Test of significance$Court trial
Null hypothesis$‘‘Every defendant is innocent until proved guilty’’
Research design$Police investigation
Data=test statistics$Evidence=exhibits
Statistical principles$Judge’s instruction
Statistical decision$Verdict
Type I error$Conviction of an innocent defendant
Type II error$Acquittal of a criminalThis analogy clarifies a very important concept: When a null hypothesis
is not rejected, it does not necessarily lead to its acceptance, because a ‘‘not
guilty’’ verdict is just an indication of ‘‘lack of evidence,’’ and ‘‘innocence’’ is
one of the possibilities. That is, when a di¤erence is not statistically significant,
there are still two possibilities:
- The null hypothesis is true.
- The null hypothesis is false, but there is not enough evidence from sample
data to support its rejection (i.e., sample size is too small).
5.2.2 Medical Screening Tests
Another analogy of hypothesis testing can be found in the application of
screening tests or diagnostic procedures. Following these procedures, clinical
observations, or laboratory techniques, people are classified as healthy or as
having a disease. Of course, these tests are imperfect: Healthy persons will
occasionally be classified wrongly as being ill, while some who are ill may fail
to be detected. The analogy between statistical tests and screening tests goes
briefly as follows:
type I error$false positives
type II error$false negativesso that
a¼ 1 specificity
b¼ 1 sensitivity5.2.3 Common Expectations
The medical care system, with its high visibility and remarkable history of
achievements, has been perceived somewhat naively by the general public as a
ANALOGIES 195