Question

A research team wants to see if youth participation in cultural and sports activities may be related to higher values of self-esteem. A group of 100 youths who do participate in such activities were found to have a mean self-esteem of 53.8 (with a standard deviation of 5.1). For the general population of youths, the mean score on the same self-esteem measure is 50, and the standard deviation is 5.9. Use this information to calculate and interpret the effect size for the mean difference between participating youths and the general youth population.

a) Effect size = 0.52; The mean self-esteem of participating youths is moderately higher than the general youth population.
b) Effect size = 0.52; The mean self-esteem of participating youths is significantly lower than the general youth population.
c) Effect size = 0.10; The mean self-esteem of participating youths is slightly higher than the general youth population.
d) Effect size = 0.10; The mean self-esteem of participating youths is significantly higher than the general youth population.

Answer 1

The calculated effect size using Cohen's d is 0.69, indicating that the mean self-esteem of participating youths is moderately higher than the general youth population.

The correct answer is A.

Step-by-step explanation:

To calculate the effect size for the mean difference in self-esteem between youths who participate in cultural and sports activities and the general youth population, we can use Cohen's d formula, which is:

d = (M1 - M2) / SDpooled

Where:

• M1 is the mean self-esteem score for participating youths, which is 53.8.
• M2 is the mean self-esteem score for the general population of youths, which is 50.
• SDpooled is the pooled standard deviation, which can be calculated as the square root of the average of the squared standard deviations since the sample sizes are equal.

First, we need to calculate the pooled standard deviation:

SDpooled = √[(SD1^2 + SD2^2) / 2] = √[(5.1^2 + 5.9^2) / 2] = √[(26.01 + 34.81) / 2] = √[30.41] ≈ 5.51

Now we can calculate the effect size:

d = (53.8 - 50) / 5.51 ≈ 0.69

Since the Cohen's d effect size is 0.69, it falls between the medium (0.5) and large (0.8) effect sizes by Cohen's standard, suggesting that the mean self-esteem of participating youths is moderately higher than the general youth population. Therefore, option a) is the correct interpretation of the effect size.