The idea of hypothesis testing
Japanese school year: Math I
What you learn
Learn hypothesis testing by evaluating the probability of observing results as extreme as or more extreme than the actual outcome under a null hypothesis. Unlike strict mathematical contradiction, probabilistic decisions inherently carry a risk of error. This statistical framework is widely applied in clinical trials and quality management.
Key points
These terms describe the two competing claims in hypothesis testing. The "null hypothesis" is the baseline claim of no difference to challenge, while the "alternative hypothesis" is the statement of an effect you wish to prove.
The -value measures whether an observed outcome could happen by pure chance. Assuming the null hypothesis of no difference is true, it represents the probability of obtaining results at least as extreme as observed.
This is the decision rule used to draw conclusions from hypothesis testing. If the -value is smaller than the chosen threshold (such as 5%), we conclude it is not a coincidence, reject the null hypothesis, and accept the claim.
This is an important caution when failing to reject the null hypothesis. It merely means there is insufficient evidence to claim a difference, not that no difference has been proven to exist.
Choose a set to practice.