The state of not being able to make a strong statement either for or against the effect, system, or theory being tested. If results are non-significant, it can never be reasoned that a hypothesis is false, only that it is not statistically proven. This is why statistical power is so important, to increase the likelihood that an experiment or study is likely to reveal an effect if it is present.
In Scottish law, courts can return three possible verdicts: "guilty", "not guilty" and "not proven", where "not guilty" is a strong statement of innocence, whereas "not proven" is when the court does not feel there is sufficient evidence to make a definitive judgement in either direction. In contrast, English courts only have the options "guilty" or "not guilty", where the latter encompasses both strong evidence of innocence and lack of evidence. Traditional hypothesis testing is more like the English court, whereas using confidence intervals or certain kinds of Bayesian statistics (where applicable) may allow a strong negative "no difference" to be distinguished from the weak "don't know".
Used on pages 63, 64