Question

1. Binge drinking on college campuses has been a hot topic in the popular media and in scholarly research. Flett, Goldstein, Wall, Hewitt, Wekerle, and Azzi (2008) report the results of a study relating perfectionism to binge drinking. In the study, students were classified inot three groups based on the number of binge drinking episondes they experienced during the past month (0, 1, 2+). 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, where higher scores represented greater perfectionism. The following results are similar to those obtained by the researchers.

                                  

Binge Drinking Episodes in Past Month
0	1	2+
9	11	12	N = 15
7	11	14
11	8	13	G = 165
8	10	16
10	10	15	ΣX2 = 1911
M = 9	M = 10	M = 14
T = 45	T = 50	T = 70
SS = 10	SS = 6	SS = 10

1. Conduct a one-way ANOVA to determine if there are differences in perfectionism if a person has experienced 0, 1, or 2+ binge drinking episodes within the last month. Set α = .01.
   1. Step 1 (û or ü)
   2. Step 2 (û or ü)
   3. Step 3
      1. MS of numerator (û, ü, or üü)
      2. MS of denominator (û, ü, or üü)
      3. F
   4. Step 4
   5. Step 5
   6. Step 6: Is this step needed (Yes or No). If Yes, complete step 6.
2. Interpretation

Answer 1

(a)

We have to test for null hypothesis

against the alternative hypothesis

Our test statistic is given by

Here,

Number of groups

Number of observations in different groups

Total number of observations

(i)

Sample means of different groups are given by

(ii)

Grand mean is given by

(iii)

Between groups mean sum of squares is given by

Within groups mean sum of squares is given by

(iv)

Degrees of freedom

[Using R-code '1-pf(16.15384,2,12)']

(v)

Level of significance

(vi)

We reject our null hypothesis if

Here, we observe that

So, we reject our null hypothesis.

(b)

Hence, based on the given data we can conclude that there are significant differences in perfectionism among persons experiencing 0, 1, or 2+ binge drinking episodes within the last month.