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?

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

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

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

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

Explanation / Answer

a. The estimated standard error is 2 points and the data produce t = 6/2 = 3.00. With
df = 15, the critical values are t = ±2.131, so the decision is to reject H0 and conclude
that there is a significant treatment effect.
b. For these data, d = 6/8 = 0.75 and r2 = 9/24 = 0.375 or 37.5%.
c. For 95% confidence and df = 15, use t = ±2.131. The confidence interval is p. = 86
±2.131(2) and extends from 81.738 to 90.262.

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