Which ANOVA assumption refers to the requirement that variances across groups be similar?

Which ANOVA assumption refers to the requirement that variances across groups be similar?

• A. Homogeneity of variances
• B. Normality of residuals
• C. Linearity
• D. Random sampling

Answer: (A)

ANOVA assumes that the variability within each group is roughly the same across all groups. This is called homogeneity of variances (also known as homoscedasticity). It matters because the F statistic relies on a pooled estimate of within-group variance, so if one group is much more variable than another, the pooled estimate can be biased and the test can mislead about whether group means differ, especially when group sizes are unequal. To assess this, tests like Levene's or Brown-Forsythe are used. If the assumption is violated, options include using Welch's ANOVA, applying a data transformation to stabilize variances, or opting for a nonparametric approach. Other listed ideas refer to different assumptions: normality of residuals deals with the shape of the error distribution, linearity with the form of the relationship, and random sampling with how the data were collected.

ANOVA assumes that the variability within each group is roughly the same across all groups. This is called homogeneity of variances (also known as homoscedasticity). It matters because the F statistic relies on a pooled estimate of within-group variance, so if one group is much more variable than another, the pooled estimate can be biased and the test can mislead about whether group means differ, especially when group sizes are unequal.

To assess this, tests like Levene's or Brown-Forsythe are used. If the assumption is violated, options include using Welch's ANOVA, applying a data transformation to stabilize variances, or opting for a nonparametric approach.

Other listed ideas refer to different assumptions: normality of residuals deals with the shape of the error distribution, linearity with the form of the relationship, and random sampling with how the data were collected.