In recent times, there has been growing concern about the continued use of Null Hypothesis Significance Testing (NHST) in scientific research. This article series will attempt to provide a brief overview of both NHST and the controversy surrounding it.
In this first article of the series, I will briefly describe some of the background concepts relevant to NHST. Later articles will elaborate on other aspects of NHST.
Proof by contradiction/ Indirect proof
Fundamental to NHST is the idea of proof by contradiction. This was first proposed by Aristotle as a principle, and states that an assertion cannot be both true and false. That is, either an assertion is true, or it is false; it can’t be both:
- An assertion/ statement cannot be true and false at the same time
- If the assertion/ statement can be proven true, then it cannot be false
- If the assertion/ statement can be proven false, then it cannot be true
- If the assertion/ statement cannot be proven true, then it is false
- If the assertion/ statement cannot be proven false, then it is true.
The problem is that we do not know the truth. Even the nature of reality has been questioned by great minds, with one belief insisting that reality is mere illusion. For instance, let us assume that I wish to establish that a candle’s flame is extinguished by forcefully blowing on it. To prove my point, I light a candle, then proceed to forcefully blow on the flame, extinguishing it. Does this prove that the flame was extinguished because I blew on it? Not really. It is quite possible that something else caused the flame to be extinguished- I can never be certain that the flame was extinguished because I blew on it.
Going by this logic, how does one prove anything at all (everything could be the result of some other factor/ phenomenon)? We can’t prove anything directly. Therefore, if I wish to establish the truth, I must attempt to do so indirectly. The essential steps of such a process are as under:
- Assume your assertion/ statement is false
- Proceed as you would to establish that it is false
- Encounter a contradiction
- State that because of the contradiction, it can’t be true that the statement is false, so it must be true.
Proof by contradiction is one of many approaches to developing mathematical proofs. Since those approaches are not relevant to this discussion, I will not describe them here.