Power of a Test Math Example 4
Follow the full solution, then compare it with the other examples linked below.
Example 4
hardA study fails to reject and concludes 'there is no effect.' Critique this conclusion using the concept of power, and explain what information is needed before accepting this conclusion.
Solution
- 1 Failure to reject ≠ evidence that is true; it only means insufficient evidence to reject
- 2 Low power: if power was 30%, we'd miss real effects 70% of the time; failure to reject could be due to small n, not because no effect exists
- 3 Information needed: (1) Was power ≥ 80% at a meaningful effect size? (2) What effect sizes would this study have detected? (3) How large is the confidence interval?
- 4 Better conclusion: 'We found no significant evidence of an effect; however, with this sample size, we could only detect effects of size X or larger'
Answer
Failure to reject ≠ no effect exists. Need power analysis to determine if the study had adequate sensitivity.
'Absence of evidence is not evidence of absence' — a classic statistical principle. A study with low power frequently misses real effects. Reporting power, effect size estimates, and confidence intervals is essential for interpreting non-significant results appropriately.
About Power of a Test
The probability that a hypothesis test correctly rejects a false null hypothesis. Power , where is the probability of a Type II error.
Learn more about Power of a Test →More Power of a Test Examples
Example 1 medium
A test has [formula] and [formula]. Calculate the power and interpret it. If the researcher wants Po
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