Answer :
Final answer:
To compute the appropriate effect size, use Cohen's d formula, which measures the difference between two means. Calculate the pooled standard deviation and then use the formula for Cohen's d to find the effect size. In this case, the effect size is 0.243.
Explanation:
To compute the appropriate effect size, we can use Cohen's d formula. Cohen's d measures the difference between two means in terms of standard deviations. It is calculated by taking the difference between the two means and dividing it by the pooled standard deviation. In this case, we have the sample mean before the treatment (μ1 = 54.3) and the sample mean after the treatment (μ2 = 51.7). The pooled standard deviation (σ) is the square root of the average of the variances (σ^2) of the two groups.
Using the given information:
μ1 = 54.3, μ2 = 51.7, n = 563, σ^2 = 113.64
First, calculate the pooled standard deviation:
σ = sqrt((σ1^2 + σ2^2) / 2) = sqrt((113.64 + 113.64) / 2) = sqrt(113.64) = 10.66
Then, calculate Cohen's d:
d = (μ1 - μ2) / σ = (54.3 - 51.7) / 10.66 = 0.243
Therefore, the appropriate effect size (Cohen's d) for this treatment is 0.243.
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