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# Analysis of Variance (ANOVA)

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4. Choose a variable and collect data for at least three different groups (samples). Compare the means of the three groups using the one-way ANOVA technique. Complete the following: (16 pts)
1. Write a brief statement of purpose of the study
2. Define the population
3. State how the sample was selected
4. What a value did you use?
5. State the hypotheses
6. What was F test value?
7. State the decision
8. Summarize the results.

5. You have been given the following information and asked to determine if the "results are significant." Please compute the mean squares between, mean squares within, the F ratio, and test it at alpha = .01. Were the results significant?

The study involved 5 samples of 20 cases each. Sum of squares between is 717 and sum of squares total is 6861.

6. Fill in the missing information for the two-way ANOVA table below:
Source Sum of Squares df Mean Square F *Level of Significance
Factor A 46.8 4 a b
Factor B 52.2 c 17.4 d
A + B 12.0 e f g
Error) 157.9 h i
Total j 55
*p (relative to alpha - .05)
7. What is the difference between a main effect and an interaction effect? Suppose we found a main effect for differences in self-esteem between underweight, average weight, and overweight subjects (it seems as those overweight subjects had the lowest self-esteem compared to the other two groups). Suppose we also found a main effect for differences in self-esteem between males and females (with males scoring higher than females on self-esteem). Finally, suppose we found a significant interaction effect for gender and weight on self-esteem. How might you interpret this? Feel free to make creative interpretations but defend your answer.
8. For each of the following, note what kind of statistical test or design it would be (e.g., one-way, t-test, two-way, etc) and the number of independent variables. Which ones might have an interaction effect?
a. 2 x 2
b. 3 x 2 x 2
c. 3 x 4