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Block 3 Unit 2 Factorial Design

1) What do you mean by factorial design? Explain with example.

A factorial design is a research design that allows researchers to study the effects of two or more independent variables (also known as factors) on a dependent variable simultaneously. In a factorial design, researchers manipulate all possible combinations of selected values (or levels) of each variable. This enables them to examine not only the independent effects of each variable (the main effects) but also the combined effects of the variables (the interaction effects).

Example: In an experiment by Tulving and Pearlstone (1965), subjects were asked to learn a list of words which varied in length (12, 24 or 48 words - Factor A with three levels). These words could be grouped into categories (e.g., apple and banana grouped as 'fruits'). Subjects were either given the list of categories at the time of recall, or they were not (Factor B with two levels). The dependent variable was the number of words recalled. This is an example of a 3 x 2 factorial design. This design allowed the researchers to examine the effect of list length and the presence of cues on recall, both separately and in combination.

2) Differentiate with illustration the between-group factorial design and within-subject factorial design.

Factorial designs can be implemented using different methods for assigning participants to conditions:

• Between-Group Factorial Design: In a between-group factorial design, different groups of participants are assigned to each combination of levels of the independent variables. Each participant experiences only one of the experimental conditions.
  • Illustration: Using the example above, if Tulving and Pearlstone had used a between-group design, they would have needed a separate group of participants for each of the six conditions. A different group would have learned a list of 12 words with cues, another would learn a list of 12 words without cues, a third would learn a list of 24 words with cues, and so on, leading to six different groups of participants.
• Within-Subject Factorial Design: In a within-subject factorial design, each participant experiences all combinations of the levels of the independent variables.
  • Illustration: Using the same example, in a within-subject design, each participant would learn all the lists of words in different conditions: 12, 24, or 48 words, both with and without cues. To control for order effects, the order of the different experimental conditions would be randomised or counterbalanced.
  • For example, Godden and Baddeley (1975) used divers in a within-subject design. Divers were asked to learn a list of 50 words either on the beach or under 10 feet of water. They were then tested on the beach or under the sea. Each diver was tested in all four experimental conditions (learning on land and tested on land, learning on land and tested under sea, learning under sea and tested on land, and learning under sea and tested under sea.)

3) Discuss the advantages and limitations of factorial design.

Advantages of Factorial Design:

• Study of Multiple Variables: Factorial designs enable researchers to manipulate and control two or more independent variables simultaneously, allowing for the study of their separate and combined effects.
• Study of Interactions: Factorial designs can determine how the effect of one independent variable is influenced by another. This allows researchers to study not only the main effects of each variable, but also the combined or interactive effects.
• Precision: Factorial designs are more precise than single-factor designs.
• Generalisability: The experimental results are more comprehensive and generalisable to a wider range of situations because of the manipulation of several independent variables in a single experiment.

Limitations of Factorial Design:

• Complexity: The experimental setup and statistical analysis can become very complicated when more than three independent variables, each with three or more levels, are manipulated together.
• Sample Homogeneity: When the number of treatment combinations becomes large, it can be difficult for the experimenter to select a homogenous group of participants.
• Time and Resources: Experiments involving multiple factors and levels require more time and resources.
• Interpretation: When interactions are present, the analysis and interpretation of data becomes more complex, requiring a detailed look at the simple effects.

4) What do you mean by interaction in factorial design? Discuss various types of interaction

In a factorial design, an interaction occurs when the effect of one independent variable on the dependent variable depends on the level of another independent variable. In other words, the effect of one variable differs across the different levels of the other variable..

• Graphical Representation: An interaction is indicated by non-parallel lines in a graph of the data.
• Types of Interaction:
  • Antagonistic interaction: In this type of interaction, the two independent variables tend to reverse each other's effects.
  • Synergistic interaction: In synergistic interactions, the two independent variables reinforce each other's effects.
  • Ceiling effect: This can occur when a dependent variable has a limit and additional changes in the independent variable have little or no effect.
  • If there is no interaction then the lines on a graph will be parallel.

Important Points

1. Factorial design is used to study the effect of more than one independent variable.

2. Interaction effect can not be studied by single factor design.

3. The independent variables of an experiment is known as factors of the experiment. 

4. In within subject factorial design each subject experience each condition. 

5. The 2×2 design means two independent variables with two levels.

6. The interaction in which two independent variables tend to reverse each other’s effect is known as antagonistic interaction. 

7. The interaction in which two independent variables tend to enhance each other’s effect is known as synergistic interaction

8. If graphical representation of a variables shows curves that are not parallel line it shows interaction between the variable.

9. The effect of one independent variable averaged over all levels of another independent variable is known as Main Effect.