ST305 / ST410 Assignment 2 28th February 2014
1. In an experiment to study the effect of salt on the boiling point of water the
treatment factor was the amount of salt added to 500 ml of water. There were five
levels 0, 8, 16, 24 and 32 grams of salt. The
ST305 / ST410 Assignment 1 30th January 2014
1.
(a) Give a simple description of a basic comparative experiment, stating what you
understand by the term experimental unit. Write a couple of sentences each on the
concepts of replication and randomisation.
ST305 / ST410 Assignment 1 30th January 2014
Answers
1.
(a) Give a simple description of a basic comparative experiment, stating what you
understand by the term experimental unit. Write a couple of sentences each on the
concepts of replication and randomi
DESIGNED EXPERIMENTS 2014
ST305 / ST410
Lecture 16: Regression and matrix algebra
One important aspect of experimental design, particularly in the industrial area, is to
determine the relationship between the value of a response (or dependent) variable,
a
DESIGNED EXPERIMENTS 2014
ST305 / ST410
Lecture 18: Confounding
Introduction
Its time to consider block structures with the factorial designs that we have recently
looked at. In agricultural experiments the empirical evidence is that trials start to lose
ST305 / ST410
Designed Experiments
Lecture 17: The 2n and 3n factorial
series
1
Binary (two levels) experiments are not infrequently used
where we want to test the impact of a standard method
against a new or alternative method for several factors
simulta
ST305 / ST410
Designed Experiments
Lecture 15: Regression
Models
A very important activity in science and industry is building
models of the process or product under investigation. Such
models can be very simple, such as that the response Y is
related to
ST305 / ST410
Designed Experiments
Lecture 18: Confounding
1
Confounding
Its time to consider block structures with factorial
designs.
In agricultural experiments the empirical evidence
is that trials start to lose their efficiency (i.e. the
blocks are no
ST305 / ST410
Designed Experiments
Lecture 16: Regression and Matrix
Algebra
Regression and matrix algebra
Suppose we have a single response variable which we will
denote by y, and that we have m explanatory variables x1, x2,
, xm. We can model the depend
DESIGNED EXPERIMENTS 2014
ST305 / ST410
Lectures 20: Response surfaces
Introduction
In experimental situations we frequently use quantitative factors, and rather than
simply estimating the means it is often far more important to develop an understanding o
DESIGNED EXPERIMENTS 2014
ST305 / ST410
Lecture 17: The 2n & 3n factorial series
Introduction
Factorial experiments in which each factor operates at two levels occupy a special
place in the theory of design. Binary experiments are not infrequently used in
ST305 / ST410
Designed Experiments
Lecture 14: Matrix approach to
analysis of variance
Model specification
The basic model that we have used
so far for most designs takes the
Yij =m +b i +t j +e ij
form
Y = X b +e
2
e ~ N (0, I )
In matrix notation we can
ST305 / ST410
Designed Experiments
Lecture 13: Random effects
Introduction
We have looked at models with only one
random term, the residual e ij or e ijk , depending
on the factor structure of the model. The only
exception was the split-plot model, where
DESIGNED EXPERIMENTS 2014
ST305 / ST410
Lecture 15 Regression
Simple Linear Regression
In general we consider a single dependent variable or response Y that depends on k
independent or regressor variables x1, x2, , xk. The relationship between these
varia
ST305 / ST410
Designed Experiments
Lecture 11: Factorial Experiments
Factorial experiments
Experiments where all levels of one treatment factor are
combined with all those of another are called factorial
experiments. Such experiments are not confined to t
DESIGNED EXPERIMENTS 2014
ST305 / ST410
Lecture 14: Matrix approach to analysis of variance
Introduction
The basic model that we have used so far for most designs takes the form
.
In matrix notation we can write this as
with
where is a vector of observati
ST305 / ST410 (2014)
Designed Experiments
Dr. John Fenlon
Dept. of Statistics
Lectures 2014 Term 2
Mondays 1500-1600
Thursdays 1400-1500
Fridays 1600-1700
B2.04/5
B2.04/5
S0. 19
Notes will be given out during lectures, and may
also be collected from the r
ST305 / ST410
Designed Experiments
Lecture 12: Split-plot designs
Split-plot designs
A split-plot experiment is a factorial experiment in which a
main effect is confounded with blocks. However, it is
assumed that there is sufficient replication to enable
DESIGNED EXPERIMENTS 2014
ST305 / ST410
Lecture 13: Random effects
Thus far we have looked at models with only one random term, the residual or ,
depending on the factor structure of the model. The only exception to this was the
split-plot model, where tw
DESIGNED EXPERIMENTS 2014
ST305 / ST410
Lecture 19: Fractional replication
Introduction
In looking at the factorial series experiments we have already considered the concept
of confounding, and the possibility of reducing the experiment size to a single
r
ST305 / ST410
Designed Experiments
Lecture 20: Response Surfaces
In many industrial situations experimenters use
quantitative factors, and rather than simply
estimating means they seek to develop an
understanding of how the response varies with the
factor
ST305 / ST410
Designed Experiments
Lecture 3: Basic Concepts of
Experimental Design
Types of study
Observational studies
Sample surveys
Designed experiments
Comparative experiments
Treatments applied at different times / places will
almost certainly produ
Project outline
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Proposal due to 1st of June, 2015, 9:00 a.m. via e-mail
Business description due to 5th of June, 2015, 9:00 a.m. via e-mail
market strategies due to 11th of June, 2015, 9:00 a.m. via e-mail
competitive analysis due
ST305 / ST410
Designed Experiments
Lecture 23: Optimal Design
- an informal approach
Example: Optimum allocation
A completely randomised design is to be used in an
experiment to compare three treatments. The three pairwise
contrasts are all of great inter