Transcript The Two-Group Randomized Experiment

The Two-Group Randomized
Experiment
The Basic Design
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Note that a pretest is not necessary in this design.
Why?
Because random assignment assures that we have
probabilistic equivalence between groups
The Basic Design
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Differences between groups on posttest indicate a
treatment effect.
Usually test this with a t-test or one-way ANOVA.
Why no pretest?
Internal Validity
History 
Maturation
Testing
Instrumentation
Mortality
Regression to the mean
Selection
Selection-history
Selection- maturation
Selection- testing
Selection- instrumentation
Selection- mortality
Selection- regression
Diffusion or imitation
Compensatory equalization
Compensatory rivalry
Resentful demoralization
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Examples
Experimental Design Variations
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The posttest-only two group design is
the simplest; there are many variations.
To better understand what the
variations try to achieve, we can use the
signal-to-noise metaphor.
Signal to Noise
What we observe can be divided into
what we see
Signal to Noise
What we observe can be divided into
Signal
what we see
Signal to Noise
What we observe can be divided into
Signal
Noise
what we see
Signal to Noise
Experimental designs can take two
approaches:
Signal to Noise
Experimental designs can take two
approaches:
Signal
Focus on (enhance)
the signal
Signal to Noise
Experimental designs can take two
approaches:
Signal
Focus on (enhance)
the signal (what is
this?)
Signal to Noise
Experimental designs can take two
approaches:
Signal to Noise
Experimental designs can take two
approaches:
or reduce the noise
Noise
(what is this?)
Signal to Noise
Experimental designs can take two
approaches:
or reduce the noise
Noise
Signal to Noise
Signal
enhancers
Noise
reducers
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Factorial designs
Covariance designs
Blocking designs
Noise and Signal in Significance Tests
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For interval and ratio dependent
variables, you can conduct a
difference in means test:
( X 2  X 1 )  2  ( std .error1 )  ( std .error 2 )
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Signal
std .error1 
ˆ1
N1
Noise
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Factorial Designs
A Simple Example
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Factor 1: Time in Instruction
Level 1:
1 hour per week
Level 2:
4 hours per week
Factor 2: Setting
Level 1:
In-class
Level 2:
Pull-out
A Simple Example
Setting
Time in Instruction
Factors:
Major independent variables
A Simple Example
Time in Instruction
In-class
Pull-out
Setting
1 hour/week
4 hours/week
Levels:
subdivisions
of factors
A Simple Example
Time in Instruction
factors
1 hour/week
4 hours/week
In-class
Group 1
average
Group 3
average
Pull-out
Setting
levels
Group 2
average
Group 4
average
Usually, averages are in the cells.
Multiplicative Notation
A 3 x 4 factorial design
How many factors?
How many levels?
How many cells with
averages?
Multiplicative Notation
A 3 x 4 factorial design
The number of numbers tells
you how many factors
there are.
There are 2 factors
because there are 2
numbers.
Multiplicative Notation
A 3 x 4 factorial design
The number values tell you
how many levels are in
each factor.
Multiplicative Notation
A 3 x 4 factorial design
The number values tell you
how many levels are in
each factor.
Factor 1 has 3 levels.
Factor 2 has 4 levels.
The Null Case
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The lines in the graphs
below overlap each
other.
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Setting
Time
A Main Effect
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A consistent difference between levels
of a factor
For instance, we would say there’s a
main effect for time if we find a
statistical difference between the
averages for the hours of instruction
between groups
Main Effects
Out
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4 hrs
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Main Effect of Time
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Main Effects
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Main Effect of Setting
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Main Effects
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Main Effects of
Time and Setting
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An Interaction Effect
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When differences on one factor depend
on the level you are on on another
factor
An interaction is between factors (not
levels)
You know there’s an interaction when
can’t talk about effect on one factor
without mentioning the other factor
Interaction Effects
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The in-class, 4-hour per
week group differs
from all the others.
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Interaction Effects
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The 1-hour amount works
well with pull-outs while
the 4 hour works as well
with in class.
