A residential treatment facility tests a new group therapy for patients with self destructive behaviors. To decrease scores of behaviors that has a mean in the overall population of 35 and a standard deviation of 4.7. The mean score for patients after new group therapy is 27. What is effect size of the new group therapy.

Cohen's d is the difference between two means divided by a standard deviation.

Calculate Cohen's d (d) and the effect-size correlation (r) using the following formulas:

d = (M1 - M2) / s

r = d / √(d^2 + 4)

With your data:

d = (35 - 27) / 4.7 = 1.7 (rounded)

r = 1.7 / √(1.7^2 + 4) = 0.65 (rounded)

Check these formulas and calculations.

To calculate the effect size of the new group therapy, we can use a statistical measure called Cohen's d. Cohen's d compares the difference between two means (in this case, the mean score before and after therapy) to the variability (standard deviation) of the scores.

To calculate Cohen's d, we can use the following formula:

Cohen's d = (mean1 - mean2) / standard deviation

In this case:
- mean1 represents the mean score before therapy (35)
- mean2 represents the mean score after therapy (27)
- standard deviation is given as 4.7

Plugging these values into the formula, we get:

Cohen's d = (35 - 27) / 4.7

Simplifying further:

Cohen's d = 8 / 4.7

Cohen's d ≈ 1.702

So, the effect size of the new group therapy is approximately 1.702.