Equal standard deviations

Definition

Equal standard deviations, also known as homoscedasticity, occur when the variability within each group being compared is similar. This is an important assumption for performing One-Way ANOVA.

5 Must Know Facts For Your Next Test

1. Homoscedasticity is crucial for the validity of One-Way ANOVA results.
2. Violation of equal standard deviations can lead to incorrect conclusions about group differences.
3. Levene's test is commonly used to check for equal standard deviations across groups.
4. If the assumption of equal standard deviations is not met, alternative methods like Welch's ANOVA may be used.
5. Graphical methods like residual plots can help assess whether the assumption of homoscedasticity holds.

Review Questions

• What are equal standard deviations and why are they important in One-Way ANOVA?
• Which statistical test can you use to check for equal standard deviations across groups?
• What alternative method might you use if the assumption of equal standard deviations is violated?

Related terms

Heteroscedasticity: A condition in which different samples have different variances; opposite of homoscedasticity.

Levene's Test: A statistical test used to assess the equality of variances for a variable calculated for two or more groups.

Welch's ANOVA: $$ANOVA$$ method that does not assume equal variances and can be used when this assumption is violated.