STAT210prob14.22: STAT210prob14.22: The Absorption Time Experiment

In thoree/stat340: Data and functions for BIAS at NMBU

STAT210prob14.22: The Absorption Time Experiment

Description

This data illustrates an experiment with a "split-split"-plot design. A researcher is studying the absorption times of a particular type of antibiotic capsule. There are three technicians, three dosage strengths, and four capsule wall thicknesses of interest to the researcher. 36 observations are required to obtain each replicate in the factorial experiment.

Usage

STAT210prob14.22

Format

A data frame with 144 observations (rows) and 5 variables (columns).

	Column name	Data type	Description	Values
[,1]	Day	factor	The replicates are run on 4 different days	(1, 2, 3, 4)
[,2]	Tech	factor	3 different technicians conduct the experiment	(1, 2, 3)
[,3]	Dose	factor	3 levels of dosage strengths	(1, 2, 3)
[,4]	Thick	factor	4 levels of thickness of the capsule wall	(1, 2, 3, 4)
[,5]	Time	integer	Absorption time of the capsule	(66 - 121)

Details

The data is from Exercise 14.22 in Design and Analysis of Experiments, 9th Edition, EMEA Edition. The experimental design is described in Example 14.4.

The experimenter has decided on four replicates, and it is necessary to run each replicate on a different day. Note that the days can be considered as blocks. Within a replicate (or a block) (day), the experiment is performed by assigning a unit of antibiotic to a technician who conducts the experiment on the three dosage strengths and the four wall thicknesses. Once a particular dosage strength is formulated, all four wall thicknesses are tested at that strength. Then another dosage strength is selected, and all four wall thicknesses are tested. Finally, the third dosage strength and the four wall thicknesses are tested. Meanwhile, two other laboratory technicians also follow this plan, each starting with a unit of antibiotic.

• There are two randomization restrictions within each replicate (or block): technician and dosage strength.

• The whole plots correspond to the technician. The order in which the technicians are assigned the units of antibiotic is randomly determined.

• The dosage strengths form three subplots. Dosage strength may be randomly assigned to a subplot.

• Within a particular dosage strength, the four capsule wall thicknesses are tested in random order, forming four sub-subplots. The wall thicknesses are usually called sub-subtreatments.

Source

Montgomery, D. C. (2019) Design and Analysis of Experiments, 9th Edition, EMEA Edition. New York: Wiley.

Examples

# The structure of the object
str(STAT210prob14.22)

# Number of replicates for each combination of the factors:
# Tech, Dose and Thick
# The four replicates shown here for each combination
# of the factor levels are run on different days
table(STAT210prob14.22[, c(3, 4, 2)])

thoree/stat340 documentation built on June 30, 2024, 4:04 p.m.