Phenomena that are statistically significant are always practically significant.

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Question restatement: The claim is that phenomena that are statistically significant are always practically significant. Answer indicator given: False.

Opening with a nuanced view: In statistics, statistical significance means that an observed effect is unlikely to have occurred by chance under a null hypothesis, given a particular sample size and chosen significance level. This does not automatically mean the effect is large or important in real-world terms.

Reasoning for why the statement is false:
- Statistical significance is sensitive to sample size. With very large samples, even tiny, trivial effects can produce p-values below common thresholds (e.g., p < .05), leading to statistical significance despite negligible practical importance.
- Practical significance concerns the size or importance of the effect in real-world terms. An effect might be small but still statistically significant, or it could be large but not reach statistical significance due to limited sample size or high variability.
- Consider measurement context and effect size: A study might find a statistically significant difference of 0.1 units on a scale where this difference is irrelevant to stakeholders. In contrast, a large effect that substantially changes outcomes might fail to reach statistical significance if the study is underpowered or poorly designed.
- Other factors can complicate the relationship, such as multiple testing, data quality, and model assumptions. These can produce statistically significant results that lack practical relevance, or miss practically important results altogether.

In sum, statistical significance addresses the question of whether an observed effect could be due to random chance, given the data and analysis method, but it does not by itself determine the effect's real-world importance. Therefore the statement "Phenomena that are statistically significant are always practically significant" is incorrect.

Note on the given answer: The provided answer is False, aligning with the distinction between statistical significance and practical significance.

STAT 1450.02 SP2025 (28132) Checkpoint 18.3

Phenomena that are statistically significant are always practically significant.

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