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Chapter 7

# CHAPTER 7 RANDOMIZED EXPERIMENTS.docx

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York University

Psychology

PSYC 2030

Krista Phillips

Fall

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PSYCH-INTRO TO RESEARCH METHODS
LORENZ SOL
CHAPTER 7 RANDOMIZED EXPERIMENTS & CAUSAL INFERENCE
In randomized experiments, the allocation of sampling units to groups or
conditions is done by a process of random assignment (also called
randomization) so that, for example, each person in a population of
subjects has an equal probability of being chosen at every draw.
In biomedical research, randomized experiments (often called trials) are
considered the “gold standard” of causal inference. Not guaranteed to
be flawless.
Randomized trials (the gold standard of causal inference in biomedical
research) can also fluctuate with regard to their potential value. [1] First,
perfect control is often hard to achieve. [2] Second, patients who
experiment adverse reactions to an experiment drug may, without telling
the researchers, decide to reduce their assigned dosage. [3] Third,
assigning patients with a terminal illness to a placebo group could have
legal ramifications. [4] Fourth, simply knowing that randomization is being
used may make some patients wary of volunteering and could jeopardize
the generalizability of the results if the volunteers’ response to the
treatment is different from the possible response of those who did not
volunteer.
Three reasons for using randomized assignment; [1] Random assignment
provides a safeguard against the possibility of researchers’ subconsciously
letting their opinions or preferences influence which sampling units will
receive any given treatment. Sampling units is simply a general way of
referring to the participants, subjects, groups, or objects being studied.
Treatment is commonly used both as a general name for the
manipulation or intervention and as a way of referring to the conditions to
which sampling units are allocated. [2] A second reason, which is the one
that most experimenters would give, is that random assignment distributes
the characteristics of the sampling units over the experimental and
control conditions in a way that will not bias the outcome of the
experiment. It is always possible (especially when sample sizes are small)
that some unintended or uncontrolled variable related to the dependent
variable will affect the outcome in one condition more than another. [3]
Random assignment permits the computation of statistics that require
certain characteristics of the data. It provides a mechanism to derive
probabilistic properties (p values) of estimates based on the data by
controlling for extraneous variables. In observational studies based on very
large samples, one option is to use a procedure that reduces relevant
characteristics of the “naturally treated” and “untreated” individuals to a
single composite variable and then estimate the “treatment effect” by
comparing results in subclassifications of this variable. Another option is
longitudinal study in which we measure a cohort of people periodically for
many years in order to identify variables or conditions correlated with
illness.
HOW IS RANDOM ASSIGNMENT ACCOMPLISHED?
Statisticians speak of random assignment rules (or plans).
Coin flips, arrangements, random assignments implemented on the
computer, etc., are all examples of randomization methods. PSYCH-INTRO TO RESEARCH METHODS
LORENZ SOL
WHAT ARE BETWEEN-SUBJECTS & WITHIN-SUBJECTS DESIGNS?
When the subjects are exposed to one condition each, the arrangement
is known as a between-subjects design. Another statistical name for the
between-subjects design is nested design, because the subjects are
“nested” within their own groups or conditions.
A traditional of analyzing two-condition between-subjects designs is by a t
test for independent samples.
In biomedical trials, the outcome is often a dichotomous measure (e.g.,
die vs. live, or sick vs. well), and the data (frequencies) are arranged in a
2X2 table where the rows are the two levels of the independent variable
(treatment absent vs. treatment present), the columns are the two levels
of the outcome variable (die vs. live, or sick vs. well), and the cell values
are independent frequencies (or counts). A typical statistical test would
2
be the chi-square (X ) procedure on the independent frequencies.
Contrasts specifically ask focused questions of data. Contrasts compare
observed group means with predicted weights, called lambda weights
(λ), with the stipulation that those weights must sum to zero (i.e., Σλ=0,
where Σ tells us to sum the lambdas).
Between-subjects designs are not limited to two groups, and lambda
weights are not limited to plus-and-minus 1.
Suppose all the subjects receive both Condition A and Condition B. This
arrangement is called a within-subject design.
The t test is the usual procedure for analyzing such data, but this time we
would use a t test for nonindependent samples. Because the subjects’
reactions are measured after each condition, this is also called a
repeated-measures design.
Another name for the basic within-subjects design is a crossed design,
because the subjects are thought of as “crossed” by conditions (i.e.,
observed under two or more conditions) rather than nested within them.
Within-subjects designs are also not limited to two groups.
WHAT ARE FACTORIAL DESIGNS & LATIN SQUARE DESIGNS?
When we think of the conditions as arranged (or arrayed) along a
continuum or single dimension, it is described as a one-factor or one-way
design, where the term factor is a general name for the overarching
variable of interest (the independent variable).
TWO-BY-TWO FACTORIAL DESIGN
GENDER DRUG PLACEBO
Women A B
Men C D
This arrangement is called a factorial design. There are 2 levels of each 2
factors; we describe this arrangement as a 2X2 factorial design (where
“2X2” is read as “two by two”) or a 2 factorial design.
Suppose that, instead of a factorial design with two between-subjects
factors, we have a within-subjects design with repeated treatments and
measurements on men and women. Now we have a more complex
design, in which one factor is between subjects (men and women) and PSYCH-INTRO TO RESEARCH METHODS
LORENZ SOL
the other is within subjects (repeated treatments and measurements). This
design is called mixed factorial design.
Counterbalancing is rotating the sequences to address the problem of
systematic differences between successive treatments (or
measurements).
A specific statistical design that has counterbalancing built in is called the
Latin square design. It is characterized by a square array of letters
(representing the treatment conditions) in which each letter appears
once and only once in each row and column.
WHY IS CAUSALITY SAID TO BE “SHROUDED IN MYSTERY”?
Aristotle identified four kinds of causality, which he called material,
formal, final, and efficient.
Material causality refers to the substance or substances necessary for the
movement of something or the coming into being of a specific event.
Formal causality refers to the plan or development that gives meaning to
the event.
Final causality (also called teleologic, which means the action is “goal-
directed”) refers to the objective or purpose of the event.
Efficient causality refers to the activating force that was responsible for

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