A researcher reviews five studies testing whether a new revision technique improves exam results. All five studies find results in the predicted direction, but all five have p-values above .05. The researcher concludes: “Because none of the individual studies was statistically significant, the research literature shows that the technique has no effect.” What is the main problem with this reasoning?

Question

BlackTom AI · Accepted Answer

Treating each non-significant p-value as a “no” vote and tallying them is vote counting, which is a flawed way to synthesize evidence.

1) Relevant concepts:
- A p-value > .05 means the data are not strong enough (given the study design) to reject the null; it is not evidence that the effect equals zero.
- Statistical power (probability of detecting a true effect) depends on effect size, sample size, and alpha; low power yields many non-significant results even when a real effect exists.
- Meta-analysis and sign/binomial tests combine information across studies (effect sizes, directions, or p-values) to assess overall evidence more effectively than vote counting.

2) Step-by-step reasoning:
- All five studies show effects in the predicted direction; that consistency is informative and should not be ignored.
- If the true effect were exactly zero and each study’s sign were random (50/50 chance of positive or negative), the chance that all five happen to be in the predicted direction is 0.5^5 = 1/32.
- Calculation: 0.5^5 = 0.5 × 0.5 × 0.5 × 0.5 × 0.5 = 0.03125 (≈ 0.03). This yields a small probability under the null of no effect and suggests the combined evidence is unlikely if there truly is no effect.

3) Intermediate steps shown above: showing the binomial/sign probability calculation (0.5^5 = 0.03125).

4) Why D is correct:
- Saying “no individual study is significant, therefore no effect” is exactly vote counting: it treats each non-significant result as evidence of absence rather than weak/inconclusive evidence. Proper synthesis would pool effect sizes or use methods that combine p-values or directions; those methods could show a statistically significant overall effect even when individual studies are underpowered.

5) Why other possible interpretations are wrong:
- Interpreting p>.05 as proof of no effect is incorrect (it shows lack of strong evidence, not evidence of absence).
- Ignoring the consistent direction or failing to consider low power misrepresents the cumulative evidence.

Conclusion: The main problem is vote counting—option D is correct.

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