After we calculate the absolute value for Cohen's d we insert a plus or minus sign according to whether the difference between the group means represents a desirable or undesirable effect.

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This statement is true. The sign of Cohen's d indicates the direction of the effect size. If the difference between the groups represents a desirable effect (for example, a treatment that leads to improvement), the sign of Cohen's d is positive. If the difference represents an undesirable effect (for example, a harmful side effect of a medication), the sign of Cohen's d is negative.

After We Calculate the Absolute Value for Cohen's D We