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Chapter 18 Questions
Complete the following questions. The questions may include pictures or graphics to illustrate or aid in solving the problem. You can check your answer by clicking View Answer. If the question is unclear, confusing, or if you need further clarification, send me an email.
1. ANOVA Activity
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2. Imagine we are interested in the development of skills over time. We offer our subjects training in painting with watercolors, allow them to practice and paint over a three-month period, and assess their skills at one-month intervals. Given the data below, did subjects? paintings differ among the three measurements?
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3. Explain why the formula for the within sum of squares for the repeated measures ANOVA is similar to the interaction sum of squares for the two-way ANOVA.
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4. Given the study and data described in number two, re-conceive of the study as a one-way ANOVA. How would the study and layout of the data have to change?
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For the test of the time variable, with 2 and 15 degrees of freedom, F = 6.17 is significant at p < .05. Because there is no subject variable in this one-way design, what had been the subject sum of squares was combined into the within sum of squares, resulting in a larger error term and smaller F-value
5. Given the study and data described in number two, re-conceive of the study as a two-way ANOVA. How would the study and layout of the data have to change? Compute this analysis and compare the results of the three analyses. How and why do they differ from one another?
Answer
For the test of the time variable, with 2 and 12 degrees of freedom, F = 10.57 is significant at p < .05. For the test of the training variable, with 1 and 12 degrees of freedom, F = 12.70 is significant at p < .05. For the test of the time by training variable, with 2 and 12 degrees of freedom, F = .51 is not significant at p < .05. Though there is no subject variable in this two-way design, there is a training and a time by training variable, which decreases the within sum or squares from what it was in the one-way design, thereby yielding a larger F-value than in the one-way design. It may be seen that the sum of the subjects sum of squares and within sum of square from the repeated measures ANOVA is equal to the sum of the training, time by training, and within cells sums of squares in the two-way design.