Step by Step
P/H
Parameter and Hypotheses
State the population parameter you're testing (like a mean or proportion), then state the null hypothesis (H₀, typically "no effect" or "no difference") and the alternative hypothesis (Hₐ, what you're testing for).
A/N
Assumptions and Name the test
Verify the conditions required for the test to be valid (like randomness, independence, and sample size conditions), then name the specific test you're using (like a one-sample t-test).
T/O
Test statistic and Obtain p-value
Calculate the test statistic (like a t-value or z-value) from your sample data, then obtain the corresponding p-value.
M/S
Make a decision and State a conclusion
Compare the p-value to your significance level (α) to decide whether to reject or fail to reject H₀, then state your conclusion in the context of the original problem — not just "reject H₀" in isolation.
Applied Walkthrough
1
A researcher wants to test whether a new teaching method changes average test scores, compared to a historical average of 75.
2
Parameter: the true mean test score under the new method (μ). Hypotheses: H₀: μ = 75, Hₐ: μ ≠ 75.
3
Assumptions: check that the sample was random and the sample size is large enough. Name the test: one-sample t-test. Test statistic: calculate t from the sample data. Obtain the p-value from the t-distribution.
4
Make a decision: if p < α (say, 0.05), reject H₀. State the conclusion in context: "There is convincing evidence that the true mean test score under the new method differs from 75" — not just a bare statistical statement.
Exam Application
Exams test whether you execute all eight PHANTOMS steps in a complete hypothesis test, and specifically whether your final conclusion is stated in the context of the original problem rather than as a bare statistical statement.
⚠ Common Trap
The most common trap is skipping the assumptions/conditions check, or stating a bare conclusion ("reject H₀") without translating it back into the context of the original question — both cost significant points on exams.
✓ Quick Self-Check
1. What does the PHANTOMS mnemonic stand for?
Parameter, Hypotheses, Assumptions, Name the test, Test statistic, Obtain p-value, Make a decision, State a conclusion.
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2. Why must you check assumptions before running a hypothesis test?
Because the test's validity depends on conditions like randomness, independence, and adequate sample size being met.
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3. What should a final conclusion always be stated in terms of?
The context of the original problem — not just a bare "reject H₀" or "fail to reject H₀" statement.
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4. What determines whether you reject or fail to reject H₀?
Comparing the p-value to the significance level α.
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5. Why is missing a PHANTOMS step costly on an exam?
Because a complete hypothesis test requires every step; missing any one (like assumptions or conclusion) results in lost points even if the rest of the work is correct.
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