仮説検定Hypothesis testing

Learn in the textbookStatistical Analysis and Inference

DefinitionHypothesis testing (仮説検定) is a method in which you set up a hypothesis you hope to reject (the null hypothesis (帰無仮説)), check how unlikely the sample data would be if it were true, and decide whether to reject it.

ExplanationThe probability used as the threshold is called the significance level (有意水準), and it is set in advance, at 5% or 1% for example. If the data would be less likely than the significance level under the null hypothesis, you reject (棄却) it and adopt the hypothesis you actually want to claim (the alternative hypothesis (対立仮説)).

AnalogyIt resembles the courtroom rule of "innocent until proven guilty." You start by assuming innocence (the null hypothesis) and find the defendant guilty only when the evidence is too strong to explain that way.

Memory hookThe Japanese term 帰無 means "to return to nothing." Remember it as a hypothesis set up from the start in the hope of being thrown out.

Learn in the textbookThe Framework of Hypothesis Testing

DefinitionHypothesis testing (仮説検定) uses data from a sample to decide, on the basis of probability, whether a hypothesis about the population can be set aside.

ExplanationFirst, state the hypothesis you want to test for rejection (the null hypothesis, such as “there is no difference in average spending between the two sales floors”) and its opposite, the alternative hypothesis. Next, express how unlikely the sample result would be if the null hypothesis were true, and if that probability falls below a cutoff fixed in advance (the significance level), reject the null hypothesis and adopt the alternative. Failing to reject does not prove the null hypothesis true, and the conclusion stays at “we cannot say there is a difference”.

AnalogyIt works like a criminal trial: the defendant is presumed innocent, and a guilty verdict comes only when the evidence is too strong to square with that presumption. When the evidence falls short and there is no conviction, innocence has not been proven either.

Memory hookThe Japanese 帰無 means “return to nothing”. The hypothesis is set up in the expectation that it will be rejected, hence the name.