Errors and limitations

Objective. Explain false positives, false negatives and model limitations.

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Learn: the key idea

A hypothesis test can make two kinds of error: a Type I error occurs when H₀ is true but is wrongly rejected, with probability equal to the actual significance level used, and a Type II error occurs when H₀ is false but is not rejected. Limitations of binomial tests include small sample sizes giving few possible critical values, meaning the actual significance level may differ noticeably from the target. For example, if the target is 5% but the actual critical region gives P(X≤2)=0.035, that 3.5% is the true Type I error probability. Understanding these errors helps explain why a test's conclusion is not absolute proof.

Worked example

State the name of the error made when a true null hypothesis is incorrectly rejected during a hypothesis test.

1 $Recall the two types of testing error$
2 $Type I: rejecting H₀ when it is actually true$
3 $Type II: failing to reject H₀ when it is actually false$
4 $The described error matches Type I$

Answer: Type I error

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Common mistake. Students confuse a Type I error (rejecting a true H₀) with a Type II error (failing to reject a false H₀). Always define Type I as 'false positive' and Type II as 'false negative' to keep them distinct.

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