Experimental Design.ppt
Transcript of Experimental Design.ppt
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Experimental Designs
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An experimentis a test or a series of tests
Experiments are used widely in theengineering world
Process characterization & optimization Evaluation of material properties
Product design & development
Component & system tolerance determination
All experiments are designedexperiments, some are poorly designed,some are well-designed
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Reduce timetodesign/develop newproducts & processes
Improve performanceofexisting processes
Improve reliabilityandperformance of products
Achieve product &process robustness
Evaluationof materials,design alternatives,
settingcomponent &system tolerances, etc.
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Basic Principles of Experimental
Designs. The Principle of Replication
The Principle of Randomization &
The Principle of Local Control
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The Principle of Replication.
According to the Princ iple of
Repl icat ion, the experiment should
be repeated more than once.Bydoing so the statistical accuracy of
the experiment is increased.
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The Principle of Randomization.
The Princ iple of Random izationprovidesprotection, when we conduct anexperiment, against the effects ofextraneous factors by randomization.
We should design or plan the experimentin such a way that the variations causedby extraneous factors can all be combinedunder the general heading of chance.
Through the application of the Principle ofrandomization, we can have a betterestimate of the experimental error.
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The Principle of Local Control.
The extraneous factor, the known
source of variability is made to vary
deliberately and this needs to bedone in such a way that the
variability it causes can be measured
and hence eliminated from theexperimental error.
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The Principle of Local Control.
We divide the field into severalhomogeneous parts, known as blocks,and then each such block is divided intoparts equal to the number of treatments.Then the treatments are randomlyassigned to these parts of a block.
Through the principle of local control wecan eliminate the variability due toextraneous factor(s) from the experimentalerror.
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Important Experimental Designs
Two group simple randomized design
Randomize Block design
Factorial design
Hybrid Design
Covariance
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Two- group simple randomized
design: The population is defined and then from
the population a sample is selected
randomly After being selected randomly from the
population, be randomly assigned to the
experimental and control groups
Thus, this design yields two groups as
representatives of the population
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Two- group simple randomized
design: The two groups (experimental and control
groups) of such a design are givendifferent treatments of the independentvariable.
Advantage:-It is simple and randomizesthe differences among the sample items.
Disadvantage: -The individual differencesamong those conducting the treatmentsare not eliminated. It doesnt control theextraneous variable and as such the resultof the experiment may not depict thecorrect picture.
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3.2 Randomized Block design
(R.B. design) In the RB. design, subjects are first
divided into groups, known as blocks,
such that within each group the subjectsare relatively homogeneous in respect to
some selected variable .
The variable selected for grouping the
subjects is one that is believed to berelated to the measures to be obtained in
respect of the dependent variable
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3.2 Cont.
The variable selected for grouping the
subjects is one that is believed to be
related to the measures to be obtained inrespect of the dependent variable.
The number of subjects in a given block
would be equal to the number of
treatments and one subject in each blockwould be randomly assigned to each
treatment .
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3.2 Cont.
The R.B. design is analyzed by the two-
way analysis of variance (two-way' ANOV
A)" technique. Example ; Suppose four different forms of
a standardized test in statistics were given
to each of five students (selected one from
each of the five I.Q. blocks) and followingare the scores which they obtained.
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Very
lowI.Q.
Low
I.Q.
Averag
eI.Q.
High
I.Q.
Very
highI.Q
Student
A
Student
B
Student
C
Student
D
Student
E
Form 1 82 67 57 71 73
Form 2 90 68 54 70 81
Form 3 86 73 51 69 84
Form 4 93 77 60 65 71
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Example Cont.
If each student separately randomized theorder in which he or she took the fourtests (by using-random numbers or some
similar device), we refer to the design ofthis experiment as a R.B. design .
The purpose of this randomization is totake care of such possible extraneous
factors (say as fatigue) or perhaps theexperience gained from repeatedly takingthe test.
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3.3 Factorial designs
Factorial designs are used in experimentswhere the effects of varying more thanone factor are to be determined.
They are specially important in severaleconomic and social phenomena whereusually a large number of factors affect a
particular problem
Factorial designs can be of two types; (I)simple factorial designs and (2) complex
factorial designs.
