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A finding is considered statistically significant when it is highly unlikely to have occurred due to random chance alone. In the context of inferential statistics, achieving statistical significance suggests that the results represent a genuine, real effect within the broader population.

Statistically Significant

Statistical conclusions in psychological research are fundamentally probabilistic, meaning that empirical findings are always subject to chance and the possibility of statistical errors, such as Type I or Type II errors. Because researchers cannot completely eliminate these potential errors, the results of any single empirical study can never provide absolute certainty or definitively prove that a scientific theory is true.

Probabilistic Nature of Statistics

In null hypothesis testing, sample size and relationship strength trade off against each other to determine statistical significance. A weak statistical relationship can still reach statistical significance if the sample size is sufficiently large, and conversely, a very strong relationship can be statistically significant even if it is based on a small sample.

Trade-off Between Sample Size and Relationship Strength

Consider two hypothetical studies comparing men and women. In the first, a large sample of $$500$$ women and $$500$$ men yields a strong relationship of Cohen's $$d = 0.50$$. Such a strong result in a large sample is highly unlikely if the null hypothesis were true, meaning the null hypothesis would be rejected. In the second, a small sample of $$3$$ women and $$3$$ men yields a weak relationship of Cohen's $$d = 0.10$$. This weak result in a small sample is quite likely to occur by chance, so the null hypothesis would be retained.

Example of Sample Size and Relationship Strength

Practical significance refers to the real-world importance, usefulness, or meaningfulness of a research finding. Even if a result is statistically significant, it may lack practical significance if the observed effect is trivial or too weak to have any meaningful impact in everyday life or practice.

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