This paper is a response to Gorard's article, ‘Damaging real lives through obstinacy: re-emphasising why significance testing is wrong’ in Sociological Research Online 21(1). For many years Gorard has criticised the way hypothesis tests are used in social science, but recently he has gone much further and argued that the logical basis for hypothesis testing is flawed: that hypothesis testing does not work, even when used properly. We have sympathy with the view that hypothesis testing is often carried out in social science contexts when it should not be, and that outcomes are often described in inappropriate terms, but this does not mean the theory of hypothesis testing, or its use, is flawed per se. There needs to be evidence to support such a contention. Gorard claims that: ‘Anyone knowing the problems, as described over one hundred years, who continues to teach, use or publish significance tests is acting unethically, and knowingly risking the damage that ensues.’ This is a very strong statement which impugns the integrity, not just the competence, of a large number of highly respected academics. We argue that the evidence he puts forward in this paper does not stand up to scrutiny: that the paper misrepresents what hypothesis tests claim to do, and uses a sample size which is far too small to discriminate properly a 10% difference in means in a simulation he constructs. He then claims that this simulates emotive contexts in which a 10% difference would be important to detect, implicitly misrepresenting the simulation as a reasonable model of those contexts.
Operating Characteristics for Binary Hypothesis Testing in Quantum Systems
