Statistics Question on Statistical and Practical Significance

Question

Which one of the following is a correct statement? Choose the correct answer below. A. A statistical study could have statistical significance but not practical significance. B. If results from a statistical study are likely to occur by chance, then the study has statistical significance. C. If results from a statistical study are not likely to occur by chance, then the study has practical significance. D. If a statistical study has statistical significance, then it must also have practical significance.

Accepted Answer

A

Answer

1. Recall the definitions of statistical significance and practical significance: 
   - **Statistical Significance**: Results are not likely to occur by chance (i.e., they are rare under the null hypothesis). 
   - **Practical Significance**: Results have real - world importance or practical value (e.g., a treatment’s effect is large enough to matter in practice). 
2. Analyze each option: 
   - **Option A**: A large - sample study might detect a tiny, statistically significant effect (due to large sample size) that is too small to be meaningful in practice (e.g., a 0.1% improvement in a medical treatment). So a study can have statistical significance (not likely by chance) but lack practical significance (no real - world value). This is correct. 
   - **Option B**: Statistical significance requires results to be *not* likely to occur by chance. If results are likely by chance, they lack statistical significance. Eliminate B. 
   - **Option C**: “Not likely to occur by chance” defines statistical significance, not practical significance. Practical significance depends on real - world impact, not just randomness. Eliminate C. 
   - **Option D**: Statistical significance (non - random results) does not guarantee practical significance (real - world importance). A tiny, statistically significant effect may be useless in practice. Eliminate D.