STAT 5615: Statistics in Research I
Fall 2013
Mon, Wed. 4:00PM 5:15PM. Torgersen 2150.
Homework 1, due in class Wednesday 09/4/13
(Without approval, any homework submitted electronically or after Weds 09/4 class will NOT be
accepted)
Be sure to complete t
Stat 5615
Lecture 15 Examples
Example 1: (Taken from Neter et. al. (1996) A person's muscle mass is expected to decrease with age. To
explore this relationship in women, a nutritionist randomly selected four women from each 10-year age group,
beginning wi
STAT 5615: Statistics in Research I
Fall 2013
Mon, Wed. 4:00PM 5:15PM. Torgersen 2150.
Homework 3, due in class Wednesday 10/09/13
(Without approval, any homework submitted electronically or after 10/09 Weds
class will NOT be accepted.)
Problem 1:
A manuf
Stat 5615
Lecture 14 Example 3
Example 3 : Consider the following heights of fathers and sons (summary information is provided) and answer the
following questions, assuming that a scatter plot has revealed linearity:
i
Father
Son
1
69
68
2
67
61
1.
3
69
6
Stat 5615
Supplementary Regression Handout
The population regression equation for SLR is
or
and the sample regression equation is
where:
True mean response when the
explanatory variable has value
True unconditional mean of the
response,
True intercept
Tru
Stat 5615
Ott & Longnecker Chapter 11
11.1, 11.2, 11.7
Regression Models
One of the most prevalent ideas in statistics is the
idea of a statistical model.
Statistical Model: An approximation of how variables
relate to each other in a population.
Ex: ANOV
STAT 5615: Statistics in Research I
Fall 2013
Mon, Wed. 4:00PM 5:15PM. Torgersen 2150.
Homework 2, due in class Wednesday 09/11/13
(Without approval, any homework submitted electronically or after 09/11 Weds class will
NOT be accepted. Keep a copy of your
STAT 5615: Statistics in Research I
Fall 2013
Mon, Wed. 4:00PM 5:15PM.
Homework 4, due in class Monday 11/11/13
(Without approval, any homework submitted electronically or after 11/11 Mondays
class will NOT be accepted.)
Problem 1:
A student decides to in
Multiple Comparisons (MC)
Methods
Ott & Longnecker 9.3-9.8 (5th ed.)
1
MC Methods
Provide ways to preserve the statistical validity
of our inferences when more than one
inference is to be made on the same data.
The goal may be just to determine if all
t
Stat 5615
Recall: Population Regression Equation for
Mean Response
= 0 + 1
The main question of interest may be whether
or not X and Y are independent.
If they are independent, we expect 1 = 0, so
we would be interested in testing this
hypothesis.
Recal
STAT 5615 Statistics in Research (I) Introduction
Ott & Longnecker Chap 1; 2.1-2.4
1
What is statistics?
Wikipedia: STATISTICS is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data
Homework 3
STAT-5615 Fall 2016
The due date is Thursday, Oct 13th by 11:59pm. The assignment is to be submitted via
canvas in a .pdf file only. The uploaded file should be Lastname Firstname HW3.pdf
Late assignments will not be accepted. Solutions will be
Homework 4
STAT-5615 Fall 2016
The due date is Friday, Oct 28th by 11:59pm. The assignment is to be submitted via canvas
in a .pdf file only. The uploaded file should be Lastname Firstname HW4.pdf
Late assignments will not be accepted. Solutions will be p
STAT 5615
Statistics in Research (I)
Sampling Distribution
Ott & Longnecker 4.11-4.13
1
Random Sample
Previous probability models are all for unobservable
population
Definition: a sample of n measurements selected from a
population is said to be a rando
Motivation
Stat 5615
Fall 2011
Outline
Laboratory for Interdisciplinary Statistical
Analysis (LISA)
Four Steps in Learning from Data
The Challenger-Lack of Communication
Stochastic versus Deterministic
Laboratory for Interdisciplinary Statistical
Anal
Power and Sample Size
The power of a hypothesis test is the
probability that we detect a specified
difference in the means WHEN that difference
exists.
