Eta squared is defined as which of the following?

Eta squared is defined as which of the following?

• A. The proportion of variance explained by a variable after controlling for other variables.
• B. The proportion of total variance explained by a variable.
• C. The correlation between a variable and the outcome.
• D. The ratio of explained to total error variance.

Answer: (B)

Eta squared captures how much of the total variability in the dependent variable is explained by a factor in an ANOVA. It is computed as the factor’s sum of squares divided by the total sum of squares, so it represents the proportion of total variance that the variable accounts for. This directly matches the idea of a proportion of total variance explained by the variable. In contrast, partial eta squared uses a different denominator (it controls for other factors and looks at variance explained after removing other influences), which is why that phrasing describes a related but distinct statistic. Correlation with the outcome is a different measure (a linear association, not a variance proportion). The notion of a ratio of explained to total error variance isn’t the standard definition for eta squared. So the statement about the proportion of total variance explained by a variable correctly defines eta squared.

Eta squared captures how much of the total variability in the dependent variable is explained by a factor in an ANOVA. It is computed as the factor’s sum of squares divided by the total sum of squares, so it represents the proportion of total variance that the variable accounts for. This directly matches the idea of a proportion of total variance explained by the variable.

In contrast, partial eta squared uses a different denominator (it controls for other factors and looks at variance explained after removing other influences), which is why that phrasing describes a related but distinct statistic. Correlation with the outcome is a different measure (a linear association, not a variance proportion). The notion of a ratio of explained to total error variance isn’t the standard definition for eta squared. So the statement about the proportion of total variance explained by a variable correctly defines eta squared.