CURVILINEAR MODEL
When a LS line does not explain all
the variation in the means, the next
logical step is to consider a quadratic
(second-degree) SL polynomial
The terms in the deterministic component equation
represent:
Y = dependent or response variabl

EXPERIMENTAL
DESIGNS:
THE FACTORIAL EXPERIMENT
(Two-way ANOVA)
Factorial Experiment
A factorial Experiment is an experiment in which
the effect of two factors (and their interaction) on
the response is investigated.
Data collection (2x2 table):
Factor B

MULTIPLE
LINEAR
REGRESSION
MULTIPLE REGRESSION
In multiple regression there is one
response and more than one predictor.
Predictors can be continuous or
categorical
Whenever there is a categorical
variable, indicators (or dummy
variables) have to be creat

Fixed, random, and
Mixed Models
Each term in a statistical model represents either a fixed effect or a random
effect.
Models in which all effects are fixed are called fixed-effects models.
Similarly, models in which all effects are randomapart from possib

Factorial (fixed, random, mixed)
and Nested
Factor a variable of interest
e.g. temperature
Level a particular value / state of a factor
e.g. hot, cold
In this example, temperature is a factor with two levels.
Fixed factor
Either
(1) The investigator choos

EXPERIMENTAL
DESIGNS:
Completely
Randomized
Design
(One-way ANOVA)
ANALYSIS OF VARIANCE
A Designed Experiment is one for which the
analyst controls the specification of the treatment
and the method of assigning the experimental
units to each treatment.
El

The Problem of
Multicollinearit
y
in Regression
Introduction
In regression models, a regression
coefficient measure the effect of an
individual predictor on the response
when all the other variables in the
model are held fixed.
Y = 1X1 + 2X2 +.+ LXL +

LATIN SQUARE DESIGN
A Latin square is a table filled with N different
symbols in such a way that each symbol occurs
exactly once in each row and exactly once in
each column.
If each entry of a Latin square is written as a triple (r,c,s), where
R is the r

Binary Logistic Regression
Odds Ratio (OR)
OR is a measure of association indicating magnitude and
direction.
Commonly used in epidemiology
Ranges from zero to infinity
Approximates how much more likely (or unlikely) it is for the
outcome to be presen

EXPERIMENTAL DESIGNS:
THE RANDOMIZED BLOCK
DESIGN
(Two-way ANOVA)
Randomized Block Design
The RBD utilizes experimental units that are matched
sets, assigning one from each set to each treatment.
The matched sets of experimental units are called
blocks. T

Design & Analysis of Split-Plot
Experiments (Univariate Analysis)
Split-Plot Designs
With a 23 full factorial design most would choose to run
the 8 treatment combinations in a completely
randomized order.
Unfortunately, limitations involving time, cost,

MAKING INFERENCE:
CONFIDENCE INTERVALS AND
TESTS OF HYPOTHESIS
STATISTICAL INFERENCE
Statistical inference means drawing
conclusions about the population
parameters based on sample data. Two
ways of making inference are:
Confidence intervals
Test of hyp