1. Design Supplemental

2. Design Completely randomized Randomized block design Repeated measures
Latin-Squares
Greco-Latin Squares
Repeated measures
Pre & post-test designs
Mixed designs (Between subjects factors and repeated measures)
Split-plot
Random effects models

3. 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)  groups 1-4
y=c(.25,.25,.25,.25)  long run probability of occurrence
sample(x, 80, replace=TRUE, prob = y)

4. 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

5. 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

6. Randomized Block Design
Independent Variables
Control:
no music
Experimental
treatment
slow music
Experimental
treatment:
fast music
Mornings and
afternoons
Evening hours
Blocking variable

7. 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

8. 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, husband-wife)
Latin-squares and Graeco-Latin squares extend the blocking to 2 and 3 nuisance variables respectively
Consult Winer or Kirk texts

9. 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.

10. Previous therapy (none, yes but no drugs, yes w/ drugs)
Latin Square
Example controlling for previous therapy experience and therapist (A is the treatment, e.g. type of therapy)
A1 A2 A3 2 A2 A3 A A3 A1 A2
Previous therapy (none, yes but no drugs, yes w/ drugs)
Example: 3 groups receive Therapy A1
Group1- therapist1, no previous
Group2- therapist2, drugs
Group3- therapist3, no drugs
Therapist

11. 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

12. 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

13. Mixed design Between subjects factors with repeated measures
Simple but common example is control-treatment, pre-post
Subjects are randomly assigned to control or treatment groups and tested twice
Pre
Post
Control
Treatment

14. 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)

15. 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

16. 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).

17. 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?

18. Random effects models Some examples: Persuasiveness of commercials
Effect of worker on machine output
Vehicle emissions impact on the environment

19. Random effects models
Determination of fixed vs. random effects affects the nature of the tests involved, how the F-statistic 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