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(i) Simple factorial designs:
we consider the effects of varying
two factors on the dependent
variable. Simple factorial design may either be
a 2x2 simple factorial design, or it
may be, say, 3 x 4 or 5x3 or the liketype of simple factorial design
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2 x 2 SIMPLE FACTORIAL
DESIGN
Experimental Variable
Treatment A Treatment BControl variable
Level I
Level II
Cell 1 Cell 3Cell 2 Cell 4
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STUDY I DATA
Training Row
mean
Treatment
A
Treatment
B
Control
(Intelligence)
Level I (Low) 15.5 23.3 19.4
Level II (High) 35.8 30.2 33.0
Column mean 25.6 26.7
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STUDY II DATA
Training Row
mean
Treatment
A
Treatment
B
Control
(Intelligence)
Level I (Low) 10.4 20.6 15.5
Level II (High) 30.6 40.4 35.5
Column mean 20.5 30.5
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study I
A
B
0
10
20
30
40
50
60
low(I) High(II)
Control level(intelligence)
Meansco
resof
d
ependentv
ariables
(Sayability)
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study I I
A
B
0
10
20
30
40
50
60
low(I) High(II)
Control level(inte lligence)
Meansco
resof
d
ependentvariables
(Sayab
ility)
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The graph relating to Study I indicates that
there is an interaction between the
treatment and the level, means that thetreatment and the level are not
independent of each other.
The graph relating to Study II shows that
there is no interaction effect which meansthat treatment and level in this study are
relatively independent of each other.
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4x3 Simple factorial designs
This will usually include four
treatments of the experimental
variable and three levels of controlvariable.
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4x3 SIMPLE FACTORIAL
DESIGNControl Variable Experimental Variable
Treatment
A
Treatment
B
Treatment
C
Treatment
D
Level I Cell 1 Cell 4 Cell 7 Cell 10
Level II Cell 2 Cell 5 Cell 8 Cell 11
Level III Cell3 Cell6 Cell 9 Cell 12
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Complex factorial designs
Experiments with more than two
factors at a time
A design which considers three ormore independent variables
simultaneously
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Experimental Variable
Treatment A Treatment B
ControlVariable 2
Level I
ControlVariable 2
Level II
ControlVariable 2
Level I
ControlVariable 2
Level II
Level Icontrol
variable1 Level II
Cell 1 Cell3 Cell5 Cell 7
Cell 2 Cell4 Cell 6 Cell 8
2x2x2 Complex factorial design
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Merit of factorial Design
(i) Provide equivalent accuracy with
less labour and as such a source of
economy(ii) Permits various other comparison
of interest which cant be obtained
by treating one single factor at atime.
3 4 Hybrid experimental designs
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3.4. Hybrid experimental designs
Just what the name implies, it consists of new
strains that are formed by combining featuresof more established designs.
They are basically design to or constructed toaddress specific threats to internal validity.
Basically there are of two types (i) SolomonFour Group Design and (ii) Switching
Replications Design
(i) The Solomon Four Group Design
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(i) The Solomon Four Group Design
It is designed to deal with a potential testing
threat (Testing threat occurs when the act oftaking a test affects how people scores on a
pretest or protest)
Usually has four groups, two of the groups
receive the treatment and two do not, further,
two of the groups receive a pretest and two donot ( a hybrid of 2x2 factorial design)
(i) The Solomon Four Group Design
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(i) The Solomon Four Group Design
It is designed to deal with a potential testing
threat (Testing threat occurs when the act oftaking a test affects how people scores on a
pretest or protest)
Usually has four groups, two of the groups
receive the treatment and two do not, further,
two of the groups receive a pretest and two donot ( a hybrid of 2x2 factorial design)
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(The Solomon Four Group Design Contd----)
Within each treatment condition we have a group
that is pretested and one that is not.
By explicitly including test as a factor in the
design, we are able to assess experimentallyweather a testing threat is operating.
P ibl O t
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Possible Outcomes:
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The graph shows the connection between
the preset and posttest average for the same
group and a line is used to connect the dotsThe two dots that are not connected by a line
represent the two post only groups.
On the posttest both treatment groups
outscore both controls
But when we look at posttest values thereappears to be no difference between the
treatment groups, even though one got a
pretest and the other did not.
