School

University of Michigan, Dearborn **We aren't endorsed by this school

Course

EMGT 570

Subject

Statistics

Date

Sep 25, 2023

Type

Other

Pages

13

Uploaded by ProfMosquito3512 on coursehero.com

Design of experiments (DOE) is defined as a branch of applied statistics that deals with
planning, conducting, analyzing, and interpreting controlled tests to evaluate the factors that
control the value of a parameter or group of parameters. DOE is a powerful data collection and
analysis tool that can be used in a variety of experimental situations.
It allows for multiple input factors to be manipulated, determining their effect on the desired
output (response). By manipulating multiple inputs at the same time, DOE can identify
important interactions that may be missed when experimenting with one factor at a time. All
possible combinations can be investigated (full factorial) or only a portion of the possible
combinations (fractional factorial).
A strategically planned and executed experiment may provide a great deal of information about
the effect on a response variable due to one or more factors. Many experiments involve holding
certain factors constant and altering the levels of another variable. This "one factor at a time"
(OFAT) approach to processing knowledge is, however, inefficient when compared with
changing factor levels simultaneously.
Many of the current statistical approaches to designed experiments originate from the work of
R. A. Fisher in the early part of the 20th century. Fisher demonstrated how taking the time to
seriously consider the design and execution of an experiment before trying it helped avoid
frequently encountered problems in analysis. Key concepts in creating a designed experiment
include blocking, randomization, and replication.
Blocking:
When randomizing a factor is impossible or too costly, blocking lets you restrict
randomization by carrying out all of the trials with one set of the factor and then all the trials
with the other setting.
Randomization:
Refers to the order in which the trials of an experiment are performed. A
randomized sequence helps eliminate the effects of unknown or uncontrolled variables.
Replication:
Repetition of a complete experimental treatment, including the setup.
A well-performed experiment may provide answers to questions such as:
What are the key factors in a process?
At what settings would the process deliver acceptable performance?
What are the key, main, and interaction effects in the process?

What settings would bring about less variation in the output?
A repetitive approach to gaining knowledge is encouraged, typically involving these
consecutive steps:
1.
A screening design that narrows the field of variables under assessment.
2.
A "full factorial" design that studies the response of every combination of factors and factor
levels, and an attempt to zone in on a region of values where the process is close to
optimization.
3.
A response surface designed to model the response.
ANOVA
ANOVA stands for Analysis of Variance. It's a statistical test that was developed by Ronald
Fisher in 1918 and has been in use ever since. Put simply, ANOVA tells you if there are any
statistical differences between the means of three or more independent groups.
One-way ANOVA is the most basic form. Other variations can be used in different situations,
including:
Two-way ANOVA
Factorial ANOVA
Welch's F-test ANOVA
Ranked ANOVA
Games-Howell pairwise test
ANOVA helps you find out whether the differences between groups of data are
statistically significant. It works by analyzing the levels of variance within the groups
through samples taken from each of them.
If there are a lot of variances (spread of data away from the mean) within the data
groups, then there is more chance that the mean of a sample selected from the data will
be different due to chance.
As well as looking at variance within the data groups, ANOVA takes into
account sample size (the larger the sample, the less chance there will be off picking
outliers for the sample by chance) and the differences between sample means (if the

means of the samples are far apart, it's more likely that the means of the whole group
will be too).
All these elements are combined into an F value, which can then be analyzed to give a
probability (p-value) of whether or not differences between your groups are statistically
significant.
A one-way ANOVA compares the effects of an independent variable (a factor that
influences other things) on multiple dependent variables. Two-way ANOVA does the
same thing, but with more than one independent variable, while a factorial ANOVA
extends the number of independent variables even further.