Any test depends on 2 factors sensitivity and specifity. What you have asked is about sensitivity. ELISA the one practised widely is very much sensitive and detects the infection precisely. Hence false negative reactions are very rare and you need not worry about that. Also the tests are different for different STDs. It is VDRL for Syphilis, ELISA for HIV, etc. So each test interpretation differs. The most important one which is HIV related is ofcourse very much sensitive and if it is negative then there is no need to worry about that. But a repeat test is required after 3 and 6 months.