Question

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Researchers wanted to explore self-esteem in adolescent boys and adolescent girls. Each respondent completed a 10-item self-esteem scale (they chose one rating for each item from a Likert-type scale, 1 = strongly disagree and 5 = strongly agree). The sum of the 10 ratings was each respondent's self-esteem score. Their results were: t = 2.01, d = .90 (40 girls, 40 boys).

Use the scenario presented above to answer the following questions:

1.        What statistical test did the researchers use to determine if there was a statistically significant difference in levels of self-esteem between the boys and the girls?

2.        What was the purpose of calculating a Cohen's d? When is a Cohen's d calculated? Interpret d=.90. What does it mean in this example?

3.        What if the researcher compared the adolescent boys before treatment and again after treating them for depression? What type of t-test would be most appropriate in this case, and why?

Answer 1

(1)

The statistical test the researchers used to determine if there was a statistically significant difference in levels of self-esteem between the boys and the girls:

2 independent samples t test

(2)

(i)

The purpose of calculating a Cohen's d is calculate Effect Size d, which is the standardized difference between two means.

(ii)

A Cohen's d is calculated when we want to find out how much is the difference between two means.

(iii)

Since d = 0.90 is greater than 0.8, we conclude the Effect Size is large, i.e., the difference between two means.is large.

(3)

If the researcher compared the adolescent boys before treatment and again after treating them for depression, dependent samples t - test (paired t test) would be most appropriate in this case because the 2 samples are not independent. The same sample is measured twice: before treatment and again after treating them for depression.