dq
Designed Experiment
Certain elements are common to almost all designed experiments, regardless of the
specific area of application. For example, the response is the variable of interest in the
experiment. The response might be the SAT scores of a high school senior, the total
sales of a firm last year, or the total income of a particular household this year. The
response is also called the dependent variable, y.We use these terms interchangeably in
this chapter.
The response variable is the variable of interest to be measured in the experiment.
We also refer to the response as the dependent variable.
The intent of most statistical experiments is to determine the effect of one or more
variables on the response.These variables, which we called the independent variables in
regression analysis, are often referred to as the factors in a designed experiment. Like
independent variables, factors are either quantitative or qualitative, depending on
whether the variable is measured on a numerical scale or not. For example, we might
want to explore the effect of the qualitative factor Gender on the response SAT score.
In other words,we want to compare the SAT scores of male and female high school sen-
iors. Or, we might wish to determine the effect of the quantitative factor Number of
salespeople on the response Total sales for retail firms.Often two or more factors are of
interest. For example, we might want to determine the effect of the quantitative factor
Number of wage earners and the qualitative factor Location on the response Household income.
Factors are those variables whose effect on the response is of interest to the experi-
menter.Quantitative factors are measured on a numerical scale,whereas qualitative
factors are those that are not (naturally) measured on a numerical scale.Factors are
also referred to as independent variables.
Levels are the values of the factors that are used in the experiment.The levels of
qualitative factors are usually nonnumerical. For example, the levels of Gender are
Male and Female, and the levels of Location might be North, East, South, and West.*
The levels of quantitative factors are numerical values. For example, the Number of
salespeople may have levels 1, 3, 5, 7, and 9. The factor Years of education may have
levels 8,12,16,and 20.
Factor levels are the values of the factor used in the experiment.
When a single factor is employed in an experiment, the treatments of the exper-
iment are the levels of the factor. For example, if the effect of the factor Gender on
the response SAT score is being investigated, the treatments of the experiment are
the two levels of Gender—Female and Male. Or, if the effect of the Number of wage
earners on Household income is the subject of the experiment, the numerical values
assumed by the quantitative factor Number of wage earners are the treatments.
If two or more factors are used in an experiment, the treatments are the factor-level
combinations used. For example, if the effects of the factors Gender and
Socioeconomic Status (SES) on the response SAT score are being investigated,
the treatments are the combinations of the levels of Gender and SES used;
thus (Female, high SES), (Male, high SES), and (Female, low SES) would all be
treatments.
The treatments of an experiment are the factor-level combinations used.
bservational.
A designed experiment is one for which the analyst controls the specification of the
treatments and the method of assigning the experimental units to each treatment.
An observational experiment is one for which the analyst simply