Experimental Psychology – PSY 270 010 20046
Review for Test on Chapter 11 and 12
Suppose you conduct an factorial experiment with a 3 by 4 design and both factors are between subjects. Assume you need 10 subjects per condition. How many subjects do you need?
3 by 4 means 12 conditions, so you you need
120 subjects.
Suppose, in a 3 by 4 factorial design, the first factor is within subjects and the second is between. If you need 10 subjects per condition, how many subjects do you need?
Because the second factor is between subjects
and it has 4 levels, you need 40 subjects. Each one of the 40 subjects gives
you an observation in each of the 3 levels of the within subjects factor,
so you have 120 observations.
Suppose in a 3 by 4 factorial design, the first factor is between subjects and the second is within. If you need 10 subjects per condition, how many subject do you need?
Because the first factor is between subjects
and it has 3 levels, you need 30 subjects. Each one of the 30 subjects gives
you an observation in each of the 4 levels of the within subjects factor,
so you have 120 observations.
Suppose in a 3 by 4 factorial design, both factors are within subjects. If you need 10 subjects per condition, how many subjects do you need?
You only need 10 subjects because each one
participates in every condition. There are 12 condition, so you have a total
of 120 observation.
Suppose some researchers in San Francisco are investigating the effects of reading different kinds of promotional material on people’s attitudes towards the value of education. They hypothesize that reading promotional material for Mensa (the organization for people with a genius IQ) might cause people to consider education more valuable than reading such material for joining a trade union.
After they have randomly assigned each of a group of subjects to their two conditions, they notice that one group is entirely white subjects, whereas the other is all Asians. They believe that the effects they are trying to support could be different depending upon the race of the subject. Although such differences might be interesting in themselves, the researchers’ main concern is that they don’t want such differences to interfere with their ability to support their hypothesis.
Discuss what the researchers could do in this situation, and the relative advantages and disadvantages of the different approaches.
Re-randomize?
Should they repeat the randomization until
the groups “look random”? No, there is no such thing as a “random
group”. It is the process that needs to be random. But neither should
the experiment be conducted without getting rid of the obvious confound that
has inadvertently occured.
Use all the same race?
They could run the experiment with only whites
or only Asians. That would remove any effect of race, but it would lower
the generalizability of the results.
Block on race?
The best thing they could do is to take all
of the whites and randomly assign each one to one of the two conditions,
and then do the same thing for the Asians. This is called “blocking
on race”. In each condition, there is an equal sized block of each
race.
Crossing Factors:
Notice that this is the same thing as considering
race to be a second factor in the study and “crossing” race with
the promotional materials factor. Crossing two factors means forming conditions
that consist of every possible combination of the levels of the two
factors.
If there are two racial groups, and two levels
of promotional materials, then you have a two by two design, and there are
four conditions.
Whenever you cross factors, the number of
conditions is the product of the number of levels of factors. Thus, if there
are either a lot of factors, or a lot of levels for any of the factors, you
can end up with a lot of conditions. If this happens, you can consider using
“nesting” instead of “crossing”.
Nesting Factors:
Suppose your first factor (e.g., textbooks)
has 9 levels and your second factor (ways of using the textbooks) has 3.
Crossing the factors requires 27 conditions. If your design is between subjects,
and you need at least 20 subjects in a condition, then you need 540
subjects.
Nesting means that you combine some levels
of the first factor (the one with a lot of levels) with one of the levels
of the other factor, and then combine some other levels of the first factor
with the other levels of the second. But you don’t combine all with
all.
Let’s call the nine levels of the first
level, A1 through A9, and the levels of the second factor B1 through B3.
Rather than crossing, and having all 27 conditions:
A1B1
A2B1
A3B1
A4B1
A5B1
A6B1
A7B1
A8B1
A9B1
A1B2
A2B2
A3B2
A4B2
A5B2
A6B2
A7B2
A8B2
A9B2
A1B3
A2B3
A3B3
A4B3
A5B3
A6B3
A7B3
A8B3
A9B3
you could nest like this, and have only 9
conditions:
A1B1
A2B1
A3B1
A4B2
A5B2
A6B2
A7B3
A8B3
A9B3
This would enable you to test the effects
of the textbooks, and the effects of the methods to some extent. But there
are a large number of ways that the textbooks could interact with the methods,
and this nested design might show only some of them. And it might not be
possible to tell whether an effect is an interaction or really a main
effect.
For example, suppose that, in general, the
first method is the worst, the second medium, and the third the best. Suppose
that, for the most part, the text seems to make no difference. But suppose
you also notice that when the first text is used, then you get just as good
performance in B1 as in B3. Does text 1 improve learning only when combined
with method 1? If so, then that is an interaction. Or would text 1 improve
learning no matter what method it was combined with. In that case it is a
main effect.