Effect Size in Studies Lacking Power

Correlation Coefficient

Cohen's $d$

What does an effect size estimate in a statistical analysis?

Even when a relationship is found to be statistically significant, an effect size should be reported because a p-value alone cannot convey the actual magnitude or importance of that relationship.

Match each hypothetical research outcome with the interpretation that accurately describes its practical and statistical significance based on the reported effect size and p-value.

A psychology researcher reports the following statistical outcomes from four separate studies. Arrange these results in order from the weakest relationship magnitude to the strongest relationship magnitude in the population, regardless of their statistical significance levels.

A researcher is evaluating two separate studies to decide which memory-enhancement technique to recommend for a clinical trial. Study 1 reports a significant result with $p < .001$ and an effect size of $d = 0.12$. Study 2 reports a significant result with $p = .04$ and an effect size of $d = 0.82$. If the researcher evaluates these findings based on the strength of the relationship in the population rather than just the probability of the results occurring by chance, they should conclude that Study ____ provides more compelling evidence of a powerful technique.

A psychology researcher is synthesizing a formal 'Discussion' section for a study that found a statistically significant difference between groups ($p = .04$) but a very low magnitude of relationship ($d = 0.10$). Arrange the following statements in the correct logical sequence to construct a scientifically rigorous interpretation that prioritizes the actual strength of the finding over its probability.