# PSYC 6140: Teams and Assignments

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## Assignment 1: due October 6

Due Week 4: October 6
Given on September 15
For team membership see [1] (http://www.math.yorku.ca/~georges/Courses/6140/index.html#Teams)
Don't forget to sign the pages you create with your team name, e.g. [[Team Hebb]]

### Part 1

Get together with your team to discuss the types of data used in your respective areas of research. Do the data tend to be experimental or observational? What role does each type play in research in your areas of Psychology? What kinds of research questions are framed as causal questions and which are predictive in your areas. What statistical methods are commonly used in your areas of reseearch? Are there some newer methods that are emerging? Are you aware of references to books or articles that discuss these issues as they apply to your fields? You have a lot of latitude in deciding how to best present the results of your discussion. You could simply write a wiki page in which each person has a section describing their field of research followed by some general observations.
Presentations and discussions of Part 1 will take place on October 20 (Note that there is no class on October 13)

### Part 2

Do your team's assigned problems in Freedman, Pisani and Purves.

### Part 3

Comment on the assigned article in a column by Judy Gerstel in the Toronto Star. Do the conclusions or implications of the article appear to be well founded on the basis of the article? Are there apparent flaws in the reasoning implicit in the article? Discuss the article as if you were explaining your point of view to an intelligent but non-technical friend.

### Part 4

Install R (see R: Getting started) and work your way through the introductory R session in Venables and Ripley. Prepare comments on the section assigned to your team.
For part 4, add links in PSYC 6140: Solutions to VR4 Section 1.
Until the due date of an assignment, only team members should edit pages that are signed by a team. After the due date, anyone can make changes and get individual credit towards your general participation mark for doing so.
Remember that controversies over the content of a page can be discussed in the talk page for a wiki page.
Don't forget to sign the pages you create with your team name, e.g. [[Team Hebb]]

• Part 2: Chapter 2 of Freedman, Pisani and Purves, pp 18 ff: Exercise set A: # 8, Review Exercises: # 1, 4.
• Part 3: Comment on Implants not always uplifting in the Toronto Star column by Judy Gerstel.
• Part 4: Complete the introductory R session and comment on the section named 'Simple Regression'.

### Team Allport

• Part 2: Chapter 2 of Freedman, Pisani and Purves, pp 18 ff: Exercise set A: # 3, 7, Review Exercises: # 2, 6.
• Part 3: Comment on For out good in the Toronto Star column by Judy Gerstel.
• Part 4: Complete the introductory R session and comment on the section named 'Scottish Hill Races'.

### Team Argyle

• Part 2: Chapter 2 of Freedman, Pisani and Purves, pp 18 ff:Exercise set A: # 4, 6, Review Exercises: # 3, 5.
• Part 3: Comment on Mind body connection given boost in the Toronto Star column by Judy Gerstel.
• Part 4: Complete the introductory R session and comment on the section named 'Michelson'.

### Team Aristotle

• Part 2: Chapter 2 of Freedman, Pisani and Purves, pp 18 ff:Exercise set A: # 2, 5, Review Exercises: # 7.
• Part 3: Comment on Spousal support a royal pain? in the Toronto Star column by Judy Gerstel.
• Part 4: Complete the introductory R session and comment on the section named 'Effect of outliers'.

## Assignment 2: Due October 27

All of the following questions are in Fox, Applied Regression Analysis. Some of them require mathematical expressions. If you happen to know how to use LaTeX, by all means go ahead and use it. If not, you might like to express the ideas in words or you might do your work by hand on a sheet of paper which you can then scan and upload. Some questions require elementary calculus. If no one on your team has taken calculus, please let me know and we'll arrange alternative questions. I have deliberately given each team questions that use many of Fox's datasets. There is no attempt to give teams sequences of related questions, on the contrary, I've avoided doing this to give each team a broader exposure to problems and datasets.

For team memberships, please see the PSYC 6140 Course Web Page (http://www.math.yorku.ca/~georges/Courses/6140/index.html).

