Disproving the Null Hypothesis
Although the null hypothesis cannot be proven true, it
The first of the following statements comes from an online document entitled “Converting Research Questions into Statistical Hypotheses.” The second statement comes from an article authored by a medical statistician at the University of Cambridge. The third statement comes from a university’s online study-skills document. (Note the phrases
The danger in thinking that null hypotheses are proven wrong if rejected is twofold. Both of these dangers are related to the word Those who think that null hypotheses can be proven false have mixed together, inappropriately, the logic of falsification and the statistical procedure of hypothesis testing. As will be indicated in the next section, nothing is truly falsified when a null hypothesis is rejected. The observation of one black swan is sufficient to falsify the claim that all swans are white. That single black swan proves that the claim is wrong. It is dangerous to accept or promote the belief that a rejected There is a second danger associated with the belief that null hypotheses can be proven wrong. This concerns the important scientific practice of replication. If a study’s null hypothesis were to be rejected, and if this rejection constituted proof that
If you test a null hypothesis, reject it, and then think that you have The only way a particular If you flip a fair (i.e., unbiased) coin 10 times, the chances are about 2 in 3 that you’ll end up with somewhere between 4 and 6 heads. However, it’s clear that you might end up with a result that’s more lopsided than this. In fact, there’s about a 2% chance that your 10 flips will produce a 9-to-1 or 10-to-0 split between heads and tails. If you actually got one of these more extreme splits (for which Researchers are encouraged to replicate their studies, and this concern for replication does not vanish simply because a researcher’s initial study leads to a rejection of the null hypothesis. The objective of replication is to see if the conclusions reached in the first investigation show up again in the second, replicated study. Clearly, the call for replication is based on the awareness that conclusions drawn from the first study might be erroneous. If the initial study had the ability to prove things, no replication would be needed.
Would you like to see some proof that To begin this assignment, go to this book’s companion Web site
Note 1: The binomial distribution was used to determine the “chances” and |