Order #403985 Topic: #3
An Applied Reference Guide to Research Designs Quantitative, Qualitative, and Mixed Methods
A Visual System for Research Designs in
Education and the Social & Behavioral Sciences
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Edmonds, W. A., & Kennedy , T. D. (2012). An applied reference guide to research designs: Quantitative, qualitative, and mixed methods. Thousand Oaks, CA: Sage.
Ch. 5 - 6
Factorial Designs
Solomon n-group designs
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Factorial designs
Can be either between- or within-subjects
Or can include a combination both between- and within-subjects. These are called mixed-subjects
Extension of the k-factor design
Includes a minimum of 2 factors and each with at least 2 levels
The simplest form of a factorial is the 2 x 2 or the 22 (sk).
Multiply the number of factors and levels to determine the number of groups or cells required:
2 x 2 = 4 groups; 2 x 3 x 2 = 12 groups (or cells)
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Family of factorial designs
Factorial designs can have mixed levels
2 x 3 (two factors- one with two levels and one with 3 levels)
These designs can have more than two factors
3 x 3 x 3 (3 total factors each with 3 levels)
Can contain both pre and posttests, but most just contain a posttest
A 2 x 4 design can utilize a within-subjects or a between-subjects approach depending on the research scenario
A 2 x 3 design can be a mixed-factorial design
The first factor at 2 levels is tested as between-subjects and the second factor at 3 levels is tested as within-subjects
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Different types of factors (i.e., independent variables)
An independent variable from a design perspective is the variable that can be manipulated
Hence the IV is controlled
An intervention can be controlled via inclusion and exclusion for example
Gender in a factorial design is an IV, but cannot be “manipulated” (thus, sometimes referred to as a quasi-IV) by the researcher the same way an intervention is manipulated
However, gender can be controlled via statistical procedures and portioned into male and female
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Experimental Research for Factorial designs
These designs can be designated as experimental research (cause-effect) so long the following can be ensured:
Covariation?
Temporal Precedence?
No Plausible Alternative Explanation?
Threats to internal validity can vary depending on:
The approach (between-, within-, or mixed-subjects)
The sequencing of observations (posttest only or if a pretest is included)
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Most common threats
Most common threats to internal validity related, but not limited, to these designs:
Experimental. Maturation, Testing, Diffusion, and Instrumentation
Quasi-experimental. Maturation, Testing, Instrumentation, Diffusion, and Selection Bias
If a factorial design includes a within-subjects component then Sequencing Effects becomes a threat to internal validity
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2 x 2 factorial Design Between-subjects
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Research Question Example Here: Fill in the blanks (consider the main and interaction effects)
Formulate a RQ which would necessitate the use of this type of design
| Group | Treatment | Posttest |
| 1 | XA1B1 | O1 |
| 2 | XA1B2 | O1 |
| 3 | XA2B1 | O1 |
| 4 | XA2B2 | O1 |
| Time ► |
| Assignment | Group | Factor (A) | Factor (B) | Posttest |
| 1 | (A1) | (B1) | ||
| 2 | (A1) | (B2) | ||
| 3 | (A2) | (B1) | ||
| 4 | (A2) | (B2) | ||
| Time ► |
2 x 2 factorial Design Between-subjects
What are the general weaknesses (in terms of internal validity) related to this design?
What are the strengths (in terms of internal validity) of this design?
Is it advisable to utilize random assignment with this design? Why or Why not?
How does one decide how to manipulate the factors?
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2 x 2 factorial Design within-subjects
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Research Question Example Here: Fill in the blanks (consider the main and interaction effects)
| Group or Individual | Treatment | Posttest |
| 1 | XA1B1 | O1 |
| 1 | XA1B2 | O1 |
| 1 | XA2B1 | O1 |
| 1 | XA2B2 | O1 |
| Time ► |
| Group | Factor (A) | Factor (B) | Posttest |
| 1 | (A1) | (B1) | |
| 1 | (A1) | (B2) | |
| 1 | (A2) | (B1) | |
| 1 | (A2) | (B2) | |
| Time ► |
2 x 2 factorial Design within-subjects
What are the general weaknesses (in terms of internal validity) related to this design?
What are the strengths (in terms of internal validity) of this design because of the removal of the pretest?
How would sequencing effects be controlled for in this design?
How does one decide this should be conducted as a within-subjects approach?
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2 x 2 x 2 factorial Design between-subjects
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Research Question Example Here: Fill in the blanks (consider the main and interaction effects)
| Group | Treatment | Posttest | Group | Treatment | Posttest | |
| 1 | XA1B1C1 | O1 | 5 | XA1B1C2 | O1 | |
| 2 | XA1B2C1 | O1 | 6 | XA1B2C2 | O1 | |
| 3 | XA2B1C1 | O1 | 7 | XA2B1C2 | O1 | |
| 4 | XA2B2C1 | O1 | 8 | XA2B2C2 | O1 | |
| Time ► Time ► |
| Assignment | Group | Factor (A) | Factor (B) | Factor (C) | Posttest |
| 1 | (A1) | (B1) | (C1) | ||
| 2 | (A1) | (B2) | (C1) | ||
| 3 | (A2) | (B1) | (C1) | ||
| 4 | (A2) | (B2) | (C1) | ||
| 5 | (A1) | (B1) | (C2) | ||
| 6 | (A1) | (B2) | (C2) | ||
| 7 | (A2) | (B1) | (C2) | ||
| 8 | (A2) | (B2) | (C2) | ||
| Time ► |
2 x 2 x 2 factorial Design between-subjects
What are the general weaknesses (in terms of internal validity) related to this design?
