Basic Logic - The Research Hypothesis

Consider again the truth table for the implies operator:

The proposition that A is related to B is called the research hypothesis H1 – i.e. it is what we are trying to prove. In this case, the research hypothesis is that the system’s correct functioning is the reason why we have the expected results. The research hypothesis for a test case becomes:

H1: IF the entire system is correct (A -> B) and IF we create a test condition (A=1) THEN the expected result will occur (B=1).

Suppose the expected result occurs (B=1). We still cannot conclude that the system is correct (H1 = True) - that would be an invalid argument – error of affirming the consequent. The existence of the expected result (B = 1) does not prove that A caused B. A defect could exist (A = 0) and a different event could have caused B, or it may have been a chance event, or we may have accidentally measured C instead of B.

Since the argument is invalid, the existence of the expected result does not support the conclusion that the system works correctly (error of affirming the consequent).

Suppose the expected result does NOT occur (B=0). We can only conclude that something is wrong, although we cannot say for certain if the software contains a defect (A does not cause B), the test contains a defect (A = 0), or if the operating environment contains a defect (A = 0, or A was prevented from causing B). We can only conclude that we did not get the expected result.

Therefore: testing cannot prove the research hypothesis!