The power of the two-sample mean comparison is maximized when we maximize ET , where
ET = = =
x - y
2 2 x /nx + y /ny x - y nx + ny 2 2 x /px + y /py x - y nx + ny 2 2 x /px + y /(1 - px )
2 Suppose the raw effect size x - y , the total sample size nx + n
Statistics 403 Problem Set 1 Due in lab on Friday, September 17th 1. Suppose we have the following probability distribution: x 1 2 3 4 5 6 7 8 9 10 P (X = x) 0.19 0.09 0.07 0.15 0.21 0.03 0.01 0.03 0.12 0.10
(a) What is the probability that X is odd? Solu
Statistics 403 Problem Set 2 Due in lab on Friday, September 24th 1. We are given the following probability distribution, where p is an unspecified probability: x P (X = x) -1 0 0.3 p 1 0.7 - p
(a) Find the value of p that maximizes the variance of this d
Statistics 403 Problem Set 3 Due in lab on Friday, October 1st 1. Suppose we are interested in estimating a quantity , and we can obtain independent measurements Xi with EXi = . We intend to use X to estimate , and we wish to have the probability of the e
Statistics 403 Problem Set 4 Due in lab on Friday, October 8th 1. Suppose we are interested in comparing the support for a certain political candidate in Michigan to the support for the candidate in Ohio. We conduct independent surveys in both states, and
Statistics 403 Problem Set 5 Due in lab on Friday, October 15th 1. The following questions are about a population of people, some of whom are home owners, and some of whom are renters. (a) Suppose 65% of the population are home-owners, the home-owners hav
Statistics 403 Problem Set 6 Due in lab on Friday, October 29th 1. Three processes for collecting data X1 , . . . , X10 are described below. For each, deter mine the 15th , 50th , and 90th percentiles of the sampling distribution of X. (a) The data are co
Statistics 403 Problem Set 7 Due in lab on Friday, November 5th 1. Suppose we are planning to studying a treatment for depression. We will obtain baseline depression scores Xi , i = 1, . . . , 30 on a set of research subjects. Three months later, after th
Statistics 403 Problem Set 8 Due in lab on Friday, November 12th 1. Suppose X1 , . . . , Xn and Y1 , . . . , Yn are both iid samples, with EXi = EYi = 0, 2 2 var(Xi ) = X , var(Yi ) = Y , cor(Xi , Yi ) = r, and cor(Xi , Yj ) = 0 if i = j. (a) What is cov(
Statistics 403 Problem Set 9 Due in lab on Friday, November 19th 1. Suppose we are planning to collect paired data Xi , Yi with the goal of estimating EX - EY . We want to have 80% power to detect a raw effect size EX - EY = 1, and based on previous exper
Statistics 403 Problem Set 10 Due in lab on Friday, December 3rd 1. Suppose we are using stratification to estimate a treatment effect (i.e. we want to estimate EY T - EY U while controlling for the effect of a known confounder X). We use five strata, and
Statistics 403 Problem Set 11 Due in lab on Friday, December 10th 1. Suppose we are conducting a study to assess whether heavy drinking is associated with the development of pancreatic cancer. We identify 50 pancreatic cancer cases from a medical center a
Statistics 403 Practice Exam Questions for Exam 2 I have not included practice problems that are very similar to the homework problems, so you should study those too, along with the solutions to the first midterm. If you are asked for a probability that c
Practice exercises for exam 1 If you are asked for a probability that cannot be calculated by hand, you can express your answer either in terms of normal probabilities (e.g. P (Z < . . .), P (Z > . . .), or in terms of R commands (e.g. pnorm(.). 1. Suppos
Outline of topics from Statistics 403 1. Basic definitions [probability, event, sample space, random variable, "and" and "or" probabilities]: cumulative probabilities, probabilities of events (1-1, 1-2). 2. Expected value [a single-number summarizing a di
Research methods: background and review
Kerby Shedden
Department of Statistics, University of Michigan
April 7, 2011
1 / 167
Author(s): Kerby Shedden, Ph.D., 2010 License: Unless otherwise noted, this material is made available under the terms of the Crea
Author(s): Kerby Shedden, Ph.D., 2010 License: Unless otherwise noted, this material is made available under the terms of the Creative Commons Attribution Share Alike 3.0 License: http:/creativecommons.org/licenses/by-sa/3.0/
We have reviewed this materia
Election polls
For each race, we have one or more polls reported as X 2SE, or with a margin of error of ME." Typical ME's are 0.03-0.04. In "X our notation, ME = 2SE. The data underlying X are X1 , . . . , Xn , which are binary variables where Xi = 1 cor
Statistics 403 Exam 1
October 27, 2009 Instructions: You may not use notes, books, formula cards, etc. You may use a calculator, but only for arithmetic. If you are asked for a probability that cannot be calculated by hand, you can express your answer eit
Statistics 403 Midterm Exam October 26th, 2010 1. Answer the questions given below for the following probability distribution (your answers may depend on a and p): x -a P (X = x) p/2 0 1-p a p/2
(a) What is the expected value EX of this distribution? Solu
Statistics 403 Final Exam December 17, 2010 1. We are planning a study in which our goal will be to accurately estimate a treatment effect, expressed as the difference in mean responses between treated and untreated subjects. Our goal is to have the stand
Statistics 403 Exam 2
December 21, 2009 Instructions: You may not use notes, books, formula cards, etc. You may use a calculator, but only for arithmetic. If you are asked for a probability that cannot be calculated by hand, you can express your answer ei
Statistics 403 Exam 2
December 9, 2008 Instructions: You may not use calculators, notes, books, formula cards, etc. If you are asked for a probability that cannot be calculated by hand, you can express your answer either in terms of normal probabilities (
Author(s): Kerby Shedden, Ph.D., 2010 License: Unless otherwise noted, this material is made available under the terms of the Creative Commons Attribution Share Alike 3.0 License: http:/creativecommons.org/licenses/by-sa/3.0/
We have reviewed this materia
Author(s): Kerby Shedden, Ph.D., 2010 License: Unless otherwise noted, this material is made available under the terms of the Creative Commons Attribution Share Alike 3.0 License: http:/creativecommons.org/licenses/by-sa/3.0/
We have reviewed this materia