Question 1207328
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Terms to know:<ul><li>Positive = the test claims the person has the disease (the test's claim may be true or false)</li><li>Negative = the test claims the person does NOT have the disease (the test's claim may be true or false)</li><li>False negative = when the test says "negative", but the person actually has the disease</li><li>False positive = when the test says "positive", but the person does NOT actually have the disease</li></ul>


Here's a chart to help remember
<table border = "1" cellpadding = "5"><tr><td></td><td>Tests Positive</td><td>Tests Negative</td></tr><tr><td>Has Disease</td><td>Correct Outcome</td><td>False Negative</td></tr><tr><td>Does Not Have Disease</td><td>False Positive</td><td>Correct Outcome</td></tr></table>


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Consider a population of 100,000 people.


"<font color=blue>A certain disease has an incidence rate of 0.8%</font>" will mean that:
0.8% of 100,000 = (0.8/100)*100000 = 800 people have the disease.
The remaining 100000 - 800 = 99,200 people do not have the disease.


We are told that "<font color=blue>the false negative rate is 6%</font>".
Of the 800 people who have the disease, 6% of them will get a false negative. 
The test mistakenly says to these unfortunate people "no you don't have the disease" when it should say "yes you do have the disease".
6% of 800 = 0.06*800 = 48 people will get a false negative when it should say "positive".
The other 800-48 = 752 people with the disease get the proper positive test result.


We are also told that "<font color=blue>the false positive rate is 2%</font>"
It means 2% of the 99,200 people who do not have the disease, will get back erroneous results of "positive" when instead it should say "negative".
2% of 99200 = 0.02*99200 = 1984 people will get false positives and 99200 - 1984 = 97216 people will get correct negative test results.


Here's a chart summarizing the values.
<table border = "1" cellpadding = "5"><tr><td></td><td>Tests Positive</td><td>Tests Negative</td><td>Total</td></tr><tr><td>Has Disease</td><td>752</td><td>48</td><td>800</td></tr><tr><td>Does Not Have Disease</td><td>1984</td><td>97,216</td><td>99,200</td></tr><tr><td>Total</td><td>2736</td><td>97,264</td><td>100,000</td></tr></table>


Based on the chart, there are 2736 people who tested positive.
Of this subgroup, 752 have the disease.
752/2736 = 0.27485380117 is the approximate probability of someone actually having the disease if they test positive.
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