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Design Supplemental

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Design Supplemental
Design
• Completely randomized
• Randomized block design
– Latin-Squares
– Greco-Latin Squares
• Repeated measures
– Pre & post-test designs
• Mixed designs (Between subjects factors and
repeated measures)
– Split-plot
• Random effects models
Completely randomized
• The typical situation with only between-subjects
factors (IVs)
• Participants are randomly assigned to treatment
groups
• Don’t trust yourself to do this, peeps is bad at
randomizing
• Example in R
– x=c(1,2,3,4)
– y=c(.25,.25,.25,.25)
пѓџ groups 1-4
пѓџ long run probability of
occurrence
– sample(x, 80, replace=TRUE, prob = y)
Randomized block design
• Suppose an effect is present that may influence results, but for
which you may not be interested in
– Nuisance variable
• We can extend the randomization process to control for a variety of
factors
• Randomized Block Design
– An extension of the completely randomized design in which a single
extraneous variable that might affect test units’ response to the
treatment has been identified and the effects of this variable are isolated
by blocking out its effects.
• Examples:
– Researchers collecting the data
• Probably a relationship between who is collecting and outcome
– Experimenter/participant expectations
– Age
• Create blocks of similarly aged individuals
Randomized block design
• In such a situation we want to randomly
assign to treatment groups within each
blocking level
• Example:
Treatment A
– Experimenter 1: condition 1 condition 2 condition 3
– Experimenter 2: condition 1 condition 2 condition 3
– Experimenter 3: condition 1 condition 2 condition 3
Randomized Block Design
Independent Variables
Blocking variable
Control:
no music
Mornings and
afternoons
Evening hours
Experimental
treatment
slow music
Experimental
treatment:
fast music
Randomized block design
• Partitioning the sums
of squares
• F-statistic is now
MSb/t/MSresidual
• This will be a more
powerful test,
although less so as
SSresdiual approaches
SSw/in
– i.e. less effect due to
blocking variable
SStotal
SSb/t
SSw/in
SSresidual
SSblocks
Randomized block design
• Conditions:
– Correlation between blocking variable and DV
– Treatment and blocking levels > 2
– Random assignment within each blocking unit
• Goal is to see homogeneous groups w/in each blocking level and
treatment levels will look similarly with respect to one another
• Methods of implementation
– Subject matching (age example)
– Repeated measures (everyone gets all conditions, subjects
serve as their own block)
– Other matched pair random assignment (e.g. twins, husbandwife)
• Latin-squares and Graeco-Latin squares extend the blocking to 2
and 3 nuisance variables respectively
– Consult Winer or Kirk texts
Latin Square Design
• A balanced, two-way classification scheme that attempts
to control or block out the effect of two or more
extraneous factors by restricting randomization with
respect to the row and column effects
– Randomly assign treatment levels according to levels of the
nuisance variable such that each level of the treatment variable
is assigned to the levels of the nuisance variables
• Can help with sequence effects with RM variables
• This special sort of balancing means that the systematic
variation between rows, or similarity between columns,
does not affect the comparison of treatments.
Latin Square
• Example controlling for previous therapy experience and
therapist (A is the treatment, e.g. type of therapy)
Therapist
Previous therapy (none, yes
but no drugs, yes w/ drugs)
1
2
3
1
A1
A2
A3
2
A2
A3
A1
3
A3
A1
A2
Example: 3 groups receive Therapy A1
Group1- therapist1, no previous
Group2- therapist2, drugs
Group3- therapist3, no drugs
• LS design has limited utility in behavioral sciences
– Not too many cases with factors all with the same number of
levels
– Kirk has suggested that with less than 5 levels it’s not very
practical due to few degrees of freedom for error term (except for
when several levels of treatment are assigned to each cell e.g. in
a mixed design situation)
• Nevertheless, we see we have various ways to control
for a number of effects that might be present in our data
but not of interest to the study
Repeated measures design
• Subjects participate in multiple levels of a
factor
• Simplest is the paired t-test situation,
however �repeated measures design’ often
implies 3 or more applications of some
treatment
• Example: pre and post-test
Mixed design
• Between subjects factors with repeated
measures
• Simple but common example is controltreatment, pre-post
• Subjects are randomly assigned to control
or treatment groups and tested twice
Pre
Control
Treatment
Post
Mixed design
• This example may appear a straightforward method for
dealing with data
• However we could analyze it in two additional ways
• ANCOVA
– Test for differences at time 2 controlling (adjusting) for
differences seen at time 1
• A simple t-test on the gain scores from pre to post
– Same result as mixed but w/ different (simpler) output
• One method may speak more to the exact nature of your
research question (e.g. only interested in time 2 or the
rate of improvement from time 1 to 2)
Mixed design
• Consider also the possibility of an effect in posttest scores (or effect
of treatment) due solely to exposure to the pretest
– E.g. with no prior training GRE scores would naturally be
assumed to increase the second time around more often than
not
• Solomon four-group design
• Split-plot factorial controls for a nuisance variable in mixed designs
• We’ll take a more in depth look at repeated measures and mixed
designs later
Random effects models
• In most ANOVA design we are dealing with fixed effects
• Random effects
– If the levels included in our analysis represent a random
sample of all the possible levels, we have a random-effects
ANOVA.
• With fixed effects the same levels of the effect would be used
again if the experiment was repeated.
• With random effects different levels of the effect would be used.
• The conclusion of the random-effect ANOVA applies to all the
levels (not only those studied).
Random effects models
•
•
•
•
Questions to ask:
Were the individual levels of the factor selected
due to a particular interest, or were they
chosen completely at random?
Will the conclusions be specific to the chosen
levels, or will they be applied to a larger
population?
If the experiment were repeated, would the
same levels be studied again, or would new
levels be drawn from the larger population of
possible levels?
Random effects models
• Some examples:
• Persuasiveness of commercials
• Effect of worker on machine output
• Vehicle emissions impact on the
environment
Random effects models
• Determination of fixed vs. random effects affects
the nature of the tests involved, how the Fstatistic will be calculated (sometimes), and the
conclusions to be drawn
• Some designs will incorporate both fixed and
random effects
– Mixed effects designs
• Don’t confuse with previous mixed design
factorial discussed previously
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