Interpret p-values, significance levels and errors
Exam questions regularly ask you to explain what a p-value means, or to identify the type of error made - not just to calculate.
In short: A p-value is the probability of getting results at least as extreme as those observed if the null hypothesis is true. If it is smaller than the significance level you reject the null hypothesis, and otherwise you do not. State the conclusion in the context of the question, and know what type I and type II errors mean.
When you'd use this
Explaining what a calculated p-value actually means, in the context of the question.
Comparing a p-value to a stated significance level to justify a conclusion, not just calculating a number.
Identifying whether a described mistake is a Type I error (rejecting a true H₀) or a Type II error (failing to reject a false H₀).
A question that gives you the p-value directly and asks only for interpretation.
Steps (the same on every model)
The p-value is the probability of getting results at least as extreme as observed, assuming H₀ is true.
If p < significance level (e.g. 0.05): reject H₀ - the result is statistically significant.
If p ≥ significance level: do not reject H₀ - insufficient evidence against it.
Type I error: rejecting H₀ when it is actually true. Probability = significance level (α).
Type II error: failing to reject H₀ when it is actually false.
Always state your conclusion in context - relate it to what H₀ and H₁ said about the real situation.
Tip: A small p-value does not prove H₁ is true - it only means the data are unlikely under H₀. 'Do not reject H₀' is not the same as 'H₀ is true'.
Here's a real IB-style question that uses exactly this technique.
MediumCalculatorPaper 2[3 marks]
A hypothesis test at the 5% significance level gives a p-value of 0.032. State the conclusion, and explain what a Type I error would mean in this context.
p = 0.032 < 0.05, so reject H₀; a Type I error would mean rejecting H₀ when it is actually true
Mark it
Correct3 / 3 marks
Worked solution & mark scheme:
R1 p < 0.05, so reject H₀
A1 Type I error: rejecting a true H₀
Common questions
When would I need to interpret p-values, significance levels and errors in IB Maths?
Exam questions regularly ask you to explain what a p-value means, or to identify the type of error made - not just to calculate. Explaining what a calculated p-value actually means, in the context of the question. Comparing a p-value to a stated significance level to justify a conclusion, not just calculating a number.
How do I interpret p-values, significance levels and errors?
1. The p-value is the probability of getting results at least as extreme as observed, assuming H₀ is true. 2. If p < significance level (e.g. 0.05): reject H₀ - the result is statistically significant. 3. If p ≥ significance level: do not reject H₀ - insufficient evidence against it. 4. Type I error: rejecting H₀ when it is actually true. Probability = significance level (α). 5. Type II error: failing to reject H₀ when it is actually false. 6. Always state your conclusion in context - relate it to what H₀ and H₁ said about the real situation.
What should I watch out for when I interpret p-values, significance levels and errors?
A small p-value does not prove H₁ is true - it only means the data are unlikely under H₀. 'Do not reject H₀' is not the same as 'H₀ is true'.
How are marks awarded when I interpret p-values, significance levels and errors in an IB exam?
In the worked example on this page (3 marks, Paper 2), the marks are: R1: p < 0.05, so reject H₀; A1: Type I error: rejecting a true H₀.
