Question

In a completed​ study, there is a known population with a normal​ distribution,

muμequals=3030​,

and

sigmaσequals=1111.

What is the estimated effect size if a sample given an experimental procedure has a mean of​

(a)

1818​,

​(b)

2222​,

​(c)

3030​,

​(d)

3535​,

and​ (e)

4040​?

For each​ part, also indicate whether the effect is approximately​ small, medium, or large

Answer 1

Solution :

The Cohen's d effect size is calculated as follows :

Where, x̅ is sample mean, μ is population mean, σ is population standard deviation.

The effect size can be categorized as follows :

The effect size from 0 to less than 0.5 is considered as small effect size.

The effect size from 0.5 to less than 0.8 is considered as medium effect size.

The effect size of 0.8 or greater is considered as large effect size.

a) We have,  x̅ = 18, μ = 30, σ = 11

The effect size is 1.09 and the effect is large.

b) We have,  x̅ = 22, μ = 30, σ = 11

The effect size is 0.73 and the effect is medium.

c) We have,  x̅ = 30, μ = 30, σ = 11

The effect size is 0 and the effect is small.

d) We have,  x̅ = 40, μ = 30, σ = 11

The effect size is 0.91 and the effect is large.

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