A random sample is obtained from a population with a mean of = 100, and a treatm

Question

A random sample is obtained from a population with a mean of = 100, and a treatment is administered to the sample. After treatment, the sample mean is found to be M = 104 and the sample variance is s2 = 400.

(a) Assuming the sample contained n = 16 individuals, measure the size of the treatment effect by computing the estimated d and r2. (Use 3 decimal places.)

(b) Assuming the sample contained n = 25 individuals, measure the size of the treatment effect by computing the estimated d and r2. (Use 3 decimal places.)

(c) Comparing your answers from parts (a) and (b), how does sample size influence measures of effect size? (chose A, B, C, D)

A) The sample size does not have any influence on Cohen's d or r2.

B) As sample size increases both Cohen's d and r2 increase.     

C) The sample size does not have any influence on Cohen's d and has only a minor effect on r2.

D) As sample size increases both Cohen's d and r2 decrease.

Explanation / Answer

Answer (a)

Mean of sample µ = 100

After treatment sample mean M = 104

Sample variance S2 = 400

Now, calculating coefficient of determination r2 = 1 – (SSres / SStotal)

= 1 – ((104-100)^2 / 400)

r2= 0.96

r = 0.979

There is a relation between Cohen’s d and coefficient (r)

                d = 2r / (1-r2) = (2 * 0.979) / (1 – 0.96)

d = 48.950

Answer (b)

Sample size changed from 16 to 25

Formula used to find r from d if sample size changes

                   r   = d / (d2 + a)

Where, a = (n1 + n2)2 / (n1 * n2) = (16 + 25)2 / (16 * 25)

                    a = 4.202

Now calculating from above r = 48.950 / ((48.950^2) + 4.202) = 0.0204

   r2 = 0.000416

Same as earlier d = (2 * 0.0204) / (1 – 0.000416)

d = 0.0408

Answer (c)

D

As the sample, size increases both Cohen’s d and r2 decreases.

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