Exam 1 (take-home only)

Data were collected on the average runs scored per game for each of the 30 teams in major league baseball in this file. The teams are divided into six divisions, each with five teams.

Write one or more sentences summarizing your conclusions for each of the following problems. Your summary should allow a person to understand your results even if they do not know the software that you used (SAS, R, etc.). Attach key parts of the computer output (ANOVA table listing, plots, not all of the output) either alongside your written answers, or else in an appendix.

1.       Conduct an analysis of variance (fill out the ANOVA table, including sums of squares, mean squares, F statistic, and P value. Be sure to include a line for total SS and df) to test the null hypothesis of equality of runs scored by division. Include a boxplot to visualize potential differences by division.

"The boxplot for runs scored shows some variability in means and potentially in variation between groups. The null hypothesis of no difference in means by division was tested by the ANOVA F test. The alternative hypothesis is that one or more division means differs from the other divisions means. The F statistic had 5 numerator and 24 denominator degrees of freedom, and was equal to 0.74. The F value was less than 1 and had a P value of .60, indicating that we fail to reject the null hypothesis and cannot conclude that the mean runs scored differs by division."

2.       Examine a residual by predicted plot and a normal plot of the residuals to assess model assumptions.

3.       Use the log(standard deviation) and log(mean) regression to examine whether a power transformation is needed. Is the test for a transformation significant? What power transformation is recommended? [You do not need to reanalyze the data]

4.       If we were going to test for a difference in runs scored by division, and the true mean values were: 4, 4.5, 4.5, 4.5, 4.5, and 5., with a variance as estimated from these data, what is the power of the ANOVA test to detect these group differences with 5 teams per division? Use alpha=.05.