Pitfalls in large scale screening tests

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Lesson 4b
Examples of Interpreting Contingency Tables

• Pitfalls in large scale screening tests
• Misleading results that can occur when tables are
  combined

Main Ideas
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• 1. Large Scale Screening Tests
• Sometimes suggested to detect the presence of
  some rare but potentially deadly disease.
• Less expensive but not as accurate as a thorough
  test.
• If applied to the general population, there can
  be a significant percentage of those who test
  positive who do not actually have the disease.

!
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• Example 1. Suppose 100,000 people in a
  population can be cross-classified according to
  two characteristics
• The first characteristic, a person has a rare
  disease or does not have the disease as
  determined by an expensive, completely accurate
  test.
• The second characteristic, the person tests
  positive for the disease or does not test
  positive according to a less expensive, less
  accurate screening test.

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Example 1 (cont). The error rates of the
screening test when applied to diseased and non
diseased groups are small (5 and 1). However,
the error rate of the screening test among those
who test positive (so called false positives) is
large (68).
25/500 5 995/9950 1
Overall disease incidence 500/100000 .5
Pct. false positives 995/1470 68
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Example 1 (cont). Because there are so many
more without the disease than with the disease,
there will be a significant number of false
positives even if the test is relatively
accurate.
Number of cases of disease small
False positives
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• 2. Combining Tables
• The following example shows what I mean by
  combining tables, and the problems this can cause
  when trying to interpret results.
• The main point is, we have to be cautious when
  trying to figure out why contingency table
  percentages are the way they are. We might come
  up with the wrong cause.

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• Example 2. Suppose a hypothetical university
  cross- classifies individuals according to
  whether
• the individual is from a rural or urban area,
• the individual is admitted or not admitted to a
  particular program.
• We wish to compare admission rates for rural and
  urban students.

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Example 2 (cont)Two tables are constructed, one
for ag. programs and one for non- ag. programs.
Then tables are combined.
Admit Rates
200/800 25
50/200 25
100/200 50
950/1900 50
300/1000 30
1000/2100 48
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Example 2 (cont). If we look at the ag and
non-ag tables, there is no difference between
admission rates for rural and urban students
(25 for ag. programs and 50 for non-ag.
programs). However, if we look at the combined
table, the admission rates are different, so
someone might logically conclude that rural
students are less prepared than urban students.
The underlying cause of the discrepancy
between overall admission rates of rural and
urban students is that rural students apply
more often to programs that are harder to get
into.
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Some say you can prove anything with statistics.
Is this correct?
The use of any statistical procedure requires
careful interpretation. For example, surveys are
often difficult to interpret because of the
possibility that underlying (unsuspected) factors
may affect the result.