# MET CS 555 Assignment 5

\$30.00

## 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)

 group iq age Physics student 34 15 Physics student 33 17 Physics student 32 15 Physics student 25 14 Physics student 36 19 Physics student 30 18 Physics student 31 16 Physics student 34 17 Physics student 29 16 Physics student 34 17 Physics student 39 16 Physics student 33 18 Physics student 39 19 Physics student 42 20 Physics student 41 20 Math student 36 20 Math student 38 28 Math student 37 22 Math student 35 18 Math student 41 19 Math student 40 23 Math student 36 19 Math student 38 16 Math student 24 18 Math student 39 20 Math student 29 19 Math student 38 20 Math student 45 23 Math student 44 24 Math student 44 22 Chemistry student 52 46 Chemistry student 46 38 Chemistry student 51 41 Chemistry student 52 39 Chemistry student 45 44 Chemistry student 49 33 Chemistry student 47 41 Chemistry student 46 36 Chemistry student 41 40 Chemistry student 47 44 Chemistry student 46 46 Chemistry student 42 38 Chemistry student 43 32 Chemistry student 47 41 Chemistry student 40 42