Physics and Radiobiology of Nuclear Medicine

Problem 4.5
The following repeat counts of a radioactive sample were obtained in a
well-counter. Use the c^2 test to see if the variations in counts are due to
statistical variations of radioactivity or the counter is not working properly.

4580 4263

4635 4481

4625 4356

4578 4699

4525 4344

4668 4483

4391 4529

Answer
The average value of 14 measurements is =4511.
Using Eq. (4.8),

From Table 4.1, for degree of freedom 13 and the p-value of 0.01,c^2 =27.69.
The computed c^2 far exceeds the theoretical value, so something in addi-
tion to the statistical fluctuations of the counts is operating. Most likely, the
well-counter is not functioning properly.

Minimum Detectable Activity

The efficiency of different detectors is limited by the dead time at high
count rates and by statistical fluctuations at low count rates of the back-
grounds. In the latter situation, the minimum detectable activity (MDA)
that gives a statistically significant count is given by

(4.9)

where sR is the standard deviation of the background count rate RB
obtained by counting over a period of time t. Equation (4.9) requires that
the sample count rate must be at least three standard deviations of the back-
ground to be significant.

Evaluation of Diagnostic Tests

It is often required to evaluate the usefulness of a new diagnostic test to
determine the presence or absence of a particular disease. This aspect of
the test is commonly described by two entities: sensitivity and specificity.
The sensitivity of a test is the probability of being able to identify correctly

MDA== 33 sR RtB

c^2

227637

4511

==50 5.

N

Evaluation of Diagnostic Tests 41