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(Treatment effect-no testing effect contd-------)
Similarly, the two control groups scored about
the same on the posttest. Thus the pretest didnot appear to affect the outcome. There is a
main effect for the treatment.
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each treatment group outscored its comparable control
group
In graph (ii) there evidence of a testing threat.
This result indicates that there is a treatment effect.
(Treatment effect and testing effect contd---)
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(Treatment effect and testing effect contd---)
But here both groups that had the pretest
outscored their comparable non-pretest group.That is evidence for a testing threat.
(ii) Switching Replication Design
Is one of the strongest of the experimental
designs. And when the circumstances are
right for this design, it addresses one of major
problems in experimental designs i.e. the
need to deny the program to some
participants through random assignment
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(Switching replication design contd-----)
It can be thought of this as two pre-post
treatment-control designs grafted together. Thatis, the implementation of the treatment is
repeated or replicated
And in the repetition of the treatment, the two
groups switch roles i.e. the original group
becomes the treatment group in phase 2 while
the original treatment acts as a control. By theend of the study all participants have received the
treatment.
(Switching replication design contd-----)
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(Switching replication design contd )
The switching replication design is most feasible
in organizational contexts where programs are
repeated at regular intervals. For instance it
works especially well in schools that are in
semester system. All students are pre-tested at
the beginning of the school year.
During the first semester, Group 1 receives the
treatment and during the second semester
Group2 gets it.
(Switching replication design contd-----)
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The designs also enhance organizational
efficiency in resources allocation. Schools only
needed to allocate enough resources to give theprogram to half of the students at a time.
Possible Outcomes.
(i) Short-term persistent treatment effect
When the program is given to the first group, the
recipients do better than the controls. In the secondphase, when the program is given to the original
controls, they "catch up" to the original program group.
Thus, we have a converge, diverge, reconverge
outcome pattern.
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(Switching replication design contd-----)
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(ii) Long- term continuing treatment effect
But now, during phase two, the original program
group continues to increase even though the
program is no longer being given them. Why would
this happen? It could happen in circumstances
where the program has continuing and longer termeffects. For instance, if the program focused on
learning skills, students might continue to improve
even after the formal program period because they
continue to apply the skills and improve in them.
Merit of Hybrid designs
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Merit of Hybrid designs
Both the Solomon Four-Group and the Switching
Replications designs addressed specific threats
to internal validity.
Remember that in randomized experiments,
especially when the groups are aware of eachother, there is the potential for socialthreats i.e.
compensatory rivalry, compensatory equalization
and resentful demoralization are all likely to be
present in educational contexts where programs
are given to some students and not to others.
(Merit of Hybrid designs contd----)
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( y g )
The switching replications design helps mitigate
these threats because it assures that everyone
will eventually get the program. And, it allocates
who gets the program first in the fairest possible
manner, through the lottery of random
assignment.
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3.5. Covariance Designs
Also referred as Noise Reduction
The pre-program measure or pretest is
sometimes also called a "covariate"because of the way it's used in the data
analysis -- we "covary" it with the outcome
variable or posttest in order to remove
variability or noise. Covariates are the variables you "adjust
for" in your study.
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Procedures: The data are collected under a completely
randomized design
Plot Y vs X for each group separately to see ifthere are any points that dontappear to followthe straight line.
The relationship between Y and X must be linearfor each group. Check this assumption bylooking at the individual plots of Y vs X for eachgroup.
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The variance must be equal for both groups
around their respective regression lines.
Check that the spread of the points is equalaround the range of X and that the spread is
comparable between the two groups.
Plot Y vs X for each group separately to see if
there are any points that dontappear to follow
the straight line.
The residuals must be normally distributed
around the regression line for each group.
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Check the regression lines for the
groups are parallel
If there is evidence that the individual
regression lines are not parallel, then aseparate regression line must be fit for
each group for prediction purposes.
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If there is no evidence of non-parallelism,
then the next task is to see if the lines
are co-incident, i.e. have both the sameintercept and the same slope.
If there is evidence that the lines are notcoincident, then a series of parallel lines
are fit to the data.
All of the data are used to estimate the
common slope.
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If there is no evidence that the lines are
not coincident, then all of the data can be
simply pooled together and a singleregression line fit for all of the data.
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