Question

ttention: Due to a bug in Google Chrome, this page may not function correctly. Click here to learn more. 11. Chapter 12, Problem 11 Aa Aa E Binge drinking on college campuses has been a hot topic in the popular media and in scholarly research. In one study relating perfectionism to binge drinking, students were classified into three groups based on the number of binge drinking episodes they experienced during the past month (0, 1, 2 or more). The students then completed a perfectionism questionnaire including one scale measuring parental criticism. One sample item is "I never felt that I could meet my parents' standards." Students rated their level of agreement with each item, and the total score was calculated for each student. [Flett, G. L., Goldstein, A., Wall, A., Hewitt, P. L., Wekerle, C., and Azzi, N. (2008). Perfectionism and binge drinking in Canadian students making the transition to university. Journal of American College Health, 57, 249-253.) The following results are similar to those obtained by the researchers. Binge Drinking Episodes in Past Month 2 or more 13 N = 15 T = 45 SS = 4 n = 5 M = 10 T = 50 SS = 10 n = 5 = 14 T = 70 SS = 10 G = 165 EX2 = 1,909 Use an ANOVA with a = .05 to determine whether there are any significant differences among the three groups. (Use two decimal places.) Degrees of Freedom Sum of Squares Mean Square Source of Variation Between treatments Within treatments Total Critical value for the F-ratio = . (Use three decimal places.)

Answer 1

Hypotheses are:

H0: All the populaitons means are equal.

Ha: At least two population means differ.

First be need to find grand mean so

GIM = 11

Since there are 3 different groups so we have k=3. Therefore degree of freedoms are:

$df_{between}=k-1=3-1=2$

df within = N - k = 15 -3 = 12

dftotal = 12 + 2 = 14

Let $\bar{x_{i}}$ shows the mean of the ith group. So

SSbetween = n111 - 2)2 + n2(22 - )2 + n3 (73 – 7)= 70

and

SS within = SS1 + SS2 + SS3 = 24

Therefore

SStotal = S Shetueen + SS within = 94

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Now

M Sbetween = SSbetween dfbetween " = 35.0

MS within = in S Surithin dfwithin - = 2.0

F test statistics is

F = M Sbetween * = 17.50 M Swithin

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Critical value of F test using excel function "=FINV(0.05,2,12)" : 3.885

Since F > 3.885 so reject H0

First option is correct.

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The effect size eta square will be

$\eta^{2}=\frac{SS_{bet}}{SS_{tot}}=\frac{70}{94}\approx 0.745$