What are the strengths (in terms of internal validity) of this design because of the removal of the pretest?
How does one decide how many factors to use and how many levels each factor is split into?
How many cells are required for a 2 x 2 x 2 design?
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2 x 2 x 2 factorial Design mixed-subjects
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Research Question Example Here: Fill in the blanks (consider the main and interaction effects)
| Group | Treatment | Posttest | Group | Treatment | Posttest | |
| 1 | XA1B1 C1C2 | O1 | 5 | XA1B1 C2C1 | O1 | |
| 2 | XA1B2 C1C2 | O1 | 6 | XA1B2 C2C1 | O1 | |
| 3 | XA2B1 C1C2 | O1 | 7 | XA2B1 C2C1 | O1 | |
| 4 | XA2B2 C1C2 | O1 | 8 | XA2B2 C2C1 | O1 | |
| Time ► Time ► |
| Assign | Group | Factor (BS) (A) | Factor (BS) (B) | Factor (WS) (C) | Posttest |
| 1 | (A1) | (B1) | (C1) and (C2) | Test | |
| 2 | (A1) | (B2) | (C1) and (C2) | " | |
| 3 | (A2) | (B1) | (C1) and (C2) | " | |
| 4 | (A2) | (B2) | (C1) and (C2) | " | |
| 5 | (A1) | (B1) | (C2) and (C1) | " | |
| 6 | (A1) | (B2) | (C2) and (C1) | " | |
| 7 | (A2) | (B1) | (C2) and (C1) | " | |
| 8 | (A2) | (B2) | (C2) and (C1) | " | |
| Time ► |
Factor C is treated as the WS variable
What are the general weaknesses (in terms of internal validity) related to this design?
What are the strengths (in terms of internal validity) of this design because of the removal of the pretest?
Is it advisable to utilize random assignment with this design? Why or Why not?
How does one decide which factor is the between-subjects and which factor is the within-subjects?
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2 x 2 x 3 Factorial design
Mixed-subjects
Solomon N-group Design
A between-subjects approach
An extension of the factorial design
Combines pretest only and the pre- and posttest design
Controls for a major threat to internal validity and construct validity
Testing
Pretest sensitization
Unique research scenarios warrant the use of the Solomon N-group Design
How can group equivalency be tested?
Should there be a certain amount of time that should elapse before the next groups receives the intervention? Why or why not?
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Solomon N-group Design
Solomon 4-group Design
1 factor
Solomon 6-group Design
2 factors
Solomon 8-group Design
3 factors
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Solomon N-group Design
Most common threats to internal validity related, but not limited, to these designs:
Experimental. This design controls for all threats to internal validity except for Instrumentation.
Quasi-experimental. Instrumentation and Selection Bias
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Solomon four-group design
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Research Question Example Here: Fill in the blanks
| Group | Pretest | Treatment | Posttest |
| 1 | O1 | XA | O2 |
| 2 | O3 | - | O4 |
| 3 | - | XA | O5 |
| 4 | - | - | O6 |
| Time ► |
| Assignment | Group | Pretest | Treatment | Posttest |
| R | 1 | |||
| R | 2 | - | ||
| R | 3 | - | ||
| R | 4 | - | - | |
| Time ► |
What are the general weaknesses (in terms of internal validity) related to this design?
What are the strengths (in terms of internal validity) of this design because of the removal of the pretest?
Is it advisable to utilize random assignment with this design? Why or Why not?
What are the logistical concerns that would keep a researcher from utilizing this design?
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Solomon four-group design
Solomon six-group design
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Research Question Example Here: Fill in the blanks
| Group | Pretest | Treatment | Posttest |
| 1 | O1 | XA | O2 |
| 2 | O3 | XB | O4 |
| 3 | - | XA | O5 |
| 4 | - | XB | O6 |
| 5 | O7 | - | O8 |
| 6 | - | - | O9 |
| Time ► |
| Assignment | Group | Pretest | Treatment | Posttest |
| 1 | ||||
| 2 | ||||
| 3 | - | |||
| 4 | - | |||
| 5 | - | |||
| 6 | - | - | ||
| Time ► |
What are the general weaknesses (in terms of internal validity) related to this design?
What are the strengths (in terms of internal validity) of this design because of the removal of the pretest?
Is it advisable to utilize random assignment with this design? Why or Why not?
What are the logistical concerns that would keep a researcher from utilizing this design?
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Solomon six-group design
Access companion website to further explore specific references of interest
http://www.sagepub.com/edmonds/
Be cautious of internet resources on research design and methodology.
Be aware that many books use different types of terminology to explain the same thing.
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Group 1
O1
X
O2
Group 2
O1
-
O2
Group 1
O1
X
O2
Group 2
O1
-
O2