[oldalum]

A very sensitive test is one that will capture all the people who had the disease. Yes.     An 80% sensitive test means that for every 5 negatives, one of those patients actually had the disease but has a negative result, though you can't say which of those 5 results is incorrect. No, this is the negative predictive value (of a negative test), not the sensitivity.

A very specific test is one that will not be positive if you did not have the disease. Yes.      So a 99% specific test means that 1 out of a hundred people who were told they had the disease, actually did not have it. This is the positive predictive value (of a positive test), not the specificity. 

I think you got yourself confused. Your two first sentences are right but the second ones aren't. It is easiest for me to understand 80% sensitivity as 80% of people with the disease will have a positive test; the other 20% with the disease are false negatives. I.e., the test will correctly identify 80% of the people with the disease. And 99% specificity means that of 100 people who do not have the disease, 99 will have (true) negative tests and 1 will have a (false) positive test. I.e., the test will correctly identify 99% of people who do not have the disease as not having the disease.

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This diagram may help: diagram

[oldalum]

A very sensitive test is one that will capture all the people who had the disease. Yes.     An 80% sensitive test means that for every 5 negatives, one of those patients actually had the disease but has a negative result, though you can't say which of those 5 results is incorrect. No, this is the negative predictive value (of a negative test), not the sensitivity.

A very specific test is one that will not be positive if you did not have the disease. Yes.      So a 99% specific test means that 1 out of a hundred people who were told they had the disease, actually did not have it. This is the positive predictive value (of a positive test), not the specificity. 

I think you got yourself confused. Your two first sentences are right but the second ones aren't. It is easiest for me to understand 80% sensitivity as 80% of people with the disease will have a positive test; the other 20% with the disease are false negatives. I.e., the test will correctly identify 80% of the people with the disease. And 99% specificity means that of 100 people who do not have the disease, 99 will have (true) negative tests and 1 will have a (false) positive test. I.e., the test will correctly identify 99% of people who do not have the disease as not having the disease.

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This diagram may help: diagram