### Team Asch

2.1 (a)
2.2 (c)
2.4  Sahlin
3.1 (c) Leinhardt
3.3 (a) Angell
4.1 (requires Calculus)
4.5 Duncan
5.2 (b)
5.2 (e)
5.4 (a-c)
5.7 Robey


### Team Atkinson

2.1 (b)
2.3 (a) Robey
3.1 (a) Angell
3.2 Davis
3.4 (b) Prestige
4.2 (b) Leinhardt
5.2 (a)
5.3
5.5 (a)
5.6 Sahlin


### Team Balint

2.2 (a) Sahlin
2.3 (b)
2.5  Robey
3.1 (d) Ornstein
3.3 (b) Leinhardt
4.2 (a) Angell
5.1 (b)
5.2 (d)
5.5 (b)
5.9 Angell


### Team Bandura

2.2 (b)
2.3 (c)
*2.6
3.1 (b) Duncan
3.4 (a) Angell
4.4 Leinhardt
5.1 (a)
5.2 (c)
5.5 (c)
5.8 Anscombe


## Assignment 3: Due December 1

All of the following questions are in Fox, Applied Regression Analysis.

For team memberships, please see the PSYC 6140 Course Web Page (http://www.math.yorku.ca/~georges/Courses/6140/index.html).

### Team Beck

5.10 (Calculus)
5.14 (Anscombe)
5.17 (requires material on standardized coefficients)
6.1 (b)
6.5 (Calculus)
6.8 (c) (Angell)
6.9 (c) (uses facts about linear transformations)
6.12 (a) (Angell)
6.14 (a)
6.17
7.4 (Ornstein)
7.6 (Sahlin)
7.10


### Team Becker

5.11
5.15 (a,b,c,d)
5.18 (requires material on standardized coefficients)
6.2
6.6 (Sahlin)
6.8 (b) (Anscombe)
6.10
6.13 (a)
6.14 (b)
6.18 (big)
7.3 (Angell)
7.7 (Davis)
8.1 (a) (Angell)


### Team Bekhterev

5.13 (Angell)
5.16 (b)
6.1 (a)
6.4
6.8 (a) (Robey)
6.9 (b) (uses facts about linear transformations)
6.12 (b) (Anscombe)
6.13 (c)
6.16
7.2
7.5 (c,d)
7.9 (Angell)
8.1 (c) (Angell)


### Team Bem

5.12 (Angell)
5.16 (a)
5.19 (requires material on standardized coefficients)
6.3
6.7 (Sahlin)
6.9 (a) (uses facts about linear transformations)
6.11 (a,b) (Angell)
6.13 (b)
6.15
7.1 (a,b,c)
7.5 (a,b)
7.8 (Duncan)
8.1 (b) (Angell)
8.2 (difficult?)


## Assignment 4: Due March 19

Don't forget to include the R code for your solutions. That is often the most useful part of the solution for people who will consult it in the future.

### Questions

Note that all teams do questions 1 to 9. Since they use randomly generated data, you will get randomly different solutions. It will be interesting to see how different they are.

Generate a set of random number to simulate the LSAT scores and GPAs of 100 new law school applicants assuming they come from a population in which the LSAT scores are jointly normally distributed with a mean of 625 and a standard deviation of 60 and GPAs are normal with a mean 3.2 and standard deviation .3. Further suppose that the correlation between LSAT scores and GPAs is 0.65. Plot the data and plot the standard ellipses for the data and for the population from which they were generated.
Use the data in the previous question and generate an additional variable, FYEAR, representing the law school grade at the end of the first year. Generate FYEAR so that is is equal to 0.5 + 0.006 x LSAT + 0.8 x GPA + e, where e is normal with mean 0 and standard deviation equal to 1.
State the true values of β0, βLSAT, βGPA and σ in this model.
What are the values of 'true' standardized βs in this model? [Note: This is not trivial because you need to find the marginal variance of Y]
Fit a regression of FYEAR on LSAT and GPA producing suitable summary tables and plots.
Test each of the following hypotheses using a GLH approach or otherwise. In each case state whether you have committed a type I error or a type II error. [Why is it impossible to do this in your usual analyses?]
1. βGPA = 0 and βLSAT = 0
2. βGPA = 0.8 and βLSAT = 0.006
3. βGPA = 1
4. βGPA = 0.81
5. βGPA = 0.8
6. $\beta_{LSAT} \times 60 = \beta_{GPA} \times 0.3$
Draw a joint 95% confidence ellipses and a 95% 'confidence-interval generating ellipse' for βGPA and βGPA in the problem above.
Describe how each hypothesis tested above relates to the confidence ellipses.
Suppose you were asked which variable is more important in determining FYEAR? Discuss possible approaches to answering this question.
10
Let $X = \begin{bmatrix} X_1 \\ X_2 \\ X_3 \end{bmatrix}$ have mean $\begin{bmatrix} 4 \\ 3 \\ 1 \end{bmatrix}$ and variance $\begin{bmatrix} 4 & 3 & 1 \\ 3 & 4 & 1 \\ 1 & 1 & 2 \end{bmatrix}$. Let W1 = X1X2 and W2 = X2 + X3. Find the mean, variance matrix and correlation matrix for

