Data
Analysis and Research Methods
Course Description and Syllabus
Introduction to Factorial
Experiments #12 -
Part 2, Activity 5
Key
Purposes:
- Students can graph the results of a 2x2
experiment on an acrylic cube and on paper.
- Students can calculate the prediction
equation of a 2x2 experiment with no
interaction.
- Students can represent the main effects as
vectors on an acrylic cube and on paper.
- Students can represent an interaction
graphically on an acrylic cube and on paper.
- Students can calculate main effects,
interactions, and the predictor equation of
the 2x2 experiment.
- Students can state the three questions
addressed in a 2x2 experiment and
corresponding hypotheses.
- Students can state the definition of an
interaction: An interaction is a situation
where factors act upon one another to
influence an outcome (response). An
interaction between two factors occurs when
the effect of changing one factor depends on
the level (setting) of the other factor.
Example: An interaction between
teaching style and learning style exists when
the effect of changing teaching style depends
on the learning style of the student.
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Plot this data on the cube.
Let A = Time spent studying (in
hours).
Two hours =
-1. Four hours = +1.
Let B = Temperature in degrees.
68 degrees =
-1. 78 degrees = +1.
Let Y = test scores, the response variable.
Variable A
Hours of Study
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Variable B
Temperature
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Y (response variable)
Scores
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-1
|
-1
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85
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+1
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-1
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95
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-1
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+1
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80
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+1
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+1
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90
|
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To see a Quick Time Movie
of the The Factorial Experiment graph, Click
the above image. File size may be large,
please allow enough time for the download.
Description:
Introduction to Factorial Experiments.
The video, DOE, produced by the Macomb
Intermediate School District, illustrates
the importance of well-designed, multi-variate
experiments in science and industry. After
the video, students graph the results of a
2x2 experiment with no interaction and
calculate the predictor equation. Then they
are given experimental results where the
previous model is inadequate because an
interaction is present. Graphical
interpretations of interactions are studied
and real life implications of interactions
are discussed.
Alignment with Michigan
Curriculum Framework:
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Mathematics
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Strand
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Standard
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Benchmark High School
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I
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Patterns, Relationships, and Functions
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1
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2, 3, 4, 5
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I
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Patterns, Relationships, and Functions
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2
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1, 2, 3, 6
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II
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Geometry and Measurement
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1
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7
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II
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Geometry and Measurement
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2
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1, 2, 5
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II
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Geometry and Measurement
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3
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1, 2, 3, 4, 5, 6
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III
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Data Analysis and Statistics
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1
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1, 2, 3, 4
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III
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Data Analysis and Statistics
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2
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1, 2, 3, 4, 5
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III
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Data Analysis and Statistics
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3
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1, 2, 3, 4, 5
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IV
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Number Sense and Numeration
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2
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5
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IV
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Number Sense and Numeration
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3
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2, 5
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V
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Numerical and Algebraic Operations and
Analytical Thinking
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1
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4
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V
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Numerical and Algebraic Operations and
Analytical Thinking
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2
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1, 2, 3, 4, 5
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Science
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Strand
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Standard
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Benchmark High School
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I
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Construct
New Scientific and Personal Knowledge
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1
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1, 2, 3, 4, 5, 6, 7, 8, 9
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II
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Reflect on
the Nature, Adequacy and Connections Across
Scientific Knowledge
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1
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1, 2, 3, 4, 5, 6
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English
Language Arts
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Strand
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Standard
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Benchmark High School
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Meaning and
Communication
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1
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1, 2, 3, 4, 5
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2
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1, 3, 4
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3
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1, 3, 4, 5, 6, 8
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Language
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4
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1
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Voice
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6
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1
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Skills and
Process
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7
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1, 2, 3, 4
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Depth of
Understanding
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9
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1, 2, 3
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Ideas in
Action
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10
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1
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Inquiry and
Research
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11
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1, 2, 3, 4
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Critical
Standard
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12
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1
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