Statistics 101A
Lab 5
Split plot factorial
Professor Esfandiari
The objective of this lab is to:
•
Introduce you to the situations in which you typically conduct splitplot factorial
•
Show you how to enter and run the data on SPSS
•
Show you how to interpret the results
I
When do we use SPF?
Example 1: I will first use the data in chapter 12 of Kirk to illustrate SPF design.
As you know the Split plot factorial is a mixed design; a combination of a within effect
factor (such a repeated measures, or making blocks of subjects based on a confounding
factor and randomly assigning them to treatments) plus a between subject factor.
Example:
•
Measuring the blood pressure of a random number of five males and five females
who are taking a blood pressure medication (after one, two, three and four weeks).
The between subject factor is gender and the within subject factor is the four
measures of blood pressure.
•
Blocking nine males and nine females based on their weight. Randomly assigning
the three males with the highest weight to three weight loss programs (A, B, and
C) and continuing this till all the nine males are assigned to the three programs
and doing the same thing with females. The between subject factor is gender and
the within subject factor is the method of weight loss. The dependent variable is
the amount of weight loss.
So, one can conclude that the above examples are like a combination of oneway
ANOVA and randomized block design. Just like two wayanova, the major reason that
we carry out a splitplot factorial design is the fact that we are interested in the
interaction between the within and the between subject factor. In example 1, we want
to find out if the trend in the change of blood pressure is similar for males and females
and in example two we want to find out if the three methods of weight loss are equally
effective for males and females.
II
Example from Kirk: (page 494).
The objective of a study was to find out if the type of signal (auditory or tone and visual
or light) had any effect on response latency during a four hour monitoring period.
Type of signal is variable A and monitoring period (first, second, third, and fourth
hour) is variable B. The dependent variable is response latency to the auditory and
1
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View Full Documentvisual signals.
A random sample of eight subjects were obtained and they were
randomly assigned to two subsamples and observed under all of four levels of
treatment B. The data is given below:
B1
B2
B3
B4
A1
S1
3
4
7
7
S2
6
5
8
8
S3
3
4
7
9
S4
3
3
6
8
A2
S5
1
2
5
10
S6
2
3
6
10
S7
2
4
5
9
S8
2
3
6
11
The linear model is as follows:
Yijk =
μ
+
α
j +
π
i(j) +
β
k +
αβ
jk + e ijk
The score of each person can be partitioned to:
•
Grand mean or the mean of all the 32 observations,
•
The effect of the type of signal (the row effect or the between subject effect)
•
The effect of the block i
•
The effect of the monitoring period (the column effect or the within subject
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 Winter '11
 MahtashEsfandiari
 Statistics, Spss, arterial blood pressure

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