Conceptual Exercises

(Chap 13, p. 415) 1, 2, 3, 4, 5, 6, 10

Do the above conceptual exercises from the Sleuth but do not hand them in as part of your homework. The answers can be found at the end of the chapter, but make an honest effort to answer them before looking. They are a useful way to gauge how much you understood and can show up on exams.

Q1

Before you start: Visit http://www.statsci.org/data/general/eysenck.html and read about the study for this homework.

The data can be read in to RStudio with

words <- read.table(url("http://www.statsci.org/data/general/eysenck.txt"), header = TRUE)
head(words)

##       Age  Process Words
## 1 Younger Counting     8
## 2 Younger Counting     6
## 3 Younger Counting     4
## 4 Younger Counting     6
## 5 Younger Counting     7
## 6 Younger Counting     6

1. Is this dataset balanced?

2. Create a plot of the raw data.

3. Produce a two-way table of sample averages, along with row and column averages. Using the table you produce:

   Under the saturated model, what is the estimated difference in mean number of words recalled between the Younger and Older groups in the Adjective treatment?

4. Fit the saturated model and examine the residuals. Is there any evidence of a need for transformation?

5. Run a extra sum of squares F-test to compare the saturated model to the additive model. Is there evidence against the simpler additive model?

6. Using the saturated model, produce a plot of the estimated mean reponses.

7. Which Processes do Young people have an advantage on? Answer this question by refitting the following reparameterization of the saturated model:

fit_sat2 <- lm(Words ~ Process + Process:Age, data  =words)

which corresponds to the model \[ \begin{eqnarray} \mu\{\text{Words} \, | \, \text{Process},\text{ AGE }\} &=& \beta_0 + \beta_1 \textit{Counting}+ \beta_2 \textit{Imagery}+ \beta_3 \textit{Intentional} + \beta_4 \textit{Rhyming} + \\ &&\beta_5(\textit{Adjective}\times\textit{Younger}) + \beta_6 (\textit{Counting}\times\textit{Younger})+ \beta_7 (\textit{Imagery}\times\textit{Younger})+ \\ &&\beta_8 (\textit{Intentional}\times\textit{Younger})+ \beta_9( \textit{Rhyming}\times\textit{Younger}) \end{eqnarray} \]

You should first verify that the parameters \( \beta_5, \beta_6, \beta_7, \beta_8, \beta_9 \), capture the difference in mean words between Older and Younger people for the Adjective, Counting, Imagery, Intentianal and Rhyming processes respectively.

If you interested in what the authors of the study concluded, read the second paragraph in the Discussion section in their paper.