Database Reference
In-Depth Information
SIDEBAR: A MINI-GLOSSARY OF RELEVANT TERMS THAT YOU NEED TO
KNOW!—cont'd
•
A “
dependent variable
,” typically denoted by “Y,” is the “quality indicator” we wish to study.
Examples we have seen in earlier chapters include the
perceived sophistication level of a design
(Chapter 2) or
the time it takes to post a job
(Chapter 3) and several other quantities throughout
the text. In this chapter, the key dependent variable is, again, the
perceived sophistication of a
design
. You can think of a dependent variable as an “output variable.”
•
An “
independent variable,
” typically denoted by “X,” is a variable whose impact on the quality
indicator (Y) we wish to study. Examples we have seen in earlier chapters includes “design”
(Chapter 2), and (again) “design” (Chapter 3). In this chapter, the independent variable is “age
group.” You can also think of an independent variable as an “input variable.”
•
The word, “
factor
” is a synonym for “
independent variable
”. Whether “independent variable” is
used, or “factor” is used, simply depends on the tradition of terminology used when performing
different techniques. In this chapter and Chapters 7 and 8, the techniques we shall introduce are
all part of the “ANOVA” [Analysis of Variance] family, and the tradition is to use the word “fac-
tor.” However, as you shall in Chapters 9, 10, and 11, where we shall introduce different types
of regression analysis, the tradition is to use “independent variable” instead of “factor.”
•
Levels of a factor
: Each factor (or independent variable) has a certain number of “levels.” The
levels represent the different possibilities for the factor/independent variable. In Chapter 2, there
were two levels of the factor/independent variable of “design:” one was the design of the demoiselle
drinking the coffee and the second design was the couple under the umbrella embracing near the
Eiffel Tower. In Chapter 3, there were also two levels of the factor/independent variable “design:” the
Long Scroller and the Wizard. Here, in this chapter, there are ive levels for the factor “age:” the 5
age brackets. In general, the levels of a factor may be numerical values or numerical ranges, such as
the age groups, or can be non-numerical or qualitative, such as the Chapter 2 designs or the Chapter 3
designs. How many levels a factor has may often determine the technique that is most appropriate for
the analysis; this has been and will be discussed as you traverse the chapters.
•
Treatment
: Depending on the tradition of the ield of study, sometimes a level of a factor is
called a “treatment.” This has its roots in the chemical and related ields, but is often used in
other ields as a replacement for levels. (Similarly, the dependent variable is often called the
“yield,” with obvious roots in the agricultural area.) Other esoteric names are sometimes used
for these quantities in selected ields.
•
ANOVA
is a technique introduced in this chapter. There can be one factor under study (as in
this chapter) or two factors under study (as in Chapters 7 and 8), or a large number of factors
under study as in Chapters 10 and 11. However, in Chapters 10 and 11, “factors” are, by custom,
referred to as “independent variables.”
•
Factors can either be
ixed
or
random
. Generally speaking, a factor is
ixed
when the levels
of the factor under study are the only levels of interest and are chosen by the experimenter.
A classic example would be two or more speciic designs that the experimenter wishes to
compare, as in Chapter 2. A factor is
random
when the levels under study are a random
sample from a larger population and the goal of the study is to make a statement regarding
the larger population. A classic example from the ield of agriculture would be the level
of rainfall; it is what it is whatever Mother Nature delivers! Another example of a random
factor is “person,” or “participant,” when we consider differences among people's opinions
and the sample of people used in the study is a random selection from the population of
eligible people. (Usually, all participants for any kind of study are considered “random”
since they are a random sample from a larger population.) See the sidebar entitled “Fixed
versus Random Factors” in Chapter 7 for a deeper dive on this topic, including why it may
matter when conducting your analysis!
•
Replication
: When you perform an experiment, you have “replication” when you have more
than one data value for at least one combination of factor levels. When there is only one factor,
Search WWH ::
Custom Search