to occur if it is concluded that activity is present
when, in fact, there is none (false positive). A type-II error occurs when it is wrongly
concluded that no activity is present (false negative). The two types of error carry
different implications. This section and the next develop some statistical proce-
dures that have been formulated to ascertain “minimum significant measured ac-
tivity” and “minimum detectable true activity.” We assume that the distributions
of gross and background counts are normal and consider only long-lived radio-
nuclides.
Example
A sample, counted for 10 min, registers 530 gross counts. A 30-min background
reading gives 1500 counts. (a) Does the sample have activity? (b) Without changing
the counting times, what minimum number of gross counts can be used as a decision
level such that the risk of making a type-I error is no greater than 0.050?
Solution
(a) The numbers of gross and background counts are
n
g
=
530 and
n
b
=
1500; the re-
spective counting times are
t
g
=
10 min and
t
b
=
30 min. The gross and background
count rates are
r
g
=
n
g
/
t
g
=
53 cpm and
r
b
=
n
b
/
t
b
=
50 cpm, giving a net count rate
r
n
=
3 cpm. The question of whether activity is present cannot be answered
in an absolute sense from these measurements. The observed net rate could occur
randomly with or without activity in the sample. We can, however, compute the
prob-
r
g
-
r
b
=
