# Statistics - Normal Distribution with t test

Here is the data for the problem:

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).

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.

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#### Solution Preview

Choosing a Test for Comparison of a treatment group

Here is the data for the problem:

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 ...

#### Solution Summary

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?