Introduction to Hypothesis Testing
Hypothesis testing is a formal procedure for using sample data to make decisions about population parameters. The core idea is simple: we start with a default assumption and ask whether our data gives us enough evidence to reject it.
Null Hypothesis (H₀): The default assumption in a statistical test, typically stating that there is no effect, no difference, or no relationship between variables. It is the hypothesis we attempt to disprove.
Alternative Hypothesis (H₁): The hypothesis we are testing for , it suggests that a difference, effect, or relationship does exist. It is accepted only when there is sufficient evidence against H₀.
The two hypotheses must be mutually exclusive and together cover all possibilities. You never "prove" H₀ , you either reject it or fail to reject it.
A researcher wants to test whether a new teaching method improves exam scores.
- H₀: The new teaching method has no effect on exam scores (mean score is unchanged).
- H₁: The new teaching method improves exam scores (mean score increases).
Notice that H₁ here specifies a direction (improvement), making it a one-tailed test.
The alternative hypothesis can be:
- One-tailed: specifies a direction (e.g., mean increases, or mean decreases).
- Two-tailed: states only that a difference exists, in either direction (e.g., means are not equal).
In IB exams, read the question carefully , the wording will indicate which type applies.
Significance Levels and p-values
Significance Level (α): The probability threshold set before the test is conducted. It represents the maximum acceptable probability of rejecting H₀ when it is actually true (a Type I error). Common values are , , and .
p-value: The probability of obtaining a test result at least as extreme as the one observed, assuming H₀ is true. A small p-value means the observed data would be very unlikely under H₀.
The decision rule is straightforward:
- If p-value < α → Reject H₀ (the result is statistically significant)
- If p-value ≥ α → Fail to reject H₀ (insufficient evidence against H₀)
Do not say "accept H₀" , this is a common mistake. Failing to reject H₀ simply means the evidence is not strong enough to dismiss it. It does not prove H₀ is true.
Think of a court trial. H₀ is "innocent until proven guilty." The p-value is like the strength of evidence against the defendant. If the evidence is strong enough (p < α), you convict (reject H₀). If not, the verdict is "not guilty" , not "definitely innocent."
In IB AI SL, you will almost always use technology (GDC or software) to compute p-values directly. Focus on interpreting the output correctly rather than computing by hand.