Question

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The effect-size is the between group difference divided by a pooled version of the standard deviations of the groups being compared.
Reason (R): Large between group differences and large within group variability result in large effect sizes.
In the light of the above statements, choose the most appropriate answer.

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

Effect size ∝ Mean difference Variability More spread → smaller effect size

Answer 1

The Correct Option is C

Concept:
Effect size (commonly Cohen’s d) is a standardized measure used to quantify the magnitude of difference between two groups. It is given by: \[ \text{Effect Size (d)} = \frac{\text{Mean}_1 - \text{Mean}_2}{\text{Pooled Standard Deviation}} \]

Step 1: Understanding Assertion (A).
The assertion correctly defines effect size as:
• Difference between group means
• Divided by pooled standard deviation Hence, Assertion (A) is correct.

Step 2: Understanding Reason (R).
The reason states:
• Large between-group difference → increases effect size (correct)
• Large within-group variability → increases effect size (incorrect) In reality:
• Larger variability (denominator) reduces effect size

Step 3: Evaluating correctness.

• Assertion is correct
• Reason is incorrect

Step 4: Conclusion.
\[ \boxed{\text{Assertion is correct but Reason is incorrect}} \]