Two way tables to illustrate test resultsDoctors and scientists often use diagnostic testing to determine the existence of a condition or disease.

Positive and false-positive resultsThe results of a test are said to be positive if the feature being investigated is found. Eg people tested positive to diabetes.The results are negative if the feature is not found.However, such tests are not 100% accurarte, so there is always a small chance that a diagnosis is incorrect. When the word false is included (eg false-positive or false-negative) it means the test result was incorrect.

Test Result

Positive Negative Totals

Condition Present True positive: condition present

and detected

False negative: disease present but

not detected

Condition Absent False positive: disease not present and

wrongly detected

True negative: disease not present

and test indicates this correctly

Totals

Example 1The police investigated a bank after money went missing. The police used a lie detector in their interviews. After the guilty person was caught the results were displayed in the table below.

Positive

Negative

Totals

Employees who lied 2 1 3

Employees who did not lie

7 25 32

Totals 9 26

The tests correctly identified 2 employees who lied

The test said that 1 employee who lied was not lying.

False-negative

3 employees lied

32 employees did not lie

The test correctly showed that 25 employees were not lying

The test said that 26 employees were not lying.

The test said that 9 employees lied.

The test wrongly labelled 7 employees who did not lie as lying.False-positive

a) How many employees were tested?b) For how many employees was the lie detector accurate?c) What percentage of the tests were false positives?

352 + 25 = 27

7/35 × 100 = 20%

a) Fill in the totals.b) How many of the women tested were pregnant?c) How many women who were not pregnant did the test indicate were

pregnant?d) What percentage of the test results were accurate?e) What percentage of the identified as “not pregnant” were pregnant?

f) What is the probability that a women selected at random from the group which the test said were “pregnant” was in fact not pregnant?

Example 2Dr Kelly is assessing a new type of pregnancy test. The results are:

Accurate

Not accurate

Totals

Pregnant 15 5

Not pregnant

26 0

Totals

20

26

4641

20

41/46 ×100= 89·1%

5

0

5/31 ×100= 16.1%Test said 5 + 26 were “not pregnant”

0/15 = 0%

Today’s workExercise 6-10

SheetAll questions