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the test (with respect to the confidence E ). Equivalently, instead of considering the
p-value, the null hypothesis can be rejected when V
V 0 .
7.6.3
Sample Significance Indexes
Analyzing a population can be aimed at selecting individuals of the population hav-
ing some property of interest. In the following we express some sampling situations
in terms of clinical tests [223]. A population D is partitioned in two sub-populations
D + and D of people having a disease, and people without the disease, respectively.
The same population is selected in other two sub-populations T + and T of people
resulting positive to a clinical test T and people resulting negative to the test, respec-
tively. Some indexes can be defined for the test T , which characterize its capacity in
discriminating correctly, a priori and a posteriori, with respect to disease D .
Table 7.2 defines four important indexes of a clinical test T for a disease D .
Ta b l e 7 . 2 Indexes of adequacy for clinical tests
Sensitivity | T + D + |/| T + |
Specificity | T D |/| T |
Positive predictability | T + D + |/| D + |
Negative predictability | T D |/| D |
We can interpret a test as a measure of reliability of statistical inference with
respect to a property of having a pathology. Table 7.3 explains the meaning of sta-
tistical inferences.
Ta b l e 7 . 3 Statistical inferential value of test indexes
High value
Reliability
Sensitivity
Positivity Disease
Specificity
Negativity Health
Positive predictability
Disease Positivity
Negative predictability
Health Negativity
Given a population X , the population of the samples of X is a second level pop-
ulation which is very important in the statistical analysis of X . In fact, it provides
some statistical distributions, called sample distributions of the samples taken from
X . The power of statistics is based on the evidence that sample distributions follow
precise mathematical laws. These are the basis for important procedures inferring
properties of populations from their samples.
 
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