Hypothesis tests — Data, 14–17
A structured way to judge whether data are surprising if a claimed starting explanation were true.
Idea
A hypothesis test starts with a cautious claim, called the null hypothesis, such as “the new treatment changes nothing”. We compare the observed data with what that claim predicts. If the data would be very unusual, we reject the null; otherwise we do not have enough evidence to reject it.
Why use it?
People often see a difference in a sample and want to call it a real effect. But samples naturally vary, even when nothing has changed. Hypothesis testing was developed to separate a difference that could easily be chance from one that would be hard to explain by chance alone.
Worked example
A coin is tossed 100 times and lands heads 62 times. Start with the null hypothesis that it is fair, so heads have probability 0.5. Results around 50 are expected; 62 is fairly unusual. A calculation gives a two-sided p-value of about 0.02, below 0.05, so we reject fairness cautiously.
Common trap
Rejecting the null hypothesis does not prove the alternative is true, and failing to reject it does not prove the null is true. This mistake is reasonable because everyday language treats a test as a verdict; statistical evidence is more limited and depends on the design.
Where it appears
Clinical researchers use tests when comparing treatments, and engineers use them when checking whether a process has changed. News reports may quote a “significant difference”, so understanding the test helps you ask how large the difference was and how the data were collected.
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