What is a 'pooled SEM' for an ANOVA and how can it be calculated?

A pooled standard error of the mean (SEM) in the context of ANOVA refers to a combined estimate of variability across different groups, allowing for a more accurate assessment of differences between group means. It is calculated by taking the square root of the pooled variance, which is the weighted average of the variances of the individual groups, using the formula:

[ \text{Pooled Variance} = \frac{\sum{(n_i - 1) s_i^2}}{\sum{(n_i - 1)}} ]

where (n_i) is the sample size and (s_i^2) is the variance for each group. The pooled SEM is then derived by dividing the pooled standard deviation by the square root of the total sample size across all groups.