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.
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.