In this story we will develop the concept of mixed designs and give a practice example.
Elegant research avoids complex
designs also called split-plot designs
or mixed designs. However, you may not
be spared of these monsters in your
student or research life.
Let’s get a whiff of these monsters.
A psychiatrist wanted to see, if two
new drugs improve the condition
of depressive and schizophrenic
patients.
He randomly assigned 4
depressive patients to Drug1 and
Drug2 conditions. That is, each of
the depressive patients will be
serving as a subject in both the
Drug conditions. This is a repeated
measures design.
He did the same with the
schizophrenic patients. He
randomly assign 4 schizophrenic
patients to Drug1 and Drug2
conditions. That is, each of the
schizophrenic patients will be
serving as a subject in both the
Drug conditions. This is a repeated
measures design.
As you see, here we have two
independent groups (depressive
patients, and schizophrenic
patients) but each patient is given
two treatments, that is he is tested
repeatedly, i.e., in both drug
conditions. We have a hybrid
situation, you would say. Both
independence and non-
independence in the same
experiment.
Here is the layout; X stands for scores.
The analysis of data in complex
designs like the above, is, as
always, an operation involving the
calculation of variance. The
interpretation of the results of such
an analysis is like the interpretations
we considered in this book so far.
ANOVA mixed split plot - formula and practice example
What is ANOVA mixed split plot design
ANOVA mixed split plot designs are complex designs that employ both independent and repeated measures. The best way to explain this is to present the layout of these experimental designs.
TABLE SHOWING THE LAYOUT
OF MIXED SPLIT-PLOT DESIGNS
Observe that there are two independent groups, depressive, and schizophrenic. Also observe that each subject of the depressive and schizophrenic groups is repeatedly tested, once with Drug 1, and later with Drug 2. This is a repeated measures arrangement So here we have a design in which independent and repeated measures are mixed. The name split plot comes from the fact that this design is extensively used in agricultural research.
ANOVA mixed split plot designs formula
As in all ANOVA, the formula for these designs is:
We read this as follows: Mean square between over mean square within. What is mean square, you ask? It is the mean of squares. What is squares, you ask. Squares is the statistical term for squared deviations (of squared differences) of each score X from the mean. What are the squared differences, you ask. Remember the formula for variance?
Look at the numerator
These are the squared differences summed. To complete our reasoning, we go back to where we started, the F formula, or F ratio, the formula for ANOVA. Why mean sums of squares? Simple because like all averages, we divide by the number of scores. If you are observant, you will notice that the F formula is a modified t formula.
FORMAT OF ANOVA MIXED SPIT PLOT SUMMARY TABLE
HOW TO CALCULATE df OF ANOVA MIXED SPIT PLOT SUMMARY TABLE
ANOVA mixed split plot- practice examples
ANOVA mixed split plot- practice example 1
An experimenter wanted to test drugs (factor A), Drug 1 (A1) and Drug 2 (A2) for their effect on serotonin level in the blood of patients (factor B) suffering from depression (B1) and schizophrenia (B2) . He randomly selected six patients suffering from depression and gave them Drug 1. He waited for one hour and then he measured the level of serotonin in nanograms per liter (ng/lt) of each subject. He recorded the data. One week later he gave these subjects Drug 2. He waited for one hour and measured the level of serotonin of each subject. He also randomly selected six patients suffering from schizophrenia and repeated the same experiment that he performed with the depressive patients. The data are presented in the table below.
ANOVA MIXED SPIT PLOT SUMMARY TABLE