Supplemental Text Material
The Staggered, Nested Design
In Section 14-1.4 we introduced the staggered, nested design as a useful way to prevent
the number of degrees of freedom from “building up” so rapidly at lower levels of the
In general, these designs are just unbalanced nested designs, and many computer
software packages that have the capability to analyze general unbalanced designs can
successfully analyze the staggered, nested design.
The general linear model routine in
Minitab is one of these packages.
To illustrate a staggered, nested design, suppose that a pharmaceutical manufacturer is
interested in testing the absorption of a drug two hours after the tablet is ingested.
product is manufactured in lots, and specific interest focuses on determining whether
there is any significant lot-to-lot variability.
Excessive lot-to-lot variability probably
indicates problems with the manufacturing process, perhaps at the stage where the
coating material that controls tablet absorption is applied.
It could also indicate a
problem with either the coating formulation, or with other formulation aspects of the
The experimenters select
= 10 lots at random from the production process, and decide
to use a staggered, nested design to sample from the lots.
Two samples are taken at
random from each lot.
The first sample contains two tablets, and the second sample
contains only one tablet.
Each tablet is test for the percentage of active drug absorbed
after two hours. The data from this experiment is shown in Table 1 below.
The Drug Absorption Experiment
The following output is from the Minitab general linear model analysis procedure.