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Advantages of Factorial Designs
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Offers great flexibility for exploring or
enhancing the “signal” (treatment)
Makes it possible to study interactions
Combines multiple studies into one
Randomized Block Designs
The Basic Design
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The Basic Design
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Homogeneous
groups
The Basic Design
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Homogeneity
on the
dependent
variable
(observations
in group one
tend to have
higher levels of
the dependent
variable than
observations in
group two, etc.)
Homogeneous
groups
Randomized Blocks Design
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Each replicate
is a block.
Randomized Blocks Design
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Can block before or after the study
Can block on a measured variable or on
unmeasured perceptions
Is a noise-reducing strategy
How Does Blocking Reduce Noise?
Posttest
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Pretest
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How Does Blocking Reduce Noise?
Range of x
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How Does Blocking Reduce Noise?
Range of x
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Variability of y
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How Does Blocking Reduce Noise?
Range of x
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Variability of y
Mean difference
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How Does Blocking Reduce Noise?
For block 3
Posttest
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How Does Blocking Reduce Noise?
For block 3
Range of x in block
Posttest
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How Does Blocking Reduce Noise?
For block 3
Range of x in block
Posttest
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Variability of y in block
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Pretest
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How Does Blocking Reduce Noise?
For block 3
Range of x in block
Posttest
Variability of y in block
Mean difference
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How Does Blocking Reduce Noise?
Posttest
For block 3
Range of x in block
Variability of y in block
Mean difference
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Same mean difference,
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but lower variability
on both x and y
Pretest
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Conclusion
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Instead of having one treatment effect
based on the full variability of y, you
have three treatment effects based on
reduced variability (but with the same
mean difference).
The average of the three estimates
gives a less noisy estimate than the
nonblock one.
Analysis of Covariance Experimental
Designs
Design Notation
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Uses a pre-measure
Can be a pretest, but doesn’t have to be
Can have multiple covariates
The Covariance Design
Posttest
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The Covariance Design
Posttest
The range of y is
about 70 points.
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How Does a Covariate Reduce Noise?
Posttest
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We fit regression lines to
describe the pretest-posttest
relationship.
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How Does a Covariate Reduce Noise?
Posttest
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We want to “adjust” the
posttest scores for
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70 variability.
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Pretest
How Does a Covariate Reduce Noise?
Posttest
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We do this by “subtracting
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out” the
pretest -- by
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“subtracting
out” the line.
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We want to “adjust” the
posttest scores for
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Pretest
How Does a Covariate Reduce Noise?
Posttest
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We do this by “subtracting
90
out” the
pretest -- by
80
“subtracting
out” the line.
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Get the
difference
between the
line and each
point.
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Pretest
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How Does a Covariate Reduce Noise?
Here is the plot with the effect of the pretest
removed. Notice the range on y is now only about
50 points instead of 70 (although the difference
between the means remains the same).
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Summary
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The Analysis of Covariance adjusts
posttest scores for variability on the
covariate (pretest).
This is what we mean by adjusting for
the effects of one variable on another.
Summary
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You can use any continuous variable as
the covariate, but the pretest is usually
best.
You can use multiple covariates, but if
they are highly intercorrelated, you don’t
improve the adjustment (and you pay a
price for each covariate).
Hybrid Experimental Designs
Hybrid Designs
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Variations on randomized designs
Help to address specific threats
Incorporates different design features
Two will be illustrated here.
The Solomon Four-Group Design
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Explicitly addresses a testing threat
Assesses the effect of taking a pretest
Possible Outcomes
Treatment Effect -- No Testing Effect
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Possible Outcomes
Treatment Effect and Testing Effect
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Tpost
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Pre
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Switching Replications Design
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Switching: the groups switch roles over
the course of the study.
Replications: the treatment is repeated
or replicated.
Possible Outcomes
Short-term Persistent Treatment Effect
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Group 1
Group 2
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Possible Outcomes
Long-term Continuing Treatment Effect
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Group 1
Group 2
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Post2
Switching Replications
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Very strong in internal validity
Looks at short and longer term effects
Strong ethically because all participants
get the treatment
Works well with some institutional
structures (for example, semester
system in schools)