P-Value Math Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
hardCorrect the following misconceptions about p-values: (a) 'p=0.03 means there's a 3% chance H₀ is true.' (b) 'p=0.03 means the effect is large.'
Solution
- 1 (a) WRONG: p-value is NOT the probability H₀ is true. It is — a conditional probability, not the posterior probability of H₀
- 2 Correct: p=0.03 means IF H₀ were true, we'd see data this extreme only 3% of the time. H₀ might still be true (3% events happen!)
- 3 (b) WRONG: small p-value indicates statistical significance, not practical significance (large effect)
- 4 Correct: with large n, even tiny effects produce small p-values; always report effect size alongside p-value
Answer
(a) p-value ≠ P(H₀ is true). (b) p-value ≠ effect size. Both are common misconceptions.
These are the two most common p-value misconceptions. P-value is a conditional probability (given H₀), not a posterior probability. And statistical significance (small p) does not imply practical significance (large effect). Distinguish between 'unlikely if null' and 'important in practice.'
About P-Value
The probability of observing a test statistic at least as extreme as the one computed from the sample data, assuming the null hypothesis is true.
Learn more about P-Value →More P-Value Examples
Example 1 medium
A hypothesis test produces [formula] for a two-tailed test. Calculate the p-value and interpret it a
Example 3 easyA one-tailed test has [formula]. Find the p-value and determine if we reject [formula] at [formula].
Example 4 hardStudy A: [formula], [formula], effect size [formula] (tiny). Study B: [formula], [formula], effect s