Psych 407
Lecture 10
Two factor studies:
ANOVA models II and III
ANOVA Model II Random factor effects
This is a factorial design with two (or more) random effect factors
Model:
Yijk = .+i+j+()ij+i
Psych 407
Lecture 12
Analysis of covariance (ANCOVA)
A technique combining features of ANOVA and regression
Used to reduce error variability
This error variability can be attributed to a quantitati
Psych 407
Lecture 5
ANOVA diagnosis
and remedial measures
This is similar to the regression situation
There are three basic assumptions of ANOVA
Independence of error term (residuals)
Normal distr
Psych 407
Lecture 7
Two-factor studies
with equal sample sizes
Examples
The one-factor-at-a-time approach
Problems:
Only explore a selected set of conditions
Interactions cannot be estimated
Full r
Psych 407
Lecture 6
ANOVA Model II
Also called random effect models
Different treatments are considered as random samples from a wider
(possibly infinite) set of possible treatments
E.g., classes i
Psych 407
Lecture 3
Alternative formulations of model
Cell mean model
Yij=i+ij
Factor effect model
i = . + (i .)
i = i . ith factor level effect or ith treatment effect
Yij=.+ i +ij
Definition
Psych 407
Lecture 2
Single factor studies
Single-factor experimental and observational studies
Relation between regression and analysis of variance
(ANOVA)
Both are based on general linear models a
Psych 407
Lecture 11
Multi-factor studies
Factorial ANOVA may be easily generalized to more than
two factors
In addition to main effects, we have two-factor (first-order)
interactions, three-factor
Psych 407
Lecture 8
Two-factor studies:
One case per treatment
In some cases, with factorial studies it is difficult to obtain
more than one observation per treatment level
For example, when the obs
Psych 407
Lecture 9
Two-factor studies
with unequal sample sizes
The presence of unequal sample sizes destroys the orthogonality of the
ANOVA decomposition
SSTR SSA + SSB + SSAB
This because the ve
Psych 407
Lecture 13
Nested designs
Distinction between nested and crossed factor
Both involve two (or more) factors
Crossed factors:
the same treatment levels are used for all levels of the
other