A raidom sample of n-16 scores is obtained from a population with a mean of = 45

Question

A raidom sample of n-16 scores is obtained from a population with a mean of = 45, After a treatment is administered to the individuals in the sample, the sample mean is found to be M 492 a. Assuming that the sample standard deviation is s = 8, compute r2 and the estimated Cohen's d to measure the size of the treatment effect. b. Assuming that the sample standard deviationis s = 20, compute r, and the estimated Cohen's d to measure the size of the treatment effect. c. Comparing your answers from parts a and b, hovw does the variability of the scores in the sample influence the measures of effect size? 21

Explanation / Answer

SolutionA:

cohens d=mean difference/sample sd

=M-mu/s

=49.2-45/8

d =0.525

r sq=variability accounted for/total variability

=t^2/t^2+df

t=samlemean-pop mean/std error

=49.2-45/8/sqrt(16)

=4.2/8/4

=2.1

df=n-1=16-1=15

r sq=2.1^2/2.1^2+15

r sq=0.23

medium effect

Solutionb:

d=49.2-45/20

d=0.21

t=49.2-45/20/sqrt(16)

=4.2/20/4

=4.2/5

t =0.84

df=n-1=16-1=15

r sq=0.84^2/0.84^2+15

r sq=0.04

small effect

SOlutionc:

for d=0.525 and r sq= .23 effect is medium

for d=0.21 an d r sq=0.04 effect is small

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