Stat 502, 2014 Homework 3
Due date: Friday, October 17. Turn in a paper copy at the beginning of class.
1. (p-values under null) Suppose Y is the random outcome of an experiment and g(Y ) is a
test statistic with continuous null distribution. Let g1 denot
Stat 502 Homework 3 Solutions
October 29, 2014
Problem 1
a)
To nd the distribution of p(Y ) under the null hypothesis, lets rst nd the CDF of p(Y ) under the
null and see if it corresponds to a CDF of a known distribution.
P (p(Y ) t) t [0, 1]
= P (P (g(Y
Stat 502, 2014 Homework 1
Due date: Wednesday, October 1. Turn in a paper copy at the beginning of class.
The main purpose of this assignment is to force you to explore our software R. You may learn R basics
from the ebook Introductory Statistics with R,
Stat 502 Homework 1 Solutions
October 3, 2014
Problem 1
You can access the juul dataset by installing the R package ISwR and typing data(juul) into the R
console. The correct query to extract the girls who were ages 7 through 14 is by writing:
j u u l [ j
Stat 502 Homework 2 Solutions
October 9, 2014
Problem 1
a)
Sample Mean
Sample Median
Sample SD
High Treatment
4.603
3.614
2.614
Low Treatment
4.491
4.349
1.608
Table 1: Exploratory Data Analysis Table
The dierence in sample means is not too large relative
Stat 502, 2014 Homework 6
Due date: Wednesday, November 12. Turn in a paper copy at the beginning of class.
1. Contrasts: Oehlert Problem 4.1
2. Polynomial contrasts: Oehlert Exercise 4.1.
3. Suggest a transformation for the data from Exercise 6.4 in Oehl
Stat 502 Homework 6 Solutions
November 14, 2014
Problem 1
a)
We know SSerror = 2.25 and we know the yi. vector is (4.6, 4.3, 4.4, 4.7, 4.8, 6.2). SStreatment = 4
6
y
i=1 (i.
y. )2 , where y. = meancfw_i. = 4.83. Thus, SStreatment = 9.65. The ANOVA tabl
Stat 502, 2014 Homework 5
Due date: Friday, October 31. Turn in a paper copy at the beginning of class.
M.S. and Ph.D. students in Statistics: Do Problem 1, 2, 4, 5 and 6.
All other students: Do Problem 1, 2, 3, 5 and 6.
1. Show that squaring the two-samp
Stat 502 Homework 5 Solutions
October 31, 2014
Problem 1
Let
1
m
(ni 1)
i=1
2
s = MSerror =
ni
m
(yij yi )2
i=1 j=1
2
be the estimator of the error variance . Let
MStreatment =
1
m1
m
ni (i y )2
y
i=1
be the mean square for the treatment, where
yi =
1
ni
Stat 502, 2014 Homework 4
Due date: Friday, October 24. Turn in a paper copy at the beginning of class.
For problem 1, write a Data analysis report, having sections with titles given below. Write in
complete sentences, providing the requested tables and p
Stat 502, 2014 Homework 2
Due date: Friday, October 10. Turn in a paper copy at the beginning of class.
1. Bacteria cultures: Biochemists are interested in comparing the amount of bacteria that grow under
two dierent temperature regimes, high and low. In
Example
Summary statistics
Hypothesis testing via randomization
Sensitivity to the alternative
Basic decision theory
II. Test Statistics and Randomization
Distributions
Mathias Drton
Dept. of Statistics
University of Washington
1 / 36
Example
Summary stat
Randomized complete block design
Latin squares
VIII. Blocking
Mathias Drton
Dept. of Statistics
University of Washington
1 / 36
Randomized complete block design
Latin squares
Motivating example
Example Do dierent tools give dierent hardness readings?
