# Quality Progress - March 2018 - 50

```Statistics Spotlight
1213231315447133415341545721157945495241262
124345464755497541275299949514654237204317
91545154134541213231315447133415341545721157945495241262
124345464755497541275299949514654237204317
91545154134541213231315447133415341545721157945495241262
124345464755497541275299949514654237204317
91545154134541213231315447133415341545721157945495241262

factor X1 is the explanation for the changes to the
response that are actually being driven by humidity.
This can lead to us falsely concluding that changes in
X1 cause changes in the response.
If the randomized run order in Figure 1 (part b) is
used, however, notice how none of the factors have
too many runs at either the high or low level in either
the first or the last half of the experiment. This offers
protection from falsely associating a change in response
driven by a lurking variable (one that is not being intentionally manipulated by the experimenter) with a factor
in the experiment.
Would it be better to have been tracking humidity or,
better yet, holding it constant throughout the experiment? Yes. But that assumes that we can anticipate
everything that will affect the response and that we
have the ability to control all of these aspects. With randomization, however, we might not realize that humidity

two (and three and four, which all of have X2 at the low
setting) could be run at the slightly low temperature.
variability is associated with the setting of each factor,
which might have an impact on the response values
obtained.
There are other reasons that randomization of the
order of experimental runs is important: The first is
related to the fact that there are other things changing
during the course of running the experiment. Perhaps
unbeknownst to the experimenter, the humidity in the
lab is slowly increasing while the experiment takes place,
and suppose that humidity affects the response.
If the experiment was run in the order shown in
Figure 1 (part a-standard order), the first eight runs
would be performed at the low level of X1, and the last
eight runs would be at the high level of X1. If humidity
is rising and is affecting the response, it will look like
FIGURE 3

16-run split-plot design with factor X1
as a hard-to-change factor
X1

X2

X3

X4

1 1

Whole plots

1

1

−1

1

X1

X2

X3

X4

1 2

Whole plots

−1

−1

1

1

2 1

1

−1

1

1

2 2

−1

−1

−1

1

3 1

1

−1

−1

−1

3 2

−1

1

1

−1

4 1

1

1

1

−1

4 2

−1

1

−1

1

5 2

−1

1

−1

1

5 1

1

1

−1

1

6 2

−1

−1

−1

−1

6 1

1

−1

−1

−1

7 2

−1

1

1

−1

7 1

1

−1

1

1

8 2

−1

−1

1

1

8 1

1

1

1

−1

9 3

1

1

−1

−1

9 3

1

−1

1

−1

10 3

1

−1

−1

1

10 3

1

1

−1

−1

11 3

1

−1

1

−1

11 3

1

−1

−1

1

12 3

1

1

1

1

12 3

1

1

1

1

13 4

−1

1

1

1

13 4

−1

−1

1

−1

14 4

−1

−1

−1

1

14 4

−1

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−1

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15 4

−1

−1

1

−1

15 4

−1

1

1

1

16 4

−1

1

−1

−1

16 4

−1

−1

−1

1

a

b

Note: The experiment is run with four subplot runs in each whole plot. Within a whole plot, the level
of factor X1 is not reset, while the levels of each of the other factors are reset for each run. Parts a
and b show different run orders for the experiment, with two randomizations having been applied.

50 QP

March 2018 ❘ qualityprogress.com

```
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Seen and Heard
Progress Report
Career Coach
My Quality Story
In the Right Direction
A Different Kind of BBQ
Gaining Ground
Impeding Progress
Innovation Imperative
Statistics Spotlight
Standard Issues
Marketplace
Footnotes
Back to Basics
Quality Progress - March 2018 - INTRO
Quality Progress - March 2018 - cover1
Quality Progress - March 2018 - cover2
Quality Progress - March 2018 - 1
Quality Progress - March 2018 - 2
Quality Progress - March 2018 - 3
Quality Progress - March 2018 - 4
Quality Progress - March 2018 - 5
Quality Progress - March 2018 - Seen and Heard
Quality Progress - March 2018 - 7
Quality Progress - March 2018 - Expert Answers
Quality Progress - March 2018 - 9
Quality Progress - March 2018 - Progress Report
Quality Progress - March 2018 - 11
Quality Progress - March 2018 - 12
Quality Progress - March 2018 - Mr. Pareto Head
Quality Progress - March 2018 - Career Coach
Quality Progress - March 2018 - 15
Quality Progress - March 2018 - My Quality Story
Quality Progress - March 2018 - 17
Quality Progress - March 2018 - In the Right Direction
Quality Progress - March 2018 - 19
Quality Progress - March 2018 - 20
Quality Progress - March 2018 - 21
Quality Progress - March 2018 - 22
Quality Progress - March 2018 - 23
Quality Progress - March 2018 - A Different Kind of BBQ
Quality Progress - March 2018 - 25
Quality Progress - March 2018 - 26
Quality Progress - March 2018 - 27
Quality Progress - March 2018 - 28
Quality Progress - March 2018 - 29
Quality Progress - March 2018 - 30
Quality Progress - March 2018 - 31
Quality Progress - March 2018 - Gaining Ground
Quality Progress - March 2018 - 33
Quality Progress - March 2018 - 34
Quality Progress - March 2018 - 35
Quality Progress - March 2018 - 36
Quality Progress - March 2018 - Impeding Progress
Quality Progress - March 2018 - 38
Quality Progress - March 2018 - 39
Quality Progress - March 2018 - 40
Quality Progress - March 2018 - 41
Quality Progress - March 2018 - 42
Quality Progress - March 2018 - 43
Quality Progress - March 2018 - Innovation Imperative
Quality Progress - March 2018 - 45
Quality Progress - March 2018 - 46
Quality Progress - March 2018 - 47
Quality Progress - March 2018 - Statistics Spotlight
Quality Progress - March 2018 - 49
Quality Progress - March 2018 - 50
Quality Progress - March 2018 - 51
Quality Progress - March 2018 - 52
Quality Progress - March 2018 - 53
Quality Progress - March 2018 - Standard Issues
Quality Progress - March 2018 - 55
Quality Progress - March 2018 - 56
Quality Progress - March 2018 - 57
Quality Progress - March 2018 - Marketplace
Quality Progress - March 2018 - 59
Quality Progress - March 2018 - Footnotes
Quality Progress - March 2018 - 61
Quality Progress - March 2018 - 62
Quality Progress - March 2018 - 63
Quality Progress - March 2018 - Back to Basics
Quality Progress - March 2018 - cover3
Quality Progress - March 2018 - cover4
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