$\begin{bmatrix} W_1 \\ W_2 \\ X_3 \end{bmatrix}$

Data for 11-15
A study was done to measure the effect of alcohol (Alc) and tranquilizers (Tran) on motor dysfunction (MD). The following table shows the (simulated) data obtained from 30 human subjects.
   Alc Tran MD
1   14    6 11
2    1    1  0
3    5    9  5
4    7    5  5
5    9    9  9
6   22    4 10
7   25    1 13
8    0    7  5
9    4    5  7
10  23    0 11
1    8    2  2
2    1    4  4
3    9    2  8
4   10    1  5
5   12    6 11
6   10    8  8
7    1    0  4
8   29    4 15
9   11    1  6
10  18    0  8
1    4    4  8
2   29    7 18
3    5    9  7
4   17    0 10
5   22    9 18
6   26    6 16
7    2    1  5
8   28    3 16
9    9    8  9
10  16    9 17

11
Fit a model that allows for interactions between 'Alc' and 'Tran' in their effect on 'MD'. Do this by including product term: 'Alc' $\times$ 'Tran'. Plot the fitted response surface.
12
Is there evidence that the interaction term is necessary in the model?
13
Estimate the effect of 'Alc' when 'Tran' = 0 and when 'Tran' = 5. Then estimate the difference in these two effects and test the hypothesis (reporting 'p'-values is adequate) that the two effects are the same.
14
Estimate the effect of 'Tran' when 'Alc' = 10 and when 'Alc' = 20. Estimate the difference in these two effects and test the hypothesis that the two effects are the same.
15
Have you just conducted three equivalent tests? Why?

Questions from Fox Chapter 9:

  9.4
9.5(a)  compute using matrix operations and using the appropriate lm method in R
9.5(b)  Note: You can get mean deviations for each column of a matrix X
by using  scale( X, center = T, scale = F )
9.6(a)  Note: You can get standardized variables with scale( X )
9.6(b)
9.6(c)  [challenging]

9.7
9.8
9.9(a)
9.9(b)
9.9(b+)  Show that X*'X* = (n - 1) x Var(X)

9.10  [Note an error. The reason that Cov(b,e) = 0 is sufficient for independence is
that b and e are JOINTLY normally distributed. "BOTH" is not enough.]
9.11
9.12

The following two questions are optional. Do them if you feel motivated.
They (and equation 9.18 they refer to) use the traditional way of expressing these
formulas.  I find the approach in class more revealing but it's useful to appreciate
that all these formulas do the same thing.
*9.13
*9.14

9.15
9.16  [Prediction]
9.17  Analyze the Moore and Krupat data showing type I, II and III SS and
explaining what is tested with each row of the anova tables


### Team Bentall

• Questions 1-9
• Question 10
• Fox 9.4, 9.6(b), 9.9(a), 9.11
• Post answers to matrix exercises 1,5,9

### Team Binet

• Questions 1-9
• Questions 11-15
• Fox 9.5(a), 9.6(c), 9.9(b), 9.12
• Post answers to matrix exercises 2,6,10

### Team Bion

• Questions 1-9
• Question 10
• Fox 9.5(b), 9.9(b+), 9.12, 9.14, 9.17
• Post answers to matrix exercises 3,7,11

### Team Birch

• Questions 1-9
• Questions 11-15
• Fox 9.6(a), 9.8, 9.10, 9.16
• Post answers to matrix exercises 4,8,12

### Team Zimbardo

1. Do a pretend assignmnent.