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 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.

Why are psychology researchers strongly encouraged to report an effect size (such as Cohen's $d$ or Pearson's $r$) in addition to a $p$-value from a null hypothesis significance test?

A quantitative measure, such as Cohen's $d$ or Pearson's $r$, that is used to estimate the strength of a statistical relationship within a population is known as an _____.

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 researcher runs two independent studies on the same phenomenon. Study A ($n = 500$) yields $p = .04$ and $d = 0.09$. Study B ($n = 25$) yields $p = .08$ and $d = 0.63$. Analyzing only the statistical significance of these outcomes, a peer reviewer would correctly conclude that Study A provides stronger evidence for a meaningful population-level relationship than Study B.

A journal reviewer is evaluating four researcher statements about statistical results. Match each statement to the critique that best assesses its reporting quality.

Based on the provided statistical guidelines, define "effect size" and list the two specific quantitative measures of effect size mentioned in the text. Finally, state why researchers are encouraged to report these measures alongside null hypothesis tests.

Explain why the researcher's conclusion about the importance and power of the study aid is misleading. In your explanation, describe how the sample size of 15,000 students affected the $p$-value, and explain what Cohen's $d = 0.03$ reveals about the actual magnitude of the relationship.

You are writing the discussion section for a psychology experiment with a sample size of 40 participants. You found a statistically significant result ($p = .035$). Apply the statistical reporting recommendations from the text to justify why you should report an effect size measure (such as Pearson's $r$) alongside this $p$-value.