Information Technology Reference
In-Depth Information
Ta b l e 3 . 1 .
Mood scores for
students answering a
questionnaire in rooms
painted different colors
Red room
Blue room
11
16
12
17
13
18
14
19
15
20
16
21
17
22
Y
=
14
Y
=
19
at least, it appears that answering the mood questions in the blue room
might have produced greater calmness than answering the questions in
the red room. The results of our ANOVA will inform us whether we can
say that these two means are significantly different.
3.2.4 THE STATISTICAL RESULTS
We have performed the ANOVA of the data already, but this chapter is
not about teaching you the details of calculating the numbers we are
presenting - Chapter 6 will take you through a worked ANOVA example.
Rather, our goals here are to talk you through the logic of the variance
partitioning process and to orient you to some of the computational
strategies that are used in ANOVA. To accomplish these goals, it is useful
to have the results of the analysis presented to you.
In the days when only hand calculations were done, it was common
practice to place the outcome of ANOVA computations in one neatly
organized place rather than have the numbers scattered about over several
pages of calculations. This organized place was known by the very appro-
priate name of a
summary table.
So useful was this practice of placing the
information in a summary table that the statistical software applications
perpetuated it. Thus, even today SPSS and SAS show a summary table as
part of their ANOVA output.
3.2.5 THE SUMMARY TABLE
Table 3.2 presents the summary table for the room color study. Sum-
mary tables have a relatively standard structure. The rows represent the
partitioning of the variance and will vary with each type of experimental
design that was used. The columns depict statistical information relevant
to the analysis; because we compute the same type of statistical informa-
tion in all of the ANOVA designs, these columns are relatively fixed in
the designs that we cover in this topic. The elements in this table, and the
concepts underlying them, are central to understanding the ANOVA tech-
nique. We will discuss the entries in the columns for sources of variance,
