NL- I spent the last couple hours reading about HIV testing & false positives. It is very interesting , but also confusing. So you can have a negative test & be positive, or you can have a positive test and be negative. Here is a very simple explanation I found on http://www.nlm.nih.gov/medlineplus/ency/article/003538.htm
ELISA/Western blot tests for HIV
HIV ELISA/Western blot is a set of blood tests used to diagnose chronic infection with human immunodeficiency virus (HIV).A negative test result is normal. However, people with early HIV infection (termed acute HIV infection or primary HIV infection) often have a negative test result.
What Abnormal Results Mean
A positive result on the ELISA screening test does not necessarily mean that the person has HIV infection. Certain conditions may lead to a false positive result, such as Lyme disease, syphilis, and lupus.
A positive ELISA test is always followed by a Western blot test. A positive Western blot confirms an HIV infection. A negative Western blot test means the ELISA test was a false positive test. The Western blot test can also be unclear, in which case more testing is done.
Negative tests do not rule out HIV infection. There is a period of time (called the "window period") between HIV infection and the appearance of anti-HIV antibodies that can be measured.
If a person might have acute or primary HIV infection, and is in the "window period," a negative HIV ELISA and Western blot will not rule out HIV infection. More tests for HIV will need to be done.