Calculate Cohen's D:

Sample Size Group 1 = 19
Sample Size Group 2 = 16
Standard Deviation Group 1 = 4.2
Standard Deviation Group 2 = 5.5
Sample Mean Group 1 = 41.9
Sample Mean Group 2 = 43.5

Question

Calculate Cohen's D:

Sample Size Group 1  =  19
Sample Size Group 2 = 16 
Standard Deviation Group 1  = 4.2
Standard Deviation Group 2 = 5.5
Sample Mean Group 1 = 41.9
Sample Mean Group 2 = 43.5

BlackTom AI · Accepted Answer

We are asked to calculate Cohen's D for two independent groups with given sample sizes, standard deviations, and means.

Step 1: Note the formula. Cohen's d for two independent samples uses the pooled standard deviation: d = (Mean1 − Mean2) / SD_pooled.

Step 2: Compute the pooled standard deviation. First find the group variances: s1^2 = 4.2^2 = 17.64, s2^2 = 5.5^2 = 30.25.
Calculate the pooled variance using the standard two-sample (unbiased) estimator: SD_pooled^2 = [ (n1−1)*s1^2 + (n2−1)*s2^2 ] / (n1 + n2 − 2).
Here, n1 = 19 and n2 = 16, so (n1−1)*s1^2 = 18 * 17.64 = 317.52, and (n2−1)*s2^2 = 15 * 30.25 = 453.75. Sum = 771.27.
Degrees of freedom = n1 + n2 − 2 = 33. So SD_pooled^2 = 771.27 / 33 ≈ 23.38, and SD_pooled = sqrt(23.38) ≈ 4.835.

Step 3: Compute the mean difference. Mean1 − Mean2 = 41.9 − 43.5 = −1.6.

Step 4: Form Cohen's d. d = −1.6 / 4.835 ≈ −0.331. The magnitude is about 0.33.

Notes:
- Some reporting conventions present Cohen's d as an absolute value, which is 0.33 here; the sign indicates that Group 1 has the lower mean in this setup. If you follow a specific direction (e.g., Group 2 minus Group 1), the sign would flip accordingly.
- The result is a small-to-moderate effect size by common benchmarks (roughly 0.2 small, 0.5 medium, 0.8 large).

Final numeric result (magnitude): approximately 0.33.

Calculate Cohen's D: Sample Size Group 1 = 19 Sample Size Group 2 = 16 Standard Deviation Group 1 = 4.2 Standard Deviation Group 2 = 5.5 Sample Mean Group 1 = 41.9 Sample Mean Group 2 = 43.5数值题

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