The assumptions of single-factor ANOVA can be described succinctly by means of the "model equation" $X _ {ij } = \mu _ { i } + \varepsilon _ { ij } \text { where } \varepsilon _ { ij }$ represents a random deviation from the population or true treatment mean $\mu _ { i }$ . Which of the following statements are true?
A) The $\varepsilon _ {ij } ^ { \prime } \mathrm { s }$
Are assumed to be independent.
B) The $\varepsilon _ { i j } ^ { \prime } \mathrm { s }$
Are normally distributed random variables.
C) $E \left( \varepsilon _ { ij } \right) = 0$
For every i and j.
D) $V \left( \varepsilon _ {ij } \right) = \sigma ^ { 2 }$
For every i and j.
E) All of the above statements are true.

Question

The assumptions of single-factor ANOVA can be described succinctly by means of the "model equation" $X _ {ij } = \mu _ { i } + \varepsilon _ {  ij } \text { where } \varepsilon _ { ij }$ represents a random deviation from the population or true treatment mean $\mu _ { i }$ . Which of the following statements are true?
A) The $\varepsilon _ {ij } ^ { \prime } \mathrm { s }$
Are assumed to be independent.
B) The $\varepsilon _ { i j } ^ { \prime } \mathrm { s }$
Are normally distributed random variables.
C) $E \left( \varepsilon _ { ij } \right) = 0$
For every i and j.
D) $V \left( \varepsilon _ {ij } \right) = \sigma ^ { 2 }$
For every i and j.
E) All of the above statements are true.

Quizplus · Accepted Answer

All of the statements A through D accurately describe the assumptions of single-factor ANOVA. The errors ($\varepsilon_{ij}$) are assumed to be independent, normally distributed with a mean of 0, and have a constant variance ($\sigma^2$) across all groups.

The Assumptions of Single-Factor ANOVA Can Be Described Succinctly by Means