A ha
Condence intervals
Power and Sample Size Determination
IV. Condence Intervals and Power
Mathias Drton
Dept. of Statistics
University of Washington
1 / 27
Condence intervals
Power and Sample Size Determination
Condence intervals via hypothesis tests
In a o
Two-way factorial designs
Additive model
Multi-way factorial designs
VIII. Factorial Treatment Structure
Mathias Drton
Dept. of Statistics
University of Washington
1 / 28
Two-way factorial designs
Additive model
Multi-way factorial designs
Motivating exam
Split-plot designs
Mixed eects modeling
XII. Split-Plot Designs / Nested Designs
Mathias Drton
Dept. of Statistics
University of Washington
1 / 22
Split-plot designs
Mixed eects modeling
Potato example:
Sulfur added to soil kills bacteria, but too much su
Two-series designs
Fractional factorial designs
Two-series in incomplete blocks
XI. Fractional Factorial Designs
Mathias Drton
Dept. of Statistics
University of Washington
1 / 28
Two-series designs
Fractional factorial designs
Two-series in incomplete blo
Stat 502, 2014 Homework 7
Due date: Wednesday, November 19. Turn in a paper copy at the beginning of class.
1. Bees: An entomologist conducted an experiment to understand the eects of temperature
and food source on the energy expenditure of honeybees. Thr
Stat 502, 2014 Homework 8
Due date: Monday, December 1. Turn in a paper copy at the beginning of class.
1. Consider the rst ANOVA table from Exercise 10.3 in Oehlert. This is about an unbalanced
two-way factorial design with two factors (called r and c).
Stat 502 Homework 4 Solutions
October 25, 2014
Problem 1
Experimental Design
In this experiment, we are applying a Nitrogen additive to fertilizer and want to see whether it aects the
growth of lettuce. From the problem description, we have 5 dierent leve
Randomized complete block design
Latin squares
VIII. Blocking
Mathias Drton
Dept. of Statistics
University of Washington
1 / 36
Randomized complete block design
Latin squares
Motivating example
Example Do dierent tools give dierent hardness readings?
A ha
Two-series designs
Fractional factorial designs
Two-series in incomplete blocks
XI. Fractional Factorial Designs
Mathias Drton
Dept. of Statistics
University of Washington
1 / 28
Two-series designs
Fractional factorial designs
Two-series in incomplete blo
IX. Incomplete Blocks
Mathias Drton
Dept. of Statistics
University of Washington
1 / 16
Incomplete-block designs
Recall:
In a complete block design, each treatment occurs an equal number of
times in each block.
So for a randomized complete block design (R
Two-way factorial designs
Additive model
Multi-way factorial designs
VIII. Factorial Treatment Structure
Mathias Drton
Dept. of Statistics
University of Washington
1 / 28
Two-way factorial designs
Additive model
Multi-way factorial designs
Motivating exam
Model diagnostics
Treatment comparisons
Multiple comparisons
VII. Practical Considerations for ANOVA
Mathias Drton
Dept. of Statistics
University of Washington
1 / 43
Model diagnostics
Treatment comparisons
Multiple comparisons
Model diagnostics
For linea
Multivariate normal distribution
Linear models
Least squares
Inference
F-tests of linear hypotheses
VI. Linear Models
Mathias Drton
Dept. of Statistics
University of Washington
1 / 42
Multivariate normal distribution
Linear models
Least squares
Inference
Example
Summary statistics
Hypothesis testing via randomization
Sensitivity to the alternative
Basic decision theory
II. Test Statistics and Randomization
Distributions
Mathias Drton
Dept. of Statistics
University of Washington
1 / 34
Example
Summary stat
Treatment variation
Sums of squares
Normal sampling models
V. Introduction to ANOVA
Mathias Drton
Dept. of Statistics
University of Washington
1 / 60
Treatment variation
Sums of squares
Normal sampling models
Response time data
Background: Psychologists a
Condence intervals
Power and Sample Size Determination
IV. Condence Intervals and Power
Mathias Drton
Dept. of Statistics
University of Washington
1 / 27
Condence intervals
Power and Sample Size Determination
Condence intervals via hypothesis tests
In a o
Population models
The t-test
Two sample tests
Checking assumptions
III. Inference Based on Population Models
Mathias Drton
Dept. of Statistics
University of Washington
1 / 42
Population models
The t-test
Two sample tests
Checking assumptions
Motivation
In