Applied Statistical Methods for Physiology and Kinesiology
STAT 890

Spring 2014
Assignment 6 Key
Here's a table of means useful for parts A and C  G
Glue
1
2
3
All
Pine 364.25 378.75 453.25 398.75
Fir 367.00 330.75 386.75 361.50
All 365.62 354.75 420.00 380.12
A. The following graph indicates interaction. The difference between pine
Applied Statistical Methods for Physiology and Kinesiology
STAT 890

Spring 2014
STAT 890: Assignment 3 Instructions: In this assignment I want you to introduce to the tools of characteristic functions. 1. Prove that in any separable metric space if Xn X in probability or almost surely then Xn X 2. Show that Fatous lemma implies the D
Applied Statistical Methods for Physiology and Kinesiology
STAT 890

Spring 2014
Metric Spaces Definition: A metric space is an ordered pair (S, d) where S is a set and d a function on S S with the properties of a metric, namely:
1. d(x, y) = d(y, x) 0.
2. d(x, y) = 0 iff x = y.
3. The triangle inequality holds: d(x, z) d(x, y) + d(y,
Applied Statistical Methods for Physiology and Kinesiology
STAT 890

Spring 2014
STAT 890: Assignment 2 Instructions: In this assignment I want you to introduce to the tools of characteristic functions. You will need some tools which you can use without proof; others I will give hints to help you develop them. Suppose that Xn , n = 1,
Applied Statistical Methods for Physiology and Kinesiology
STAT 890

Spring 2014
Probability Definitions Probability Space : ordered triple (, F , P ).
is a set (possible outcomes); elements are called elementary outcomes.
F is a family of subsets (events) of with the property that F is a field (or algebra): 1. Empty set and are m
Applied Statistical Methods for Physiology and Kinesiology
STAT 890

Spring 2014
Convergence in Distribution Undergraduate version of central limit theorem: if X1, . . . , Xn are iid from a population with mean and standard deviation then n1/2(X )/ has approximately a normal distribution. Also Binomial(n, p) random variable has approx
Applied Statistical Methods for Physiology and Kinesiology
STAT 890

Spring 2014
Another example: estimating equations. Suppose Y1, . . . , Yn independent and x1, . . . , xn constants. Given: a function g(y, x, ) such that E [g(Yi, xi, o)] = 0 for all i and some particular o. Includes linear and generalized linear model problems. Dene