Statistics worksheet

Name________________________________Sect______

Sensitivity and Specificity as Conditional Statements

The aim of this worksheet is to tie together conditional reasoning with sensitivity/specificity.

Throughout the course of your life there will be different times that you will need to take some kind

of diagnostic test. These tests may include HPT, FST, drug test, cancer screening, pap test, HIV test,

etc. Each of these test has one of two outcomes, either you are positive or negative. Ideally we

would like the test to always be correct. We have specific names for the two ways a test can be

correct, sensitivity and specificity.

We can write sensitivity and specificity as conditional statements. Since we are interested in how

well the test performs, we can condition on the reality and see what percentage of the time the test

was able to match up with reality. We can write the following:

Sensitivity Rate: What is the chance the test is positive, given that the person is positive in reality.

Specificity Rate: What is the chance the test is negative, given that the person is negative in reality.

Given the following types of diagnostic test, write out what sensitivity and specificity are as conditional

statements.

Example: If we consider the FST, we can write the following conditional statements.

Sensitivity: What is the chance the FST is positive, given that the person had a BAC ≥ .04.

Specificity: What is the chance the FST is negative, given that the person had a BAC <.04.

HPT:

Sensitivity:

Specificity:

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Drug Test:

Sensitivity:

Specificity:

In a similar fashion we can also write the FPR and FNR as conditional statements. Given the following

types of diagnostic test, write out what FPR and FNR are as conditional statements.

Example: If we consider the FST, we can write the following conditional statements.

FPR: What is the chance the FST is positive, given that the person had a BAC < .04.

FNR: What is the chance the FST is negative, given that the person had a BAC ≥.04.

HPT:

FPR:

FNR:

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Drug Test:

FPR:

FNR:

Given the following tables calculate the requested rates. Attempt this without using the formulas;

instead calculate them as conditional probabilities. You need only write the fractions.

Example: Consider a FST where the cut off is 3

BAC ≥ .04 BAC <.04 Total

FST < 3 3 8 11

FST ≥ 3 17 2 19

Total 20 10 30

Sensitivity Rate: We are given that the person had a BAC ≥ .04, there are 20 total people that fit

this description (This goes in the denominator). Out of those 20, 17 have a FST ≥ 3 (This goes in

the numerator). So the answer is:

(Example continued on next page…)

Specificity Rate: We are given that the person had a BAC < .04, there are 10 total people that

fit this description (This goes in the denominator). Out of those 10, 8 have a FST < 3 (This goes

in the numerator). So the answer is:

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HPT:

Pregnant Not Pregnant Total

Positive HPT 2 11 13

Negative 20 1 21

Total 22 12 34

Sensitivity Rate:

Specificity Rate:

False Positive Rate:

False Negative Rate:

Drug Test:

Took Drugs Did Not Take Drugs Total

Positive Drug Test 4 4 8

Negative Drug Test 17 13 30

Total 21 17 38

Sensitivity Rate:

Specificity Rate:

False Positive Rate:

False Negative Rate: