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Statistics for The Behavioral Scie...

10th Edition
Frederick J Gravetter + 1 other
ISBN: 9781305504912

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BuyFindarrow_forward

Statistics for The Behavioral Scie...

10th Edition
Frederick J Gravetter + 1 other
ISBN: 9781305504912
Textbook Problem

A random sample of n = 16 scores is obtained from a population with a mean of μ = 45 . After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 49.2 .

a. Assuming that the sample standard deviation is s = 8 , computer r 2 and the estimated Cohen’s d to measure the size of the treatment effect.

b. Assuming that the sample standard deviation is s = 20 . computer r 2 and the estimated Cohen’s d to measure the size of the treatment effect.

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

To determine

The r2 and Cohen's d for varying values of s for other fixed values.

Explanation

Given:

n=16, μ = 45, M = 49.2

Formula used:

Cohen's d is given as:d=Mμσr2=t2t2+df Where t is calculated t value. I.e. t= t=Mμσn

Calculations:

a. s = 8 since σ is unknown we use its estimate which is s.

t=49.24584 = 2.1; r2=2.122

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