How is Cohen's d calculated when comparing two group means?

Match each component of the Cohen's $d$ formula ($d = \frac{|M_1 - M_2|}{SD}$) with its correct description and role in calculating effect size.

Based on the formula for Cohen's $d$ ($d = \\frac{|M_1 - M_2|}{SD}$), rank the following experimental modifications from the smallest resulting effect size (top) to the largest resulting effect size (bottom).

A researcher evaluates two separate studies to determine which results are more substantial. Study A shows a raw mean difference of $|M_1 - M_2| = 12$ with a standard deviation of $SD = 12$. Study B shows a raw mean difference of $|M_1 - M_2| = 6$ with a standard deviation of $SD = 2$. The researcher concludes that Study B has a larger effect size than Study A. This conclusion represents a correct evaluation of the findings according to the logic of the Cohen's $d$ formula.

In the Cohen's $d$ formula ($d = \frac{|M_1 - M_2|}{SD}$), what is the primary purpose of using the absolute difference ($|M_1 - M_2|$) in the numerator?

In the formula for Cohen's $d$ ($d = \frac{|M_1 - M_2|}{SD}$), the purpose of dividing the difference between the means by the standard deviation is to express the resulting effect size in units of ______.

A researcher compares the memory performance of two groups. The 'Visual Imagery' group recalls a mean of 32 items, while the 'Rote Rehearsal' group recalls a mean of 24 items. The standard deviation for both groups is 20. Using the formula $d = \frac{|M_1 - M_2|}{SD}$, Cohen's $d$ for this study is _____.

A researcher comparing exam scores between a laptop note-taking group ($M = 83$) and a handwritten note-taking group ($M = 74$), with $SD = 9$, designates $M_1 = 74$ and $M_2 = 83$. She computes $(74 - 83)/9 = -1.0$ and reports Cohen's $d = -1.0$.

Each row describes a scenario involving Cohen's $d = \frac{|M_1 - M_2|}{SD}$. Match each scenario to the analytical conclusion that correctly explains what it reveals about the formula.

A junior researcher reports Cohen's $d = -0.80$ for a two-group experiment. Arrange the following critical-evaluation steps in the order a reviewer should apply them—from first (1) to last (5)—when judging whether the reported value is valid and whether it supports the researcher's conclusions.

State the mathematical formula for calculating Cohen's $d$ and explain the convention researchers use regarding the group means in the numerator to ensure the calculated effect size remains positive.

Diagnose the error in the researcher's final effect size value based on the standard conventions of Cohen's $d$, and justify how they should reorganize the means or calculation steps to obtain a correct, conventional value.

A psychology researcher compares the cognitive test scores of two groups. Group A has a mean score of $M = 45$, and Group B has a mean score of $M = 30$. The standard deviation for the scores is $SD = 10$. Apply the Cohen's $d$ formula to calculate the effect size for this study, showing your steps.