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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

A random sample is obtained from a population with n mean of μ = 45. After a treatment is administered to the individuals in the sample, the sample mean is M = 49 with a standard deviation of s = 12.

a. Assuming that the sample consists of n = 9 scores, compute r2 and the estimated Cohen's d to measure the size of treatment effect.

b. Assuming that the sample consists of n = 16 scores, compute r2 and the estimated Cohen's d to measure the size of treatment effect.

c. Comparing your answers from parts a and b, how does the number of scores in the sample influence the measures of effect size?

a.

To determine

To find: The r2 and the estimated Cohen’s d to measure the size of treatment effect.

Explanation

Given info:

A sample of 9 individual is selected from a population with mean 45. The sample mean, and standard deviation is 49 and 12 and the level of significance is α=0.05.

Calculations:

Formula for Cohen’s d is:

Cohens d=Mμs2

Substitute 49 for M, 45 for μ and 12 for s

Cohens d=494512=412=0.33

Formula for r2 is:

r2=t2t2+df

The t-statistics is obtained by,

t=

b.

To determine

To find: Whether or not the treatment has a significant effect for α=0.05.

c.

To determine

To state: The impact of sample size on the measure of effective size.

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