MET CS 555 Assignment 5 solution

Description

The data in this document is from 3 groups of students (math, chemistry, and physics) on an IQ related test.  Save the data to CSV/Excel file and read the data into R.  Use this data to address the following questions:

• How many students are in each group? Summarize the data relating to both test score and age by the student group (separately).  Use appropriate numerical and/or graphical summaries.  (3 points)

• Do the test scores vary by student group? Perform a one way ANOVA using the aov or Anova function in R to assess.  Summarize the results using the 5 step procedure.  If the results of the overall model are significant, perform the appropriate pairwise comparisons using Tukey’s procedure to adjust for multiple comparisons and summarize these results.  (7 points)

• Create an appropriate number of dummy variables for student group and re-run the one-way ANOVA using the lm function with the newly created dummy variables. Set chemistry students as the reference group.  Confirm if the results are the same.  What is the interpretation of the beta estimates from the regression model?  (4 points)

• Re-do the one-way ANOVA adjusting for age. Focus on the output relating to the comparisons of test score by student type.  Explain how this analysis differs from the analysis in step 2 above (not the results but how does this analysis differ in terms of the questions it answers as opposed to the one above).  Did you obtain different results?  Summarize briefly (no need to go through the 5 –step procedure here).   Present the least square means and interpret these. (6 points)