Homework 7

Due Thurs 11 Nov in class

Assignment:

This assignment contains homework problems from the text.

1. As usual, I recommend going thru the conceptual exercises in Chapters 5 and 6.
2. Chapter 5 Exercises: 20 (don't do c, use the data below), 21, 23.
3. Chapter 6 Exercises: 17, 20.

• For problem 5.20, you don't need to go thru the computations the book is asking for, you can simply use the hypothetical data set ex0520.asc and read off the appropriate values from the Splus output. The data here was artificially constructed to match the summary in Display 5.22. You don't need to make any transformations since this data is already on the log scale.
• For (d), you can do part (i) by creating a new grouping variable which separates the first 6 species from the last 3. If the data were read into the dataframe cav, the code below could do it:

  > cav$spgroup_rep(1,294)
  > cav$spgroup[271:294]_2
  

  Now running the ANOVA for using this new grouping variable will address item (i).
• Item (ii) can be done by building a F statistic based on comapring the 9 means model to the 2 means model. This is analagous to comparing the 9 means model to the one mean model. If RSS(9) and RSS(2) are the residual sum of squares from the 9 and 2 means models respecively, we can fill in the SS parts of the ANOVA table. You'll just need to fill in the rest:

  ANOVA Table
  
  Source      SS          df      MS        F     p-val
  model  RSS(2)-RSS(9)   9-2      ?         ?       ?
  resid     RSS(9)       n-9      ?
  

  You'll have to use the pf() function to compute the p-value (ie. the chance of seeing an F as extreme, or more extreme than observed. If the F was 2.7, and the degrees of freedom were 7 and 285, then the p-val is

  > 1-pf(2.7,df1=7,df2=285)
  

• In Exercise 23 of Ch 5, before using analysis variance with Ex0523.asc, you need to tell Splus that the column bonegrp is to be treated as a factor, not a numerical value. You can do this by importing the data and then highlighting the "bonegrp" column in the spreadsheet. To change this column to a factor hit
  Data > Change Data Type...
  and then change Column type from double to factor.
  
  Once you've done this, Exercise 20 in Chap 5 is fairly straight forward. Be sure to write short paragraphs on the statistical findings and the scope of the inference. The scope of inference question is fairly interesting. There is clearly evidence that the group means differ, but is this evidence that Tyranosaurus was cold blooded? What additional data could help answer the question? If you're interested, check out the reference (Barrick and Showers, Science 265 (1994): 222-224) to see what the authors did to address the question.
• Ch 6, Ex 17: I'll talk about contrasts on Tues, but the contrast to look at here is the mean of the first 6 species compared to the mean of the last three. The contrast to look at would be

  -1/6 -1/6 -1/6 -1/6 -1/6 -1/6  1/3 1/3 1/3
  

  You'll have to follow the details in 6.2.2 to do this.
• For Ch 6 Ex 20 I'm only looking for a summary of statistical findings paragraph and a scope of inference paragraph. I'd recommend you make a case to ignore the cause of death info so that the test is realy a comparison of 3 groups. You could make the case graphically.