STAT3010: Lecture 14
Logistic Regression Analysis (Section 10.4, Page 487)
In logistic regression analysis, we consider applications involving a single
dependent variable, Y, which is dichotomous (ie., Success versus Failure.) We
will be discussing this f
STAT3010: Lecture 3
REVIEW OF HPYOTHESIS TESTS-CONTD
Two Independent Populations (not equal variances)
Example: An experiment was conducted involving the comparison of the
mean heart rates following 30 minutes of aerobic exercise in females
aged 20 to 24
STAT3010: Lecture 4
CHAPTER 9: ANALYSIS OF VARIANCE
Analysis of Variance (ANOVA) is one of the most widely used
statistical techniques for testing the equality of population
means. ANOVA is used to test the equality of more than two
treatment means.
Recal
STAT3010: Lecture 5
Notation and Examples (Section 9.2, Page 413)
To make a decision of reject/do not reject the null hypothesis,
we simplify the test by the use of the ANOVA table. Here are
the formulas which make up the ANOVA table:
Analysis of Variance
STAT3010: Lecture 6
Multiple Comparisons Procedures- Contd (Section 9.5,
Page 425)
Recall: Last class we looked at the Scheffe Multiple
Comparison Procedure. These calculations take some time
(especially when you have a lot more than 3 treatments!), and a
STAT3010: Lecture 7
Repeated Measures Analysis of Variance (Section 9.6,
Page 436)
Repeated Measurements are measurements made on your
subjects over a particular time. The purpose of these repeated
measurements is to assess changes in the measurements of
STAT3010: Lecture 8
TWO-WAY ANALYSIS OF VARIANCE
(Your text book doesnt cover 2-way ANOVA so youll have to
use my lecture notes. )
In chapter 9, we used analysis of variance to decide whether
three or more populations have the same mean. Those were
called
Homework Solutions to week 4
Page 454-461:
15.
Repeated Measures ANOVA
H0: 1 = 2 = 3
H1: at least 2 means differ.
Source
= 0.05
SS
Df
MS
3149.1
4
787.3
1.2
2
0.6
Within
248.1
8
31.0
Total
3398.4
14
Between Subjects
Between
Treatments
F
0.02
Reject H0 if
STAT3010: Lecture 9
TWO-WAY ANALYSIS OF VARIANCE
Recall: Last class we set up the complete Two-Way ANOVA
table for the Poplar Tree example:
ANOVA TABLE:
Source of
Variation
df
Sum of
Squares
Mean
Square
F
Treatments
3
7.547
2.51566
7.5049
Site
1
0.27225
0
Solutions to example 1:
2-WAY, EQUAL NS, INDEPENDENT SAMPLES ANOVA
Plot of behavior*dosage. Symbol is value of therapy.
behavior
27
G
26
P
n
B
25
P
24
B
G
23
n
P
22
B
21
G
20 n
absent
low
high
dosage
2-WAY, EQUAL NS, INDEPENDENT SAMPLES ANOVA
The
STAT3010: Lecture 10
TWO-WAY ANALYSIS OF VARIANCE
Recall: Last lecture, we looked at the Two-way ANOVA based
on equal sample sizes in each cell, but what if we had unequal
sample sizes?
Two-way ANOVA with unequal cell numbers "Unbalanced
designs"
Much mor
STAT3010: Lecture 2
Lecture 2:
REVIEW OF DISTRIBUTIONS CONTD
DISCRETE DISTRIBUTIONS:
THE BINOMIAL DISTRIBUTION
Definition
A population or process distribution for a discrete variable
mass function
p (x)
and
p(x) = 1 ;
where the summation is over all poss
Lecture 1:
REVIEW OF DISTRIBUTIONS
Continuous Distributions:
Definitions
A density function f (x) is used to describe (at least
approximately) the population or process distribution of a
continuous variable x . The graph of f (x) is called the density
cur
STAT3010: Lecture 13
Multiple Regression Analysis (Section 10.3, Page 485)
In multiple regression analysis, we consider applications involving a single
continuous dependent variable, such as systolic blood pressure (Y), and multiple
independent variables,
STAT3010: Lecture 12
CORRELATION AND REGRESSION
Simple Linear Regression Contd (Section 10.2, Page 477)
The least squares estimates:
These estimates are called the least squares estimates of the slope and
intercept. The estimate of the simple linear regre
STAT3010: Lecture 15
LOGISTIC REGRESSION ANALYSIS
Multiple Logistic Regression (Section 11.3, Page 517)
The simple logistic model is based on a linear relationship between the natural
logarithm (ln) of the odds of an event and a continuous independent var
STAT3010: Lecture 17 and 18
CHAPTER 12: NONPARAMETRIC TESTS
Recall in STAT2010 and Chapter 9, we presented techniques for tests of
hypothesis concerning one, two, or more than 2 population means. Remember,
when we use these types of tests, we had two assu
STAT3010: Lecture 10
TWO-WAY ANALYSIS OF VARIANCE
Two-way ANOVA with unequal cell numbers "Unbalanced designs"
Much more common than equal cell numbers because o in observational
studies you often can't control the number of observations falling into par
STAT3010: Lecture 7
Repeated Measures Analysis of Variance (Section 9.6, Page 436)
Repeated Measurements are measurements made on your subjects over a
particular time. The purpose of these repeated measurements is to assess
changes in the measurements of
STAT3010: Lecture 8/9
TWO-WAY ANALYSIS OF VARIANCE
In chapter 9, we used analysis of variance to decide whether three or more
populations have the same mean. Those were called one-way ANOVAs (or
single-factor ANOVA) because the data are categorized into g
Final Lectures
CHAPTER 12: NONPARAMETRIC TESTS
The Kruskal-Wallis Test - k Independent Samples Test Contd (Section
12.4, Page 558)
Post Hoc (Multiple Comparison Procedures)
Post Hoc comparisons for the Kruskal-Wallis Test are done if andonly if o H was
re
STAT3010: Lecture 2
Lecture 2:
REVIEW OF DISTRIBUTIONS CONTD
DISCRETE DISTRIBUTIONS:
THE BINOMIAL DISTRIBUTION
Definition
A population or process distribution for a discrete variable x is specified by a
mass function p(x) satisfying
p(x) 0 and p(x) = 1;
w
STAT3010: Lecture 3
REVIEW OF HPYOTHESIS TESTS-CONTD
Two Independent Populations (not equal variances)
Two Dependent Populations (paired data)
relevant formulas:
Categorical Data - Chi-Square Tests
relevant formulas:
NOTE: The Chi Square distribution is a
Lecture 1: STAT 3010U
REVIEW OF DISTRIBUTIONS
Continuous Distributions:
Definitions
A density function f (x) is used to describe
(approximately) the process distribution of a continuous variable x . The graph of
f (x) is called the density curve. The foll
STAT3010: Lecture 6
The Tukey Procedure
The Tukey procedure is also called the Studentized Range test.
The Tukey procedure is appropriate for pairwise comparisons, but it doesnt
handle general contrasts. However, this procedure has better statistical powe
STAT3010: Lecture 5
Fixed Versus Random Effects Models (Section 9.3, Page
424)
Theres two types of analysis of variance applications: fixed effects models and
random effects models.
Note: We will only be using fixed effects models in the upcoming sections
Class Activity 1
Rules: Name the test as either a Z-test, t-test, chi square test, oneway ANOVA, repeated measures or two-way ANOVA;
If the test is either a Z or t-test, state whether its a single mean,
paired, independent or pooled means.
If the test is