Asked by Pranshu Saini on Jun 09, 2024
Verified
Which of the following statements about a two-way analysis of variance model is/are TRUE?
A) The population of interest is classified according to two categorical variables,or factors.
B) An experiment involving the simultaneous use of two factors offers advantages over two one-way experiments with respect to such matters as efficiency and reduction of residual variation.
C) The two-way type of experiment requires twice as many experimental observations as would be required in two one-way experiments of the same factors.
D) An experiment involving the simultaneous study of two factors allows for the investigation of interactions between the factors.
E) Only A,B,and D are true.
Two-Way Analysis
A statistical method used to examine the effects of two independent variables on a dependent variable, often to understand interactions between the two variables.
Categorical Variables
Variables that represent types or categories, allowing for classification of individuals or items into distinct groups.
Residual Variation
The variation in a dataset that is not explained by the model being used, essentially the difference between observed and predicted values.
- Understand the basic concepts and purposes of a two-way Analysis of Variance (ANOVA).
- Understand the conditions and assumptions underlying the use of two-way ANOVA.
Verified Answer
JB
Jolonnie BirdenJun 14, 2024
Final Answer :
E
Explanation :
A two-way analysis of variance (ANOVA) involves two independent categorical variables (factors) and examines their effect on a dependent variable, which allows for the assessment of interactions between these factors (D). It is more efficient and can reduce residual variation compared to conducting two separate one-way ANOVAs (B). The statement in C is incorrect because a two-way ANOVA does not necessarily require twice as many observations as two one-way ANOVAs.
Learning Objectives
- Understand the basic concepts and purposes of a two-way Analysis of Variance (ANOVA).
- Understand the conditions and assumptions underlying the use of two-way ANOVA.