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In a 4 × 3 factorial design with A and B as two factors, the sum of squares for A is 42, and the mean square for error is 5. What will be the "F" ratio associated with the main effect of A?

Correct option is C

The F ratio is calculated as:

• Degrees of Freedom for Factor A (dfA):
  k−1=4−1=3, where k is the number of levels for Factor A.
  
  

Thus, the F ratio associated with the main effect of Factor A is 8.8.

Information Booster

Key Features of ANOVA

1. Purpose:

• ANOVA tests whether the means of different groups are significantly different from one another.

• It identifies the impact of one or more independent variables (factors) on a dependent variable.

2. Types of ANOVA:

• One-way ANOVA: Compares the means of three or more groups based on one independent variable.

• Two-way ANOVA: Examines the effect of two independent variables and their interaction on the dependent variable.

• Repeated Measures ANOVA: Compares means where the same subjects are measured under different conditions or at different times.

• Factorial ANOVA: Used when more than one independent variable is present.

3. Components of Variance:

• Between-group variance: Measures differences between group means due to the effect of the independent variable.

• Within-group variance: Reflects variability within each group due to random error.