A sample is selected from a population with μ = 46, and a treatment is administered to the sample. After treatment, the sample mean is M = 48 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen’s d?

Question

​A sample is selected from a population with μ = 46, and a treatment is administered to the sample. After treatment, the sample mean is M = 48 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen’s d?

BlackTom AI · Accepted Answer

We begin by identifying the values needed to compute Cohen's d. The formula for Cohen's d in the one-sample or treatment context is d = (M − μ) / s, where M is the post-treatment sample mean, μ is the population mean under the null or baseline, and s is the sample standard deviation.

First, compute the standard deviation from the given variance: s^2 = 16, so s = sqrt(16) = 4.

Next, determine the difference between the sample mean after treatment and the population mean: M − μ = 48 − 46 = 2.

Now plug into the formula: d = 2 / 4 = 0.5.

Explanation of why this value makes sense: Cohen's d expresses the size of the treatment effect in standard deviation units. A difference of 2 points on a scale with a standard deviation of 4 equals half a standard deviation, which corresponds to d = 0.5.

A few potential misunderstandings to avoid: if one were to use the variance directly without taking a square root, that would mix units (variance vs. standard deviation) and yield an incorrect effect size. Also, if μ were misidentified (e.g., using the post-treatment mean as μ), the calculation would be erroneous. Finally, since no alternative options are provided here, there are no other choices to compare against in this question.

A sample is selected from a population with μ = 46, and a treatment is administered to the sample. After treatment, the sample mean is M = 48 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen’s d?单项选择题

类似问题

Two samples from the same population both have M = 84 and s2 = 20, but one sample has n = 10 and the other has n = 20 scores. Both samples are used to evaluate a hypothesis stating that μ = 80 and to compute Cohen’s d. How will the outcomes for the two samples compare?

Calculate Cohen's D: Sample Size Group 1 = 19 Sample Size Group 2 = 16 Standard Deviation Group 1 = 4.2 Standard Deviation Group 2 = 5.5 Sample Mean Group 1 = 41.9 Sample Mean Group 2 = 43.5

Calculate Cohen's D: Sample Mean Difference Score (time 1 - time 2) = 1.7 Standard Deviation Difference Scores = 3.2 Sample Size = 39

Please consider the following information: Sample mean (M) = 50 Population mean (µ) = µM = 47 Sample standard deviation (s) = 4 Sample size (N) = 25 Based on this information, compute the effect size measure, Cohen's d. Please include at least two decimal places when reporting your answer.

According to Cohen's guidelines for the effect size measure d, which of the following would be an example of a medium effect size?

Consider the following information used for a one-sample t test: N = 100, µ = 30, s = 20, and M = 33. Based on this information, what is the measure of effect size, Cohen's d, rounded to two decimal places?

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​A sample is selected from a population with μ = 46, and a treatment is administered to the sample. After treatment, the sample mean is M = 48 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen’s d?单项选择题