When would you use a pooled standard deviation for error estimation?

A pooled standard deviation is used for error estimation when data from two or more independent samples or groups are assumed to originate from populations with the same underlying standard deviation (i.e., homogeneity of variances). By combining the variances from these samples, a more robust and precise estimate of the common standard deviation is obtained, especially beneficial when individual sample sizes are small. This technique is often employed in statistical tests like t-tests or ANOVA when comparing means across groups, as it provides a single best estimate of the common within-group variability.