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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

Researchers can develop the ability to intuitively predict whether a result is likely to be statistically significant by evaluating descriptive statistics—specifically the combination of relationship strength and sample size. As a general heuristic, strong relationships in medium or large samples are reliably statistically significant, whereas weak relationships in small or medium samples are not. Cultivating this intuitive judgment allows researchers to form accurate expectations before conducting formal null hypothesis tests, serving as an essential safeguard to detect potential computational or interpretive errors in their analyses.

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