Question

General Information: Use the following information to ensure successful completion of the assignment: 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). This assignment uses a rubric. Please review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion. Doctoral learners are required to use APA style for their writing assignments. The APA Style Guide is located in the Student Success Center. This assignment requires that at least two additional scholarly research sources related to this topic, and at least one in-text citation from each source be included. Directions: In an essay (250-500 words), use the scenario presented above to thoroughly answer the following questions: 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? 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? 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

Since researchers want to explore self-esteem in adolescent boys and adolescent girls and so they collect two samples (sample of boys and sample of girls) independently and assume, they come from two independent normal populations with equal variances, hence we use 2 sample t test with equal variances.

Cohen's d is an essential component when evaluating the strength of a statistical claim. It is standardized measure of effect i.e. the difference between two means divided by a standard deviation of the data.

Since Cohen's d is an appropriate effect size for the comparison between two means and Cohen's d is the appropriate effect size measure if two groups have similar standard deviations and are of the same size, so when we have two independent populations with almost same standard deviations and we are interested in comparing two population means of these two populations then we compute Cohen's d as an effect size.

d=0.90 implies effect size is large.

Since the researcher compared the adolescent boys before treatment and again after treating them for depression so this is a bivariate sample i.e. pair observations (measurement before treatment, measurement after treatment) are correlated. Hence we use paired t test.