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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----)

    http://www.socialresearchmethods.net/kb/intsoc.htmhttp://www.socialresearchmethods.net/kb/intsoc.htm
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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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