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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

In the context of hypothesis testing, what is the most likely statistical conclusion if a study comparing two groups uses a very small sample (e.g., 3 individuals per group) and yields a weak relationship (e.g., Cohen's d = 0.10)?

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