Experimental Designs Week 4 Solution
Experimental Designs
2. Explain the difference between multiple independent variables and multiple levels of independent
variables. Which is better?
Answer:
The general purpose of multivariate analysis of variance (MANOVA) is to determine
whether multiple levels of independent variables on their own or in combination with
one another have an effect on the dependent variables. MANOVA requires that the
dependent variables meet parametric requirements.
MANOVA is used under the same circumstances as ANOVA but when
there are multiple dependent variables as well as independent variables within the model
which the researcher wishes to test. MANOVA is also considered a valid alternative to
the repeated measures ANOVA when sphericity is violated.
Like an ANOVA, MANOVA examines the degree of variance within the
independent variables and determines whether it is smaller than the degree of variance
between the independent variables. If the within subjects variance is smaller than the betw-
een subjects variance it means the independent variable has had a significant effect on the
dependent variables. There are two main differences between MANOVAs and ANOVAs.
The first is that MANOVAs are able to take into account multiple independent and multiple
dependent variables within the same model, permitting greater complexity. Secondly,rather
than using the F value as the indicator of significance a number of multivariate measures.
MANOVAs the independent variables relevant to each main effect are weighted to give
them priority in the calculations performed. In interactions the independent variables are
equally weighted to determine whether or not they have an additive effect in terms of the
combined variance they account for in the dependent variable/s.
The main effects of the independent variables and of the interactions are examined with
all else held constant. The effect of each of the independent variables is tested separately.
Any multiple interactions are tested separately from one another and from any significant
main effects. Assuming there are equal sample sizes both in the main effects and the inter-
actions, each test performed will be independent of the next or previous calculation (exce-
pt for the error term which is calculated across the independent variables).

3. What is blocking and how does it reduce “noise”? What is a disadvantage of blocking?
Sol:
The Randomized Block Design is research design's equivalent to stratified
random sampling. Like stratified sampling, randomized block designs are
constructed to reduce noise or variance in the data (see Classifying the Exper-
imental Designs). How do they do it? They require that the researcher divide
the sample into relatively homogeneous subgroups or blocks (analogous to
"strata" in stratified sampling). Then, the experimental design you want to impl-
ement is implemented within each block or homogeneous subgroup. The key
idea is that the variability within each block is less than the variability of the
entire sample. Thus each estimate of the treatment effect within a block is more
efficient than estimates across the entire sample. And, when we pool these more
efficient estimates across blocks, we should get an overall more efficient estimate
than we would without blocking.
How Blocking Reduces Noise
So how does blocking work to reduce noise in the data? To see how it works,
you have to begin by thinking about the non-blocked study. The figure shows
the pretest-posttest distribution for a hypothetical pre-post randomized experi-
mental design. We use the 'X' symbol to indicate a program group case and the
'O' symbol for a comparison group member. You can see that for any specific
pretest value, the program group tends to outscore the comparison group by
about 10 points on the posttest. That is, there is about a 10-point posttest mean
difference.

Now, let's consider an example where we divide the sample into three relatively
homogeneous blocks. To see what happens graphically, we'll use the pretest mea-
sure to block. This will assure that the groups are very homogeneous. Let's look at
what is happening within the third block. Notice that the mean difference is still the
same as it was for the entire sample about 10 points within each block. But also
notice that the variability of the posttest is much less than it was for the entire samp
le. Remember that the treatment effect estimate is a signal-to-noise ratio. The signal
in this case is the mean difference. The noise is the variability. The two figures show
that we haven't changed the signal in moving to blocking there is still about a 10-point
posttest difference. But, we have changed the noise -- the variability on the posttest is
much smaller within each block that it is for the entire sample. So, the treatment effect
will have less noise for the same signal.

Experimental Designs Week 4 Solution

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