The pooled standard deviation is a method for estimating a single standard deviation to represent all independent samples or groups in your study when they are assumed to come from populations with a common standard deviation. The pooled standard deviation is the average spread of all data points about their group mean (not the overall mean). It is a weighted average of each group's standard deviation. The weighting gives larger groups a proportionally greater effect on the overall estimate. Pooled standard deviations are used in 2-sample t-tests, ANOVAs, control charts, and capability analysis.
The first three groups are equal in size (n=50) with standard deviations around 3. The fourth group is much larger (n=200) and has a higher standard deviation (6.8). Because the pooled standard deviation uses a weighted average, its value (5.486) is closer to the standard deviation of the largest group. If you used a simple average, then all groups would have had an equal effect.
Suppose C1 contains the response, and C3 contains the mean for each factor level. For example:
Usewith the following expression:
SQRT((SUM((C1 - C3)^2)) / (total number of observations - number of groups))
For the previous example, the expression for pooled standard deviation would be:
SQRT((SUM(('Response' - 'Mean')^2)) / (6 - 2))
The value that Minitab stores is 3.75489.