One-Way Between-Subjects Design - Analysis of Variance Designs - page 91

independent variable. We can see from the summary table in Table 6.2
that the F ratio is statistically significant based on an alpha level of .05.
Eta squared is a whopping .853, indicating that the treatment variable
accounted for about 85 percent of the total variance in the data. This rather
spectacular finding resulted from contriving the small number of scores
in our hypothetical study to get the most out of our numerical example. In
the normal course of empirical research that you might be doing, values
of

2

η ≤ . 10 are not that uncommon.

6.5 COMPUTING THE OMNIBUS ANALYSIS BY HAND

With this overview of the omnibus analysis in place, we can now examine
the specific computations involved in the calculation of the various sums
of squares, degrees of freedom, mean squares, and F value. Many of you
will be using a statistical software application, such as SPSS or SAS, to
routinely analyze data you have collected in your research, and we will
show you how to run these programs at the end of the chapter. Invoking
such an application is an efficient and useful way to analyze your data, but
going through the actual arithmetic operations can make it clear what is
involved in computing an ANOVA.
The computational process for an ANOVA results in a few key values.
We will place a box around these values when we have obtained them with
the computations.

6.5.1 TERMINOLOGY AND NOTATION
Consider the previous study on the effects of months of study-preparation
time on subsequent SAT performance on a sample of high school seniors.
The scores (an individual's average of the Verbal and Quantitative portions
of the SAT) comprise the dependent variable and can be arranged as shown
in Table 6.1.
We begin by noting that a single independent variable, such as prepa-
ration time, can be referred to in generic terms as Factor A . If additional
independent variables are involved in the research design (as we will see
in Chapters 8-15), we will refer to them as Factors B , C , and so forth
(although we will not discuss designs with more than three factors in this
topic).
Independent variables must have two or more levels or classification
groups. In the present example, the five levels of preparation time (zero,
two, four, six, and eight months) are designated with a lower case a and a
subscripted number to indicate which of the five treatment conditions are
beingconsidered.Thus,wehave a 1 , a 2 , a 3 , and so forth and these are read as
“little 'a' one,” “little 'a' two,” and “little 'a' three,” and so on, respectively.
The dependent variable - the scores on the dependent measure -
are designated by the letter Y . As we noted previously in Chapter 3,
we add the subscripted letters i and j to denote the ordinal position of
each case or participant and treatment group or level, respectively. These