A result's statistical significance indicates that an effect is unlikely to be caused by random chance, whereas its practical significance measures its actual importance or usefulness in a real-world context. Because large sample sizes can make even very weak effects statistically significant, researchers must independently evaluate whether those findings hold any practical value.

Statistical Significance Versus Practical Significance

Clinical significance is the specific term used in clinical settings to describe practical significance. It evaluates whether the observed positive effect of a psychological treatment or intervention is substantial enough to justify its real-world implementation, taking into account factors such as time, effort, and cost when compared to existing alternatives.

Clinical Significance

An example of a finding that lacks practical significance is a study where a new treatment for social phobia produces a statistically significant positive effect, but the effect is too weak to justify the time, effort, and costs of implementing it over cheaper, existing treatments. Another example is finding statistically significant gender differences in mathematical problem-solving that are actually so small they are considered trivial in real-world contexts.

Example of Lacking Practical Significance

What does the term 'practical significance' refer to in the context of research findings?

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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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

https://kpu.pressbooks.pub/psychmethods4e/

KPU Research Methods in Psychology - 4th American Edition

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.

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