Y603
Lectures Online
Lecture
#5
1. Review Questions/concepts on
One-way ANOVA
What is the null
hypothesis under testing within the one-way ANOVA
framework?
What is an effect?
State the general linear
model used to analyze the treatment effect of an ANOVA
design.
Fixed-effects versus
random-effects models underlying one-way
ANOVA.
Identify 4 assumptions
necessary for imposing the general linear model on
data.
How to derive the F statistic
used for testing 
in ANOVA.
What are the degrees of
freedom associated with the F ratio stated
above?
Can complete a typical ANOVA
summary table and determine if an obtained F value is
significant at a particular alpha level.
Distinguish the difference
between a predesignated alpha level and p-level which
is reported in almost all published manuscripts (also
read Chapter 1 in Huck, Cormier, and Bounds and
the article titled "Mind your pís and alphas"
by William Stallings.)
Exploratory data analysis
(alas, data preprocessing)--checking assumptions,
looking for outliers, and deciding if there is a need
to conduct the overall (or omnibus)
F-test.
2. Explorary data analyses on
data on p. 167 of Kirk:
3. Tukey and Scheffe Post-Hoc
(A Posteriori) Comparison procedures
Tukey Procedure:
All-pair (or all pairwise) comparison
procedures.
Controls the type I
error rate at the same level as the overall
F-test.
Requires that all sample
sizes be equal.
Declares a pair-wise
comparison to be signifcant if it exceeds
HSD
,
q-values are found in Table
E.6
(p.
808-809)
Harmonic average of
nís is needed if sample sizes are not
equal.
For example, if n=4,5,6 in
a 3-group one-way ANOVA, then the
harmonic
average of 4,5,6 equals
Scheffe
Procedure: Suitable for pair-wise as well as
complex comparisons (or contrasts).
Does not require
equal sample sizes.
Controls the type I error
rate at the same level as the overall
F-test.
It is the only authentic
post-hoc comparison procedure following the sig.
F-test
Declares a contrast to be
significant if it exceeds the critical
difference:
MSD=
This procedure is too
conservative to be of any good
use.
4. Omega
squared
Indicates the strength
of association between the qualitative or quantitative
independent variable and a quantitative dependent
variable.
It also expresses the percent
or proportion of the population variance in the
dependent variable that is accounted for by specifying
the treatment-level classification.
The SAS printout gives you a
quantity which is a biased estimate of the Omega
squared in the population; it is called R
squared and equals SS between/ SS
total.
Three references may be used
in interpreting omega squared:
(a) the absolute using the
range from 0.00 to 1.00 or by Cohenís guideline
(p. 178),
(b) the relative based on
meta analysis of similar studies, or
(c) the relative based on
frequency distribution of omegaís compiled from
published studies of the same journal in the past 5
years (for example).
5. Assignments:
(1) Review Sections
4.5-4.6, 5.4-5.5 in Kirk
(2) Do questions parts (a),
(b), and (j) of questions 2, 3, 4 at the end of
Chapter 5 in Kirk.
For questions 5, 7, and 8 in
Chapter 5, perform an exploratory data analysis, an
overall ANOVA test, omega squared calculation, the
Scheffe, and the Tukey post-hoc analyses.
(3) Read the article titled
Mind Your pís and Alphas by William M.
Stallings.
(4) Preview Sections 4.1-4.2
in Kirk.
