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.

Correlation Coefficient

Sample Statistic

Descriptive Statistics in Experimental Research

Descriptive Statistics in Non-Experimental Research

Inferential Statistics

Understanding Descriptive Statistics

Scatterplot

Measures of Central Tendency

Measures of Dispersion

Forms of Statistical Relationship

Cohen's $d$

Mean

Standard Deviation

Bar Graph

Line Graph

What is the primary purpose of using descriptive statistics in psychological research?

Match each category of descriptive statistics with the specific goal it accomplishes when a researcher is summarizing their data.

A researcher finds that a distribution of scores on a memory task is negatively skewed, meaning there are a few extremely low scores that pull the tail of the distribution to the left. Arrange the following measures of central tendency in order from the lowest numerical value to the highest numerical value based on this distribution's shape.

In a psychological study where a distribution of scores is highly skewed by a single extreme outlier, the mean is a more valid descriptive statistic than the median for evaluating the typical performance of the sample.

Measures of dispersion, such as the standard deviation and variance, are descriptive statistics used to describe the average scores within a research sample.

Tables in Research Reports

A psychologist studies the sleep patterns of college students and wants to summarize the collected data. Why must the psychologist report both a measure of central tendency (such as the mean) and a measure of dispersion (such as the standard deviation) to provide a complete descriptive summary of the sample's sleep duration?

A researcher records the number of errors made by five participants on a memory task: 3, 8, 2, 5, and 7. The range for this sample is _____.

A research team is summarizing data from a psychology study. Match each descriptive statistic on the left to the research situation on the right where it would be the most appropriate single summary to report.

A researcher reports that two groups of participants completed an identical mood-rating scale (scored 0–100). Group A had a mean of 60 and a standard deviation of 4, while Group B had a mean of 60 and a standard deviation of 22. Although both groups share the same measure of central tendency, a student analyzing these results should conclude that Group B's scores show substantially greater _____ than Group A's scores.

A researcher has collected scores on a stress questionnaire from 80 undergraduate participants and must decide which descriptive statistics to select and report. Arrange the following evaluative steps in the order that best supports an accurate, justified statistical summary of the data.