Power depends on
The significance level of the test,
The difference of interest, 1 2
The variance
1
In previous Lectures
Deriveded sampling
distributions for and
Developed confidence intervals
for and
Sample size calculations
Today
Hypothesis testing for
means and proportions
Connection between
hypothesis testing and
confidence intervals
2
Inferenti
STAT 5615
Statistics in Research (I)
Analysis of Variance (ANOVA)
Part 1
Ott & Longnecker Chapter 8
1
Motivation
Recall: Previously we have made inferences for
quantitative responses when the explanatory
variable was qualitative with two levels (twosampl
STAT 5615
Statistics in Research (I)
Contrasts
Ott & Longnecker 9.2
1
What comes Next?
Question:
Now that we have rejected 0 , what comes next?
Answer:
Need to explore the actual differences using
ANOVA follow-up analyses.
These analyses can be exten
STAT 5615
Statistics in Research (I)
Analysis of Variance (ANOVA)
Part 2
Ott & Longnecker Chapter 8
1
ANOVA Model
An additive-noise model for ANOVA is
yij = i + ij,
where the ij are mean-zero random errors and ij ~ Normal
(0, ).
Mean i: signal from the
STAT 5615
Statistics in Research (I)
Analysis of Variance (ANOVA)
Part 1
Ott & Longnecker Chapter 8
1
Motivation
Recall: Previously we have made inferences for
quantitative responses when the explanatory
variable was qualitative with two levels (twosampl
STAT 5615 Statistics in Research (I) Descriptive Graphs
Ott & Longnecker 3.3, 3.6
1
Descriptive Statistics
Objective: to summarize data Graphical Techniques - Pie charts - Bar charts - Histograms - Stem-and-Leaf plots - Time series plots - Boxplot
SAS is one of the most standard and comprehensive computer packages for statistical analysis. Two useful procedures for exploratory analysis are: PROC MEANS: calculates basic summary statistics PROC UNIVARIATE: calculates a wide array of summary st
STAT 5615 Statistics in Research (I) Discrete Random Variables
Ott & Longnecker 4.6-4.8, 10.5 (before tests using Poisson distribution)
1
Population Models
Population - an unobservable realization of sample space - outcomes not equally represented
STAT 5615 Statistics in Research (I) Probability
Ott & Longnecker 4.1-4.4
Probability
Example: A population of size N = 8 might consists of {1,0,0,2,1,1,1,2}, or equivalently, 3 distinct values 0, 1, 2 with respective frequencies 2, 4, 2. What are
Histogram The following program produces a histogram for the birth variable, distance from birth place, in the data set students:
title2 Histogram of Distance to Birth Place; proc univariate data=students noprint; histogram birth / cfill=red; run;
O
STAT 5615 Statistics in Research (I) Summary Statistics
Ott & Longnecker 3.4, 3.5
1
Summary Statistics Numerical Descriptive Measures Summary statistics provide quantitative descriptions of data. They form the basis for statistical inference. Th
Motivation
Stat 5615
Outline
Laboratory for Interdisciplinary Statistical
Analysis (LISA)
Four Steps in Learning from Data
The Challenger-Lack of Communication
Stochastic versus Deterministic
Four Steps in Learning from Data
1. Defining the problem.
2
STAT 5615
Statistics in Research
(I)
Introduction
Ott & Longnecker
5th Ed: Chap 1; 2.1-2.4
6th Ed: Chap 1; 2.1-2.5
1
What is statistics?
Wikipedia: STATISTICS is a mathematical science
pertaining to the collection, analysis, interpretation or
explanation,
STAT 5615
Statistics in Research (I)
Graphical Procedures&
Summary Statistics
Ott & Longnecker Chapter 3
Sections 3.3-3.6
Exploratory Data Analysis
(EDA)
EDA is a set of techniques used to explore and
summarize data via graphical and numerical
methods.