In descriptive statistics, how are differences between groups or conditions mathematically characterized?

To mathematically characterize the differences between groups in descriptive statistics, it is sufficient for a researcher to only compare the mean scores of each group.

A researcher is comparing the test scores of students who used a new interactive software (Group X) against those who used a standard textbook (Group Y). Match each statistical procedure to the specific research question it helps the researcher answer about these groups.

A researcher is comparing the results of three different studies investigating the impact of a new teaching method on student performance. Each study calculated descriptive statistics to characterize the difference between the experimental and control groups. Based on the provided means and standard deviations, arrange the studies in order from the largest standardized difference between groups (highest Cohen's d) to the smallest standardized difference between groups (lowest Cohen's d).

In the study of psychology research methods, the difference between groups or conditions is identified as one of the two primary forms of which concept?

In psychology research, characterizing the differences between groups or conditions involves several descriptive statistics. Match each term to the specific conceptual role it plays in providing a mathematical picture of this form of statistical relationship.

A clinical researcher is evaluating two separate studies investigating the impact of a new therapy on anxiety. Study 1 shows a mean difference of $12$ points between the treatment and control groups with a Cohen's $d$ of $0.25$. Study 2 shows a mean difference of $8$ points between groups with a Cohen's $d$ of $0.85$. When judging which study provides more robust evidence of a substantial difference between groups relative to the internal variability of the scores, the researcher concludes that Study _____ produced the stronger effect size.

A researcher studying the effect of exercise on mood reports that the exercise group had a Cohen's $d$ of 0.55 compared to the control group, but does not report the means or standard deviations for either group. Applying the principle that group differences in descriptive statistics are characterized by comparing means and standard deviations as well as calculating Cohen's $d$, this report provides a complete descriptive characterization of the group differences.

A researcher analyzes two independent studies that both report a mean difference of 10 points between their experimental and control groups. Study A has $SD = 5$ for both groups, while Study B has $SD = 20$ for both groups. Without computing the exact values, the researcher correctly concludes that Cohen's $d$ will be _____ in Study A than in Study B, because a smaller standard deviation produces a larger standardized effect size when the mean difference remains constant.

A researcher has collected data comparing problem-solving scores between an experimental group and a control group and must now characterize the group differences following best practices for descriptive statistics. Arrange the following steps in the order that reflects the most logically sound and evaluatively rigorous approach:

Identify the broader category of statistical concept that the differences between groups or conditions belong to, and list the specific descriptive statistics and effect size metrics used to mathematically characterize these differences.

Explain why the researcher's conclusion is incomplete based on the standard methods of characterizing group differences in descriptive statistics. What additional metrics must the researcher compare or calculate, and why?

A clinical psychologist is investigating whether a new therapy group has a different average anxiety score than a control group. Apply the descriptive statistics framework to identify the three specific metrics the psychologist needs to report to mathematically characterize this difference.